Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. Publishers: Finnish Society of Forest Science, Vantaa, Finland Finnish Forest Research Institute, Vantaa, Finland Department of Forest Sciences, University of Helsinki, Helsinki, Finland Editorial office: Finnish Society of Forest Science PO Box 18 01301 Vantaa Finland tel: +358 40 801 5596 e-mail: sms@helsinki.fi iii Foreword These are the proceedings of the 7th event in a series of workshops on functional-structural plant models (FSPMs). Functional-structural plant models describe plants as entities consisting of individual elements, describe the characteristics and behaviour of these elements, and integrate the activities of the elements for modelling the functioning of a whole plant or a plant part. As this is already the seventh in the series of FSPM meetings and there are a solid number of contributors and participants, we decided call this meeting a conference. The chain of the FSPM workshops is as follows: • The first workshop in Helsinki in December 1996 focused on the modelling of the distribution of growth within an individual tree, and the mathematical description and measurement of three-dimensional tree structure. Selected papers were published in a special issue of Silva Fennica, Vol 31, No. 3. • The second workshop, with the same scientific profile, was held in Clermont-Ferrand, France, in October 1998. Selected papers were published in a special issue of Annals of Forest Science, Vol. 57, No 5/6. • The third workshop was held in Montreal, Canada, in September, 2001. It broadened the scope of the series to include models of tree stand structure and functions. • The fourth workshop in Montpellier, France, in June 2004 broadened the scope further to include all types of plants (woody and herbaceous), and functional-structural plant models operating at the molecular and tissue levels. Selected papers were published in a special issue of New Phytologist, Vol 166, No 3. • The fifth workshop took place in Napier, New Zealand, in November 2007. The scope of this workshop was similar to the previous workshop. Selected papers were published in special issue of Functional Plant Biology, Vol 35, No’s 9&10. • The format of the sixth workshop in Davis, California, USA, in September 2010 was similar to the previous two workshops. An increasing number of models were applied to study practical issues in crop and plant production. Selected papers were published in a special issue of Annals of Botany, Vol 108, No. 6. We received 156 abstracts for oral and poster presentations. They fitted into the topic categories of the previous meetings. The automated reconstruction plant structure on the basis of LiDAR and other data is a popular topic and cellular level models get less attention than in the two previous meetings. Number of applications of FSPMs is increasing. This time we structured the programme following criteria based on the type of modelling effort, instead of the target (e.g. roots or nutrients). We applied a number of broad categories: Methods for FSPMs (session 3); modelling and measuring plant structures (sessions 1A and 1B); modelling processes from organ to plant community level (sessions 2A and 2B); growth and development of plants (session 4A) and plant communities (session 4B); and using models for problem solving (session 5). Papers of the presentations in this conference may be submitted for publication in a 2014 special issue of Annals of Botany. Risto Sievänen Finnish Forest Research Institute Chair, International Programme Committee iv Seventh International Conference on Functional-Structural Plant Models (FSPM2013), Saariselkä, Finland, 9-14 June 2013 Local organising committee RISTO SIEVÄNEN (Chair), Finnish Forest Research Institute, E-mail: risto.sievanen@metla.fi PEKKA NYGREN (Secretary), Finnish Society of Forest Science, E-mail: pekka.nygren@metla.fi ANNA LINTUNEN (Editor) , University of Helsinki, E-mail: anna.lintunen@helsinki.fi PEKKA KAITANIEMI, University of Helsinki TUOMO KALLIOKOSKI, Finnish Forest Research Institute EERO NIKINMAA, University of Helsinki JARI PERTTUNEN, Finnish Forest Research Institute Technical assistance MIRJA VUOPIO, Finnish Forest Research Institute JARI HIETANEN, Finnish Forest Research Institute Sponsors League of Finnish Learned Societies, Finland Annals of Botany, United Kingdom INRIA, France Tree Physiology, United Kingdom International programme committee RISTO SIEVÄNEN (Chair), Finnish Forest Research Institute, Finland EERO NIKINMAA (Co-chair), University of Helsinki, Finland CHRISTOPHE GODIN (Co-chair), Institut national de recherche en informatique et en automatique (INRIA), France BRUNO ANDRIEU, Institut national de la recherche agronomique (INRA), France GERHARD BUCK-SORLIN, Institut de Recherche en Horticulture et Semences (IRHS), France ERIC CASELLA, Forest Research, UK MICHAËL CHELLE, INRA, France KARINE CHENU, The University of Queensland, Australia EVELYNE COSTES, INRA, France PAUL-HENRY COURNÈDE, Ècole Centrale Paris, France THEODORE DEJONG, University of California - Davis, USA YVES DUMONT, Centre international de la recherche agronomigue pour le développement (CIRAD), France LIONEL DUPUY, The James Hutton Institute, UK ABRAHAM ESCOBAR-GUTIÉRREZ, INRA, France v JOCHEM EVERS, Wageningen University and Research Centre, The Netherlands PAULINA FERNÁNDEZ, Pontificia Universidad Católica de Chile, Chile DAVID E. FORD, University of Washington, USA THIERRY FOURCAUD, CIRAD, France YANN GUÉDON, CIRAD, France YAN GUO, China Agricultural University, China JIM HANAN, The University of Queensland, Australia TEEMU HÖLTTÄ, University of Helsinki, Finland HENRIK JÖNSSON, Lund University, Sweden MIKKO KAASALAINEN, Tampere University of Technology, Finland KATRIN KAHLEN, Forschungsanstalt Geisenheim, Germany PEKKA KAITANIEMI, University of Helsinki, Finland TUOMO KALLIOKOSKI, University of Helsinki & Finnish Forest Research Institute, Finland WINFRIED KURTH, University of Göttingen, Germany ANDRÉ LACOINTE, INRA, France CHRISTIAN MESSIER, Université de Québec à Montréal, Canada PETER MINCHIN, The New Zealand Institute for Plant & Food Research Limited, New Zealand PEKKA NYGREN, Finnish Society of Forest Science, Finland HARRY OZIER-LAFONTAINE, INRA, Guadeloupe LOÏC PAGÈS, INRA, France MIKKO PELTONIEMI, Finnish Forest Research Institute, Finland JARI PERTTUNEN, Finnish Forest Research Institute, Finland PRZEMYSLAW PRUSINKIEWICZ, University of Calgary, Canada MICHAEL RENTON, The University of Western Australia, Australia ALLA SELEZNYOVA, Plant & Food Research, New Zealand KATARINA SMOLENOVA, University of Göttingen, Germany HARTMUT STÜTZEL, University of Hannover, Germany KIYOSHI UMEKI, Chiba University, Japan JAN VOS, Wageningen University and Research Centre, The Netherlands Permanent FSPM board THEODORE DEJONG, University of California - Davis, USA CHRISTOPHE GODIN, INRIA, France YAN GUO, China Agricultural University, China KATRIN KAHLEN, Forschungsanstalt Geisenheim, Germany RISTO SIEVÄNEN, Finnish Forest Research Institute, Finland JAN VOS, Wageningen University and Research Centre, The Netherlands vi Contents Modelling Plant Structure Keynote talk Functional-structural modelling with L-systems: Where from and where to Jim Hanan 1 Oral presentations Biomechanics of bark patterning in grasstree Holly Jennifer Dale, Adam Runions, David Hobill, Przemyslaw Prusinkiewicz 4 Floral phyllotaxis of magnolia in computer simulations - towards understanding phyllotactic fingerprint Beata Zagórska-Marek, Marta Fijak 7 Modelling the spatial arrangement of vascular bundles in plants Fabrizio Carteni, Francesco Giannino, Gianni Boris Pezzatti, Stefano Mazzoleni 10 Estimating the genetic value of F1 apple progenies for irregular bearing during first years of production Jean-Baptiste Durand, Baptiste Guitton, Jean Peyhardi, Yan Holtz, Yann Guédon, Catherine Trottier, Evelyne Costes 13 Posters Biomechanical modelation of Ravenala madagascariensis petiole Andrés Valencia-Escobar, M. Paulina Fernández, Diego J. Celentano 16 Modeling and analyzing the topology development of young Michelia chapensis Dong Li, Mengzhen Kang 19 Automated parameter estimation for a plant architecture model Florian Schöler, Jenny Balfer, Volker Steinhage 22 Modeling the blade shape of landscape trees Fuping Lin, Dong Li 25 Biomass-based rapeseed (Brassica napus L.) leaf geometric parameter model Hongxin Cao, Wenyu Zhang, Weixing Zhang, Yan Liu, Yongxia Liu, Jim Hanan, Yuli Chen, Yanbin Yue, Zhiyou Zhang, Daokuo Ge 26 Optimize tree shape: Targeting for best light interception Jing Hua, MengZhen Kang 27 A novel plant cell division algorithm based on ellipse/ellipsoid fitting Metadel Kassahun Abera, Pieter Verboven, Thijs Defraeye, maarten Hertog, Bart M Nicolai 30 Modeling cucumber leaf orientation as growing in heterogeneous canopy Tingting Qian, Shenglian Lu, Chunjiang Zhao, Xinyu Guo 33 vii Reconstructing and observing plant structure Oral presentations A combined method for quantifying 3D root architecture of field-grown maize Jie Wu, Bo Yang, Yan Guo 37 Semantic skeletonization for structural plant analysis Jenny Balfer, Florian Schöler, Volker Steinhage 42 PlantScan™: a three-dimensional phenotyping platform for capturing the structural dynamic of plant development and growth Xavier Sirault, Jurgen Frip, Anthony Paproki, Peter Kuffner, Chuong Nguyen,Rongxin Li, Helen Daily, Jianming Guo, Robert Furbank 45 Improving branch distribution models in trees using X-ray computed tomography Emmanuel Duchateau, David Auty, Alexis Achim 49 tLiDAR methodologies can overcome limitations in estimating forest canopy LAI from conventional hemispherical photograph analyses Eric Casella, Mat Disney, James Morison, Helen McKay 52 Shape reconstruction of fruit tree from colored 3D point cloud Shenglian Lu, Xinyu Guo, Chunjiang Zhao, Weiliang Wen, Jianjun Du 55 Optimal 3D reconstruction of plants canopy from terrestrial laser scanner data by fusion of the 3D point information and the intensity value Mathilde Balduzzi, Frédéric Boudon, Christophe Godin 58 Bayes trees and forests: combining precise empirical and theoretical tree models Mikko Kaasalainen, Pasi Raumonen, Markku Åkerblom, Risto Sievänen, Sanna Kaasalainen 61 Quantitative assessement of automatic reconstructions of branching systems Frédéric Boudon, Chakkrit Preuksakarn, Pascal Ferraro, Julien Diener, Eero Nikinmaa, Christophe Godin 64 Posters Rank distributions and biomass partitioning of plants Alexander S. Komarov, Elena V. Zubkova, Maija Salemaa, Raisa Mäkipää 67 Inference of structural plant growth from discrete samples Christoph Stocker, Franz Uhrmann, Oliver Scholz 70 A spectral clustering approach of vegetation components for describing plant topology and geometry from terrestrial waveform LiDAR data Dobrina Boltcheva, Eric Casella, Rémy Cumont, Franck Hétroy 71 Modeling and analyzing rice canopies of different cultivars and densities by 3D digitizing method Dong Li, Liyong Cao, Shihua Cheng 72 The use of x-ray computed tomography for creating computational models of corn stalks and other plants: advantages, benefits, and common challenges Douglas Cook, Margaret Julias 75 A model-based approach to extract leaf features from 3D scans Franz Uhrmann, Christian Hügel, Sabine Paris, Oliver Scholz, Michael Zollhöfer, Günther Greiner 78 viii Root growth and distribution of gooseberry (Physalis peruviana) under field conditions in the Andean soil Gabriel Roveda, Liz Patricia Moreno Fonseca 81 Defining a reliability coefficient in an automated method of identification of radial files in microscopic images of gymnosperms Guilhem Brunel, Philippe Borianne, Marc Jaeger, Gérard Subsol, Yves Caraglio 82 An automated image-processing pipeline for high-throughput analysis of root architecture in OpenAlea Julien Diener, P. Nacry, C. Périn, A. Dievart, X. Draye, F. Boudon, A. Gaujon, C. Godin 85 Terrestrial LiDAR-based tree/stand model that can simulate light interception and photosynthesis of branches, individuals, and a stand Kiyoshi Umeki, Akira Kato 88 Fast automatic method for constructing topologically and geometrically precise tree models from TLS Data Pasi Raumonen, Eric Casella, Mathias Disney, Markku Åkerblom, Mikko Kaasalainen 89 A geometrical model generator for quasi-axisymmetric fruit based on X-ray tomography Seppe Rogge, Shiferaw Beyene, Els Herremans, Thijs Defraeye, Pieter Verboven, Bart Nicolai 92 Automatic 3D plant reconstruction from photographies, segmentation and classification of leaves and internodes using clustering Thiago Teixeira Santos, Julio Akira Ueda 95 Monitoring the diel growth of individual Arabidopsis leaves using a laser scanning approach Tino Dornbusch, Olivier Michaud, Christian Fankhauser 98 A Blender addon for the 3-d digitizer FASTRAK for plant structure acquisition Winfried Kurth, Katarzyna Wasilczuk, Michael Henke, Katarina Smolenova, Yongzhi Ong 101 Exchange and transport processes in plants Keynote talk Interplay between material flows and structural properties in dynamics of tree growth Teemu Hölttä 105 Oral presentations Transpiration from stomata via the leaf boundary layer: a microscale modelling approach Thijs Defraeye, Pieter Verboven, Jan Carmeliet, Dominique Derome, Bart Nicolai 109 LEAFC3-N: Modeling effects of drought stress on photosynthesis, stomatal conductance and transpiration Jens Bastet, Johannes Müller, Olaf Christen 112 Modelling transport processes in tissues and organs at a mesoscopic scale Ansgar Bohmann, Juliane Claus, Andrés Chavarría-Krauser 115 Spatial and temporal variability of leaf gas exchanges and temperature responses to drought on apple trees assessed by a 3D turbid medium model Jérôme Ngao, Boris Adam, Marie Charreyron, Marc Saudreau 118 ix Dynamic properties of foliage photosynthesis Edward David Ford, Shawn Behling 121 Revealing the relative importance of photosynthetic limitations in cucumber canopy Tsu-Wei Chen, Michael Henke, Katrin Kahlen, Pieter de Visser, Gerhard Buck-Sorlin, Hartmut Stützel 124 Integrating architecture and physiological perspectives in fruit development Mikolaj Cieslak, Michel Génard, Frédéric Boudon, Valentina Baldazzi, Christophe Godin, Nadia Bertin 127 Up-scaling salt effects in cucumber: trade-off between photosynthesis and toxic ion accumulation Tsu-Wei Chen, Katrin Kahlen, Hartmut Stützel 131 Posters A model of mechanics and gas exchange in a neighborhood of a single stoma Ansgar Bohmann, Andres Chavarria-Krauser 134 A mechanistic model for the estimation of the quantum yield of photochemistry based on light, temperature, and chlorophyll a fluorescence Beñat Olascoaga, Albert Porcar-Castell 135 Simulated interaction between tree structure and xylem and phloem transport in 3D tree crowns using model LIGNUM Eero Nikinmaa, Risto Sievänen, Jari Perttunen, Teemu Hölttä 136 Integrating water transport into L-kiwi model using an aspect-oriented approach Helge Dzierzon, Alla N. Seleznyova 137 Integration of a mechanistic biochemical and biophysical leaf gas exchange model in L-PEACH Inigo Auzmendi, Romeo Favreau, David Da Silva, Theodore DeJong 138 Towards integrating primary C-N metabolism and physiology of crop growth across different plant scales: the ProNet-CN model – a multiscale approach for functional-structural plant modeling Johannes Müller, André Eschenröder, Olaf Christen 139 Modelling zinc uptake and radial transport in roots Juliane Claus, Ansgar Bohmann, Andrés Chavarría 142 Simulating the impact of (“long-distance” or “root-to-shoot”) hormonal signaling and non-uniform soil water distribution on plant transpiration Katrin Huber, Jan Vanderborght, Mathieu Javaux, Natalie Schroeder, Ian Dodd, Harry Vereecken 143 Modelling spatial and temporal leaf temperature dynamics - a focus on the leaf boundary layer Marc Saudreau, Boris Adam, Amélie Ezanic, Sylvain Pincebourde 146 Hydraulic constraints influence the distribution of canopy photosynthetic properties Mikko Peltoniemi, Remko Duursma, Belinda Medlyn 149 Reliable estimation of parameters of the Farquhar-Von Caemmer-Berry biochemical model cannot be obtained by fitting An/Ci curves Qingguo Wang, David H Fleisher, Jong Ahn Chu, Jonathan Resop, Dennis Timlin, V.R. Reddy 150 x Distribution of resources and growth in plants Oral presentations Stem diameter variation: endogenous regulation versus environmental dynamics and its implication for functional modelling Maurits Willem Vandegehuchte, Adrien Guyot, David Lockington, Kathy Steppe 153 Crop load effects on stem diameter variations in peach evaluated with an integrated plant and fruit model Tom De Swaef, Carmen Diana Mellisho, Annelies Baert, Veerle De Schepper, Wenceslao Conejero, Kathy Steppe 156 Physiological growth model CASSIA predicts carbon allocation and wood formation of Scots pine Pauliina Schiestl-Aalto, Liisa Kulmala, Harri Mäkinen, Tuomo Kalliokoski, Annikki Mäkelä 159 Understanding and evaluating some allometric relationships useful for functional-structural plant modeling María Paulina Fernández 162 What are the processes driving carbon allocation to stem and fine roots in a mature coppice of Quercus ilex in the Mediterranean? A data model analysis Nicolas K. Martin-StPaul, Morine Lempereur, Nicolas Delpierre, Jean-Marc Ourcival, Hendrik Davi, Francois Christophe, Leadley Paul, Eric Dufrene, Serge Rambal 165 Modelling temperature-modulated internode elongation in greenhouse grown cucumber canopies Katrin Kahlen, Tsu-Wei Chen, Jana Zinkernagel, Hartmut Stützel 168 Posters Height increment formation of hybrid aspen: empirical model Aris Jansons, Juris Rieksts Riekstins, Martins Zeps, Oskars Krisans 171 Masting changes canopy structure, light interception, and photosynthesis in Fagus crenata Atsuhiro Iio 174 The effect of low phosphorus on morphological and physiological characters of gooseberry plants (Physalis peruviana) Gabriel Roveda, Liz Patricia Moreno-Fonseca 175 A fifty-year-old conceptual plant dormancy model provides new insights into dynamic phenology modelling Heikki Hänninen, Robin Lundell, Olavi Junttila 176 A single tree basal area growth model Jan Hoogesteger 177 Towards a FSPM of bud outgrowth for rosebush: experimental analysis of sugar effect Jessica Bertheloot, François Barbier, Yves Gibon, Rachid Boumaza, Soulaiman Sakr, Sabine Demotes 180 Geometrically saturated growth and the pipe model of tree form Lars Hellström, Linus Carlsson, Åke Brännström 181 Functional-structural modelling of tree and wood formation: new parameters and relations María Paulina Fernández, Iván Lillo 182 xi Functional overwintering types as basis for modelling the overwintering of northern field layer plants under climate warming Robin Lundell, Heikki Hänninen, Timo Saarinen, Helena Åström 185 Patterns of carbon and nitrogen allocation in trees predicted by a model of optimal plant function Ross Edward McMurtrie, Roderick C. Dewar 186 L-Rose: a model simulating organ expansion of individual plants within a rose bush crop Sabine Demotes-Mainard, Jessica Bertheloot, Bruno Andrieu, Gaelle Guéritaine, Lydie Huché-Thélier, Vincent Guérin, Rachid Boumaza 187 Methods for functional-stuctural plant models Keynote talk Biotic systems as multilevel dynamic information processing systems Paulien Hogeweg 191 Oral presentations Integrating multiple scale dynamics: Application to Fagus sylvatica under ozone exposure Yongzhi Ong, Katarína Smoleňová, Michael Henke, Winfried Kurth 192 Simulating the evolution of optimal rooting strategies in shallow soils and extreme climates Michael Renton, Pieter Poot 195 AMAPstudio: a 3D interactive software suite for plants’ architecture modelling Sébastien Griffon, François de Coligny 198 Modelling competition in crop populations via reaction-diffusion foliage dynamics with an outlook on tree modelling Robert Beyer, Paul-Henry Cournède 201 Improving finite element models of roots-soil mechanical interactions Ming Yang, Pauline Défossez, Thierry Fourcaud 204 Integrative models for analyzing jointly shoot growth and branching patterns Jean Peyhardi, Evelyne Costes, Yves Caraglio, Pierre-Éric Lauri, Catherine Trottier, Yann Guédon 207 Deciphering mango tree asynchronisms using Markov tree and probabilistic graphical models Anaëlle Dambreville, Pierre Fernique, Christophe Pradal, Pierre-Eric Lauri, Frédéric Normand, Yann Guédon, Jean-Baptiste Durand 210 Posters OpenAlea 2.0: Architecture of an integrated modeling environment on the web Christophe Pradal, Julien Coste, Frédérique Boudon, Christian Fournier, Christophe Godin 213 Rule-based integration of LIGNUM into GroIMP Katarina Smolenova, Michael Henke, Yongzhi Ong, Winfried Kurth 214 An extension of the graph-grammar based simulator GroIMP for visual specification of plant models using components Michael Henke, Katarína Smoleňová, Yongzhi Ong, Winfried Kurth 217 xii Global sensitivity analysis of the NEMA model for its parameterization and biological diagnosis Qiong-Li Wu, Jessica Bertheloot, Paul-Henry Cournède 220 Reconstruction of leaf area time series using data assimilation on the GreenLab plant growth model and remote sensing Xing Gong, Thomas Corpetti, Mengzhen Kang, Baogang Hu, Laurence Hubert-Moy 223 Structural development of plants and light environment Keynote talk A critical role for root models in feeding 1010 people Jonathan Lynch 229 Oral presentations Integration of root system in a ryegrass perennial model based on self-regulation Vincent Migault, Didier Combes, Gaëtan Louarn, Loïc Pagès, Abraham Escobar-Gutiérrez 231 Modelling Sugar maple development along its whole ontogeny: modelling hypotheses and calibration methodology Olivier Taugourdeau, Sylvain Delagrange, Philippe de Reffye, Christian Messier 234 Characterizing the balance between ontogeny and environmental constraints in forest tree development using growth phase duration distributions Yann Guédon, Olivier Taugourdeau, Yves Caraglio, Sylvie Sabatier 237 Influence of canopy architecture and parameters of leaf level photosynthesis on dry matter production in greenhouse cucumber Dirk Wiechers, Katrin Kahlen, Hartmut Stützel 240 Light signal perception in Arabidopsis rosettes Jochem B Evers, Ronald Pierik, Alexander A R van der Krol 243 How do variations of architectural parameters affect light partitioning within wheat pea mixtures? A simulation study based on a virtual plant approach Romain Barillot, Christian Fournier, Pierre Huynh, Abraham J Gutiérrez, Didier Combes 246 Influence of the genetic variation of branching during early growth on light interception efficiency of apple trees: a modelling study with MappleT David Da Silva, Liqi Han, Robert Faivre, Evelyne Costes 249 Quantitative characterization of clumping in Scots pine crowns Pauline Stenberg, Matti Mõttus, Miina Rautiainen, Risto Sievänen 252 Towards three-dimensional modeling light capture of crop canopy considering regional variation of incident radiation Tongyu Hou, Tao Duan, Zhaoli Xu, Yuntao Ma, Bangyou Zheng, Yuhong Yang, Yan Guo 255 Modeling seasonal patterns of carbohydrate storage and mobilization in peach trees David Da Silva, Liangchun Qin, Carolyn Debuse, Theodore DeJong 258 xiii Posters Simulation of small footprint full waveform LiDAR signals from seedling stand vegetation using Monte Carlo ray tracing and statistical models of 3D vegetation structure Aarne Hovi, Ilkka Korpela 262 Between- and within-tree shading in mixed stands: shoot-level simulation Anna Lintunen, Pekka Kaitaniemi, Jari Perttunen, Risto Sievänen 263 A modeling approach to simulate the whole-plant leaf expansion responses to light in three annual dicotyledonous species Benoit Pallas, Jérémie Lecoeur, Karine Chenu, Hervé Rey, Frédéric Gay, Angélique Christophe 264 Characterization of the relationship between quantity and quality of solar radiation in canopy under contrasting sky conditions Cailian Lao, Zhaoli Xu, Yan Guo, Yan Jin, Yuhong Yang 265 Artificial neural networks in modeling of environmental time series for yerba-mate growth dynamics Fabio Takeshi Matsunaga, Miroslava Rakocevic, Jacques Duílio Brancher 266 Building the foundations of a Coffea arabica FSPM Jean Dauzat, Sébastien Griffon, Olivier Roupsard, Philippe Vaast, Gustavo Rodrigues 269 Evaluation of a photon tracing model and virtual plants to simulate light distribution within a canopy in a growth chamber Julien Le Gall, Hervé Autret, Didier Combes, Christophe Renaud, Jessica Berthloot, Nathalie Leduc, Bruno Andrieu, Vincent Guérin, Michael Chelle, Sabine Demotes-Mainard 272 Simulating maize plasticity in leaf appearance and size using regulation rules Junqi Zhu, Bruno Andrieu, Vos Jan, wopke van der Werf, Christian Fournier, Jochem B Evers 273 How petiole flexibility changes light interception at the tree scale Loïc Nabil Tadrist, Emmanuel de Langre, Marc Saudreau 276 Concept and calibration of virtual wheat including stochastic tillering Lu Feng, Hervé Rey, Jean-Claude Mailhol, Mengzhen Kang, Philippe de Reffye 279 The effect of canopy structure on photochemical reflectance signal Matti Mõttus, Miina Rautiainen 282 The effect of canopy structure on photochemical reflectance signal Miina Rautiainen, Matti Mõttus, Lucia Yáñez-Rausell, Lucie Homolová, Zbyněk Malenovský, Michael E. Schaepman 283 Protocol for foliage modeling and light partitioning in Coffea arabica Miroslava Rakocevic, Fabio Takeshi Matsunaga, Evelyne Costes, Jonas Barbosa Tosti, Yann Guédon, Letícia de Cássia Santin, André Luiz Johann 284 A self-organising model of Macadamia with application to pruning in orchards Neil Andrew White, Jim Hanan 287 Simulating the effect of extreme climatic events on tree architecture with a minimal FSPM Olivier Taugourdeau, Jean-Francois Barczi 288 xiv Testing a radiation transmission model for stands consisting of individual 3D Scots pine and silver birch trees Pekka Kaitaniemi, Risto Sievänen, Anna Lintunen, Jari Perttunen 291 Variation in structural and optical properties of sun exposed and shaded leaves: A model based approach Petr Lukeš, Pauline Stenberg, Miina Rautiainen, Matti Mõttus, Kalle M. Vanhatalo 292 Influence of morphological traits on wood litter production Raffaele Rani, Konrad Abramowicz, Åke Brännström, Daniel Falster 293 L-Pea: an architectural model of pea (Pisum sativum) development Romain Barillot, Pierre Huynh, Abraham J. Escobar-Gutiérrez, Didier Combes 294 Modeled and measured fPAR in a boreal forest Titta Majasalmi, Miina Rautiainen, Pauline Stenberg 295 Modeled and measured fPAR in a boreal forest Weiliang Wen, Xinyu Guo, Boxiang Xiao, Shenglian Lu 296 Growth and development of plant communities Oral presentations Plant structure in crop production: considerations on application of FSPM Jan Vos, Jochem Bas Evers 301 Reparametrisation of Adel-wheat allows reducing the experimental effort to simulate the 3D development of winter wheat Mariem Abichou, Christian Fournier, Tino Dornbusch, Camille Chambon, Rim Baccar, Jessica Bertheloot, Tiphaine Vidal, Corinne Robert, David Gouache, Bruno Andrieu 304 Perspectives for improving carbon and nitrogen allocation in forest models from stand to global scale Oskar Franklin, Peter M. van Bodegom 307 Photosynthesis, transpiration and LAI: Scale effects of spatial patterns Moritz Kupisch, Anja Stadler, Matthias Langensiepen, Frank Ewert 310 Plant diversity and drought Magnus Lindh, Lai Zhang, Daniel Falster, Oskar Franklin, Mark Westoby, Åke Brännström 313 Quantifying the potential yield benefit of root traits in a target population of environments Mathieu Veyradier, Jack Christopher, Karine Chenu 316 X-Palm, a functional structural plant model for analysing temporal, genotypic and inter-tree variability of oil palm growth and yield Benoît Pallas, Jean-Christophe Soulié, Grégory Aguilar, Lauriane Rouan, Delphine Luquet 319 Modeling forest stand structure within a process-based model Joannès Guillemot, Nicolas Delpierre, Patrick Vallet, Christophe François, Kamel Soudani, Manuel Nicolas, Eric Dufrêne 322 xv Posters Effects of defoliation intensity on the genetic and phenotypic composition of virtual ray-grass populations Didier Combes, Isabelle Litrico, Stéphane Grenier, Philippe Barre, Abraham J. Escobar-Gutiérrez, Gaëtan Louarn 325 Formation of crown structure in Scots pine trees Kourosh Kabiri Koupaei, Eero Nikinmaa, Pertti Hari 326 FSM-Rice: a simulation study on rice morphology using functional–structural plant modeling Liang Tang, LeiLei Liu, Yonghui Zhang, Dongxiang Gu, Weixing Cao, Yan Zhu 329 Parameterisation and evaluation of stand level process-based PipeQual-model for Norway spruce Tuomo Kalliokoski, Harri Mäkinen, Annikki Mäkelä 330 The model of root spreading and belowground competition in boreal mixed forests Vladimir Shanin, Maxim Shashkov, Natalia Ivanova, Svetlana Moskalenko, Maria Bezrukova, Raisa Mäkipää, Kapitolina Bobkova, Alexey Manov, Alexander Komarov 331 Analysis of hybrid vigor for cucumber with functional-structural model Greenlab Xiujuan Wang, Mengzhen Kang, Lili Yang, Baogui Zhang 332 “Virtual grassland”: an OpenAlea package to deal with herbaceous plant architecture and grassland community dynamics Gaëtan Louarn, Abraham Escobar-Guttierrez, Didier Combes 335 Functional-structural plant models for problem solving in vegetation management Oral presentations A generic model of interactions between FSPM, foliar pathogens, and microclimate Guillaume Garin, Christophe Pradal, Bruno Andrieu, Vianney Houlès, Corinne Robert, Christian Fournier 339 Using 3D virtual plants to evaluate the canopy role in the progression of a splash-dispersed crop disease: a case study based on wheat cultivar mixtures Christophe Gigot, Claude de Vallavieille-Pope, Marc Leconte,Claude Maumené, Laurent Huber, Sébastien Saint-Jean 342 An integrated and modular model for simulating and evaluating how canopy architecture can help reduce fungicide applications Christian Fournier, Christophe Pradal, Mariem Abichou, Bruno Andrieu, Marie-Odile Bancal, Carole Bedos, Pierre Benoit, Camille Chambon, Eric Cotteux, Laure Mamy, Neil Paveley, Valérie Pot, Sebastien Saint-Jean, Claire Richard, Carole Sinfort, Alexandra Ter Halle, Eric Van Den Berg, Anne Sophie Walker, Corinne Robert 345 Weeds In Space – field-level epidemiology of herbicide resistance David Thornby 349 Using functional-structural plant modeling to explore the response of cotton to mepiquat chloride application and plant population density Shenghao Gu, Jochem Evers, Lizhen Zhang, Lili Mao, Jan Vos, Zhaohu Li 352 xvi Posters Model assisted phenotyping of the source-sink relationships underlying the genetic diversity of sugarcane productivity Delphine Luquet, Matthieu Gouy, Lauriane Rouan, Jean Francois Martiné, Eric Gozé, Audrey Thong-Chane, Jean Christophe Soulié 355 Modelling the colonization of the decay fungus Heterobasidion annosum in Scots pine (Pinus sylvestris L.) root system Jari Perttunen, Risto Sievänen, Tuula Piri 356 StressMaster: a web application for dynamic modelling of the environment to assist in crop improvement for drought adaptation Karine Chenu, Al Doherty, Greg J. Rebetzke, Scott C. Chapman 357 Arbuscular mycorrhizal fungi (AMF) diversity obtained from gooseberry plantations (Physalis peruviana) in the Colombian Andean region María Margarita Ramírez, Fritz Oehl, Adrian Pérez, Alia Rodríguez 360 Adaptation of timber plantations (Gmelina arborea and Pachira quinata) with arbuscular mycorrhizal fungi in the Caribbean region, Colombia María Margarita Ramírez, Gabriel Roveda Hoyos, César Baquero Mestre, Judith Martínez-Atencia, Braulio Gutiérrez, Miguel Rodríguez 361 CyberPlantS: a European initiative towards collaborative plant modeling Michaël Chelle, Christophe Godin, Risto Sievänen, Jan Vos, Mathieu Javaux, Gerhard Buck-Sorlin, Hartmut Stützel, Ana María Tarquis 362 Modeling parthenium weed early canopy architecture in response to environmental factors and the impacts on biological control activity of the summer rust Ruey Toh, Kunjithapatham Dhileepan, Roger G. Shivas, Steve W. Adkins, Jim Hanan 363 Cotton fiber quality determined by fruit position, temperature and management Xuejiao Wang, Jochem Evers, Lizhen Zhang, Lili Mao, Xuebiao Pan, Zhaohu Li 366 Mathematical Modelling of the biocontrol of Rubus alceifolius, an invasive plant in Réunion Island Yves Dumont, Alexandre Mathieu, Serge Quilici 369 MODELLING PLANT STRUCTURE Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 1 KEYNOTE: Functional-structural modelling with L-systems: Where from and where to Jim Hanan The University of Queensland, Queensland Alliance for Agriculture & Food Innovation, St. Lucia, Queensland, Australia 4072 *correspondence: j.hanan@uq.edu.au Highlights: The L-systems formalism with turtle interpretation captures plant structural topology and geometry, signalling within the branching structure, and development over time, forming a basis for plant modelling languages. With the addition of environmental interfaces, they have been successfully used to model a variety of plants. Areas for future development include integration of different aspects of plant function, multi-scale modelling and development as a platform for further simulation. Keywords: Lindenmayer-systems, plant modelling language WHERE FROM Since their inception by Aristid Lindenmayer (1968a&b), L-systems have provided an inspiration and formal foundation for a range of functional-structural plant modelling systems. The original formalism incorporated internal and environmental signalling and branching topology, aiming to capture elements of filamentous growth at a cellular level. Inspired by the ideas of Cohen (1967), Frijters and Lindenmayer (1974) moved from the cellular to the organ level of abstraction, developing an L-system model of aster incorporating signals for control of branching and “vigour” controlling flowering positions. This is the first example of L-systems capturing functional-structural aspects of plant growth and development. In these early models, plant geometry was added in a post-processing phase. Hogeweg and Hesper (1974) explored patterns generated by a variety of such L-systems and found recurrence relations in line with higher plant growth. Following on from this work, Smith (1984) demonstrated the potential of L-systems for the synthesis of realistic images of plants, while Aono and Kunii (1984) explored modelling of trees. Szilard and Quinton (1979) proposed representation of geometry within the strings defining the plant structure based on a LOGO-style turtle (Abelson and diSessa 1982). This turtle interpretation scheme was further developed by Prusinkiewicz (1986, 1987) and is the standard approach used in L-systems-based systems today. With a formalism that captures component topology and geometry, signalling within the branching structure, and development over time, the stage was set for development of plant modelling languages that could support functional-structural plant modelling of a broad range of phenotypes (Prusinkiewicz et al. 1988, Prusinkiewicz and Hanan 1989, Prusinkiewicz et al. 2000). With the addition of continuous parameters (Lindenmayer 1974; Prusinkiewicz and Hanan 1990, Hanan 1992), a greater variety of lineage and endogenous processes could be simulated (Prusinkiewicz and Lindenmayer 1996). Extension of this line of research continued with the inclusion of environmental effects in open L-systems (Mech and Prusinkiewicz 1996) through communication with an external program capturing environmental processes. Kurth (1994) developed a sensitive growth grammar approach representing an alternative line of development of the L- systems idea, initially aimed at eco-forestry applications. This work continued with transformation of the representation of the plant from strings to graphs (Kurth et al. 2005, Kniemeyer 2008), extending the possible range of applications. Other lines of L-system-inspired research (Lindenmayer 1987) moved away from the plant level to the tissue and cellular scale (Prusinkiewicz and Runions 2012). L-system models of a variety of plants, from herbaceous to trees can be found, for example, in journal special issues (Godin and Sinoquet 2005, Hanan and Prusinkiewicz 2008, Fourcaud et al. 2008, Vos et al. 2010, de Jong et al. 2011, Guo et al. 2011), and are too many to list individually here. L-systems have also proved a useful reference for other plant modelling approaches, being compared with Greenlab (Loi and Cournede 2008) for example. They have also been incorporated into other plant modelling systems, such as Lignum (Perttunen and Sievänen 2005), and openALEA (Boudon et al. 2012). WHERE TO Many advances have been made in simulating individual processes in plants using L-systems-based approaches. Models of light interception (Chelle et al. 2004, Cieslak et al. 2008) allow local estimation of 2 leaf photosynthesis, while carbon allocation models (Allen et al. 2005) disburse photosynthate to drive vegetative and reproductive development. Biomechanics of bending of branches under fruit load (Costes et al. 2008) make feedback to the developmental processes possible. Some key future pathways for L-systems modelling will be development of methods to integrate these different aspects easily (Cieslak et al. 2011). Development of techniques supporting modelling of self-organisational processes (Palubiki et al. 2009) may play an important role, particularly for tree development, where what isn’t there plays almost as important a role as what is. Multi-scale modelling will also feature in L-systems models of the future. For example, current models of genetic and hormonal processes at a plant scale (Buck-Sorlin et al. 2005, Han et al. 2010) will need to become more localised to drive accurate modelling of genotype-environment-management scenarios. By combining with carbon allocation models, hypothesis-driven modelling of branching and flowering processes can then be explored. In common with other FSPM systems, another key area of future application will be as a platform for further simulation. Examples include eco-physiological models, spray deposition (Dorr et al. 2008), insect- plant interactions (Hanan et al. 2002), and plant-pathogen interactions (Pangga et al. 2011). L-systems have proved to be a robust formalism for describing growth and development, forming an integral part of many modern plant modelling languages and systems. As more detailed multi-scaled issues are tackled, both down to genetic scale and up to eco-scale, the challenge will be to extend the underlying formalism, to meet the needs of new scientific issues. ACKNOWLEDGMENTS I’d like to thank Gerhard Buck-Sorlin, Christophe Godin, Winfried Kurth, Przemek Prusinkiewicz, Philippe de Reffye, and Risto Sievanen for sharing their thoughts about the influence of L-systems on their work. LITERATURE CITED Abelson H, diSessa A. 1982. Turtle geometry. M.I.T. Press, Cambridge. Allen M, Prusinkiewicz P, DeJong T. 2005. Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. New Phytologist 166, 869-880. Aono M, Kunii TL. 1984. Botanical tree image generation. IEEE Computer Graphics and Applications, 4(5):10-34 Boudon F, Pradal C, Cokelaer T, Prusinkiewicz P, Godin C. 2012. L-Py: an L-system simulation framework for modeling plant architecture development based on a dynamic language. Front. Plant Sci. 3:76. doi: 10.3389/fpls.2012.00076 Buck-Sorlin GH, Kniemeyer O, Kurth W. 2005. Barley morphology, genetics and hormonal regulation of internode elongation modelled by a relational growth grammar. New Phytologist 166: 859–867. Chelle M, Hanan J, Autret H. 2004. Lighting virtual crops: the CARIBU solution for open L-Systems. In ‘Proceedings of the 4th International workshop on functional–structural plant models’. p. 194. (UMR AMAP: Montpellier, France) Cieslak M, Lemieux C, Hanan J, Prusinkiewicz P. 2008. Quasi-Monte Carlo simulation of the light environment of plants. Functional Plant Biology, 35: 837-849. Cieslak M, Seleznyova AN, Prusinkiewicz P, Hanan J. 2011. Towards aspect-oriented functional-structural plant modelling. Annals of Botany 108(6):1025-1041. Cohen. 1967. Computer simulation of biological pattern generation processes. Nature, 216:246-248, 1967. Costes E, Smith C, Renton M, Guédon Y, Prusinkiewicz P, Godin C. 2008 MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models. Functional Plant Biology 35(10), pp. 936-950. DeJong TM, Da Silva D, Vos J, Escobar-Gutiérrez AJ. 2011. Using functional–structural plant models to study, understand and integrate plant development and ecophysiology, Annals of Botany 108(6): 987-989 Dorr G, Hanan J, Adkins S, Hewitt A, O’Donnell CO, Noller B, 2008. Spray deposition on plant surfaces: a modelling approach., Functional Plant Biology 35:988–996 Fourcaud T, Zhang X, Stokes A, Lambers H, Körner C. 2008. Plant Growth Modelling and Applications: The Increasing Importance of Plant Architecture in Growth Models. Ann Bot 101(8): 1053-1063 Frijters D, Lindenmayer A. 1974. A model for the growth and flowering of Aster novae-angliae on the basis of table (l,O)Lsystems. In G. Rozenberg and A. Salomaa, editors, L Systems, Lecture Notes in Computer Science 15, pages 24-52. Springer-Verlag, Berlin. Godin C, Sinoquet H, Costes E. 2005. Plant architecture modelling: virtual plants and complex systems. In: Turnbull C, ed. Plant architecture and its manipulation. Oxford, UK: Blackwell, 238–287. Godin C, Sinoquet H. 2005. Functional–structural plant modelling. New Phytologist, 166: 705–708. Guo Y, Fourcaud T, Jaeger M, Zhang X, Li B. 2011. Plant growth and architectural modelling and its applications. Ann Bot 107(5): 723-727 Han L, Gresshoff PM, Hanan J. 2010. A functional-structural modelling approach to autoregulation of nodulation. Annals of Botany 107(5): 855-863 3 Hanan J. 1992. Parametric L-systems and Their Application To the Modelling and Visualization of Plants. Ph.D. dissertation, University of Regina. Hanan J, Prusinkiewicz P. 2008. Foreword: Studying plants with functional–structural models. Functional Plant Biology 35(10) vi – viii. Hanan JS, Prusinkiewicz PW, Zalucki M, Skirvin D. 2002. Simulation of insect movement with respect to plant architecture and morphogenesis, Computers and Electronics in Agriculture, 35:255-269. Hogeweg P, Hesper B. 1974. A model study on biomorphological description. Pattern Recognition, 6:165-179. Kniemeyer O, 2008. Design and Implementation of a Graph Grammar Based Language for Functional-Structural Plant Modelling. PhD thesis, University of Cottbus. Kurth W, 1994. Growth Grammar Interpreter GROGRA 2.4: a software tool for the 3-dimensional interpretation of stochastic, sensitive growth grammars in the context of plant modelling. Berichte des Forschungszentrums Waldökosysteme der Universität Göttingen, Ser. B (38). Kurth W, Kniemeyer O, Buck-Sorlin G, 2005. Relational Growth Grammars - a graph rewriting approach to dynamical systems with a dynamical structure. Lecture Notes in Computer Science 3566, Springer, Berlin 2005, 56- 72. Lindenmayer A. 1968a. Mathematical models for cellular interactions in development I. Filaments with one-sided inputs. Journal of Theoretical Biology 18: 280-299. Lindenmayer A. 1968b. Mathematical models for cellular interactions in development II. Simple and branching filaments with two-sided inputs. Journal of Theoretical Biology 18: 300-315. Lindenmayer A. 1987. An introduction to parallel map generating systems. In H. Ehrig, M. Nagl, A. Rosenfeld, and G. Rozenberg, editors, Graph grammars and their application to computer science; Third International Workshop, Lecture Notes in Computer Science 291, pages 27-40. Springer-Verlag, Berlin. Lindenmayer A. 1974 Adding continuous components to L-systems. In G. Rozenberg and A. Salomaa, editors, L Systems, Lecture Notes in Computer Science 15, pages 53-68. Springer-Verlag, Berlin. Loi C, Cournede P-H. 2008. Description of the Greenlab development model with stochastic L-systems and monte- carlo simulations. Technical report, INRIA. Mech R, Prusinkiewicz P. 1996. Visual Models of Plants Interacting with Their Environment. Proceedings of SIGGRAPH 96 (New Orleans, Louisiana, August 4-9, 1996). In Computer Graphics Proceedings, Annual Conference Series, 1996, ACM SIGGRAPH, pp. 397-410. Palubicki W, Horel K, Longay S, Runions A, Lane B, Mech R, Prusinkiewicz P. 2009. Self-organizing tree models for image synthesis. ACM Transactions on Graphics 28(3), 58:1-10. Pangga IB, Hanan J, Chakraborty S. 2011. Pathogen dynamics in a crop canopy and their evolution under changing climate. Plant Pathology 60:1, 70-81 Prusinkiewicz P. 1986. Graphical applications of L-systems. In Proceedings of Graphics Interface '86 -- Vision Interface '86, pages 247-253. CIPS. Prusinkiewicz P. 1987. Applications of L-systems to computer imagery. In Ehrig, Nagl, Rosenfeld, and Rozenberg, eds, Graph grammars and their application to computer science; Third International Workshop, pages 534-548. Springer- Verlag, Berlin, 1987. Lecture Notes in Computer Science 291. Prusinkiewicz P, Hanan J. 1989. Lindenmayer systems, fractals, and plants, volume 79 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin. Prusinkiewicz P, Hanan J. 1990. Visualization of botanical structures and processes using parametric L-systems. In Thalmann, ed., Scientific Visualization and Graphics Simulation, pp. 183-201. Wiley & Sons. Prusinkiewicz P, Hanan J, Mech R. 2000. L-system-based plant modelling language. In: Nagl M, Schuerr A, Muench M. eds. Applications of graph transformations with industrial relevance. Lecture Notes in Computer Science. Berlin: Springer, 395–410. Prusinkiewicz P, Lindenmayer A. 1996. The algorithmic beauty of plants. New York: Springer-Verlag. Prusinkiewicz P, Lindenmayer A, Hanan J. 1988. Developmental models of herbaceous plants for computer imagery purposes. Proceedings of SIGGRAPH '88 (Atlanta, Georgia, August 1-5, 1988), in Computer Graphics 22,4 (August 1988):141-150, ACM SIGGRAPH, New York. Prusinkiewicz P, Runions A. 2012. Computational models of plant development and form. New Phytologist 193, pp. 549-569. Perttunen J, Sievänen R. 2005. Incorporating Lindenmayer systems for architectural development in a functional- structural tree model, Ecological Modelling, 181:479-491. Room PM, Hanan J, Prusinkiewicz P. 1996. Virtual plants: new perspectives for ecologists, pathologists and agricultural scientists. Trends in Plant Science 1: 33-38. Smith AR. 1984. Plants, fractals, and formal languages. Proceedings of SIGGRAPH '84 (Minneapolis, Minnesota, July 22-27, 1984) in Computer Graphics, 1,8, (July 1984), pages 1-10. Szilard AL, Quinton RE. 1979. An interpretation for DOL systems by computer graphics. The Science Terrapin, 4:8- 13. Vos J, Evers JB, Buck-Sorlin GH, Andrieu B, Chelle M, de Visser PHB. 2010. Functional-structural plant modelling: a new versatile tool in crop science. J Exp Bot 61:2101–2115 Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 4 Biomechanics of Bark Patterning in Grasstree Holly Dale*1, Adam Runions2, David Hobill1 and Przemyslaw Prusinkiewicz2 1Department of Physics and Astronomy and 2Department of Computer Science, University of Calgary, AB T2N 1N4, Canada *Correspondence: hjdale@ucalgary.ca Highlights: Bark patterns are a visually important characteristic of trees, attributed to fractures caused by secondary growth of the trunk and branches. A detailed understanding of bark patterns has been impeded by insufficient information regarding biomechanical properties of bark and the corresponding difficulties in faithfully modeling bark fractures using continuum mechanics. Here we focus on grasstrees, which have an unusual bark-like structure composed of distinct leaf bases connected by sticky resin. Due to its discrete character, this structure is exceptionally well suited for computational studies. We created a dynamic grasstree model, which captures both the phyllotactic patterning of the leaf bases during primary growth and the emergence of fractures due to secondary growth. The model reproduces key features of grasstree bark patterns, including inhomogeneities due to compression of leaf bases at the sites of inflorescences. Keywords: Bark pattern, fracture mechanics, primary and secondary growth, biomechanical model. INTRODUCTION Grasstrees (Xanthorrhoea, Fig. 1) are a genus of monocots native to Australia with a morphology adapted to frequent fires. Their stems are pseudomonopodial. The straight course of the stem is disturbed when the terminal apex produces an inflorescence and an auxillary bud takes over further vegetative development (Borsboom 2005). Leaves are arranged into dense spiral phyllotactic patterns (Staff 1968). During fires, leaves are burnt back to their bases, which are cemented together by melting resin to form a type of bark that protects the tree from disease and future fires (Lamont et al. 2004). Over time, this resin fractures, partitioning interconnected leaf bases into separate regions. As a result, grasstree bark gradually progresses from a regular lattice of interconnected leaf bases near the top of the tree to a fractured pattern of patches similar to that observed in other tress near the base. Here we show that this progression, and its disturbances at the sites supporting past inflorescences, can be explained in mechanical terms. To this end, we have constructed a virtual grasstree that combines a descriptive model of primary growth and phyllotaxis with a mechanical model of fractures operating on the discrete lattice of parastichies induced by this phyllotaxis. PREVIOUS WORK Fractures have been simulated using both discrete and continuous models. Skjeltorp and Meakin (1988) introduced a mass- spring model to simulate fractures in an elastic layer under tension. Federl and Prusinkiewicz (1996) adopted this system to model fractures in tree bark. In contrast to the work presented here, they considered the mass-spring as an (imperfect) approxi-mation of bark thought of as a homogeneous material. Improving this approximation, Federl and Prusinkiewicz (2002) modified their previous model by replacing masses and springs with a finite- element method. The resulting model produced several plausible bark patterns, but the question of whether real bark is adequately approximated as a continuous, homogenous sheet was not addressed. The grasstree offers a unique opportunity to create a faithful bark model due to the macroscopic lattice structure induced by the underlying phyllotactic arrangement of leaf bases. This structure justifies the use of a discrete model. Figure 1. Young and older grasstree. 5 SIMULATIONS The shoot apical meristem produces leaves sequentially in a phyllotactic pattern. Parameters of this pattern were inferred from photographs of real grasstrees (Fig. 2). In the model, we represented leaf bases as masses and their resin connections as (Hookean) springs, connecting each base to its four nearest neighbors (Fig. 3). The bark layer increased in radius, and thus in circumference, due to secondary growth. This was simulated by gradually pushing each mass outwards with springs that connected leaf bases to the inner core of the tree. Consequently, the spring forces between masses increased until a critical threshold value was reached and some springs broke (the threshold value was subject to small random variations, needed to break the symmetry of the system). The bark pattern was defined by the resulting fractures, which separated patches of bases connected by the remaining springs. To simulate the influence of inflorescence sites, we have periodically shifted the growth axis and/or the radius of the bark layer. We used measurements of a real grasstree (Lamont et al. 1979) to calibrate proportions of this system. We also observed that leaf bases near the flowering sites have different aspect ratios, compared to the stem segments between flowering sites (Fig. 2c), and we incorporated these changes into the model by modifying parameters of the phyllotactic pattern. RESULTS AND DISCUSSION We have created a model of grasstree development (Fig. 4) as a basis for studying the emergence of grasstree bark patterns. These patterns are different near the sites of inflorescences and between these sites (Fig. 5). The areas near flowering sites are characterize by a network of diagonal fractures that run along the parastichies. Areas between flowering sites have long fractures running approximately parallel to the stem axis. Our biomechanical model emergently captures these differences. Although the generality of this result is qualified by the unusual structure of grasstree bark, it supports the hypothesis that bark pattern formation is primarily a biomechanical phenomenon. From a broader perspective, this result increases the spectrum of morphogenetic phenomena in which biomechanics and properties of space, rather than detailed genetic patterning, play a key role (Prusinkiewicz and de Reuille, 2010). Figure 3. (a,b) Mesh of masses and springs. Yellow mass belongs to the inner layer that cau-ses growth in diameter. Blue masses complete leaf bases. (c) Resulting pattern of leaf bases. Figure 2. Estimating parameters of the phyllotactic pattern. (a,b) Number of ba- ses that a horizontal line intersects in a real image (~37) and in the model (~40). (c-e) Estimation of the angle between parastichies (~56°). (f-j) The horizontal stretch of bases: (f,i) at the location be- tween inflorescences, (g) at a bend of the stem where leaf bases are severely deformed, and (h,j) at the location of an inflorescence. a b c d e f i a g j h c b 6 ACKNOWLEDGMENTS Thanks to Steven Longay for creating Fig. 3. Support of this work by Undergraduate Student Research Award and Discovery Grant from the National Sciences and Engineering Research Council of Canada is gratefully acknowledged. LITERATURE CITED Borsboom AC. 2005. Xanthorrhoea: A review of current knowledge with a focus on X. johnsonii and X. latifolia, two Queensland protected plants-in-trade. Environmental Protection Agency, Queensland, 87 pp. Federl P, Prusinkiewicz P. 1996. A texture model for cracked surfaces. In Proceedings of the Seventh Western Computer Graphics Symposium, pp. 23-29. Federl P, Prusinkiewicz P. 2002. Finite element model of fracture formation on growing surfaces. In Proceedings of ICCS 2004, Part II, LNCS 3037, pp. 138-145. Lamont BB, Downes S. 1979. The longevity, flowering and fire history of the grasstrees Xanthorrhoea preissii and Kingia Australis. Journal of Applied Ecology 16:893-899. Lamont BB, Wittkuhn R, Korczynskyj D. 2004. Ecology and ecophysiology of grasstrees. Australian Journal of Botany 52:561-582. Prusinkiewicz, P, Barbier de Reuille, P. 2010. Constraints of space in plant development. Journal of Experimental Botany 61:2117-2129. Skjeltorp AT, Meakin P. 1988. Fracture in microsphere monolayers studied by experiment and computer simulation. Nature 335:424-426. Staff IA. 1968. A study of the apex and growth patterns in the shoot of Xanthorrhoea media R. Br. Phytomorphology 18:153-165. Figure 4. Simulation of grasstree development Figure 5. Fracture patterns in a real grasstree stem (a,c) and simulation (b,d). Areas near inflorescence sites have compressed bases with more diagonal fractures (a,b), regions without flowering have primarily vertical fractures (c,d). a b c d Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 7 Floral phyllotaxis of magnolia in computer simulations - towards understanding phyllotactic fingerprint Beata Zagórska-Marek and Marta Fijak Institute of Experimental Biology, University of Wroclaw,Kanonia Str.6/8, 50-328 Wroclaw, Poland *correspondence: beata@biol.uni.wroc.pl Highlights: Magnolia’s floral shoot, with its uniquely rich and diverse phyllotaxis, has been modeled with application of a special program based on geometric model of phyllotaxis. First survey of phyllotactic diversity obtained in the library of 1200 computer simulations proved that, besides the most common main Fibonacci, also other patterns, frequently encountered in nature, such as Lucas and bijugy, are readily formed. This is a part of extensive studies aimed to elucidate the mechanism of phyllotactic fingerprint – the species or genet specific pattern of phyllotactic diversity, first in magnolia flowers and then in other plant structures and taxa. Keywords: phyllotaxis, Magnolia, floral parts, phyllotactic fingerprint, plant development, shoot apical meristem INTRODUCTION Double change in the identity of floral organ primordia, associated with the change in their sizes (Zagórska-Marek 1994, Xu 2006, Xu and Rudall 2006, Zagórska-Marek and Szpak 2008), creates the potential for extreme diversity of floral phyllotaxis in magnolia (Erbar and Leins 1982, Zagórska-Marek 1994). Yet different magnolia species or even genets execute this potential in different ways. Some have exceptionally rich, others rather limited spectrum of the diversity (Wiss and Zagórska-Marek 2012). The spectrum is so specific and persistent in consecutive blooming seasons that it can be treated as the individual tree’s fingerprint (Zagórska-Marek 2011). Understanding this phenomenon seems to be a great challenge. The aim of our work was to test, in computer simulations, how the changes in geometric parameters of primordia generated by apical meristem affect phyllotactic pattern formation in virtual magnolia flower. For that purpose we have used geometric model of phyllotaxis and special computer program Phyllotaxis ver. 0.3 (Zagórska-Marek and Szpak 2008). RESULTS AND DISCUSSION In the first step of testing we asked ourselves, is there a connection between evidently high and changing number of spirally arranged stamens and the number of patterns and phyllotactic transitions in magnolia gynoecium. We have noted in preliminary tests that the number indeed affects the quality of gynoecial phyllotaxis, defined (following Adler 1974) by modified contact parastichy pair formula (as:bz), in which s and z indices stand for parastichy orientation (Fig.1). Fig. 1. Magnolia’s virtual floral shoots. The parameters of all three simulations are the same except for the number of stamens (in red). Decreasing it by one in two consecutive steps, changes gynoecial phyllotaxis dramatically from Lucas (left), through main Fibonacci (middle) to bijugy (right); green, red and blue circles denote respectively the perianth elements, stamens and carpels. Gynoecial phyllotaxis is defined by contact parastichy pair formula. 8 Over 1200 pictures were created, divided into 3 groups. The only difference between them was the ratio between stable size of perianth elements and the size of the first stamen. The starting pattern of the perianth was always tricussate, with the 118° intersection angle between the 3s:3z connecting lines. In agreement with developmental changes observed in nature, we set the program to gradually increase the size of circles representing stamens and carpels. Speed of an increase was set to 1.001 for stamens and 1.004 for carpels, which means that every next stamen was bigger by 0.001 of the radius, and carpel was bigger by 0.004. To add a more realistic feel to the simulation we set a tolerance in radius change for 5%. The software allows setting a seed for the random number generator. The groups of simulations were created as follows: the small group (S), with the initial size of stamens set to 6.5 and of carpels to 8.0, the medium group (M) with the size of stamens set to 7 and of carpels to 8.5, and the large group (L) with the size of stamens set to 7.5 and of carpels to 9.0. We generated 400 pictures for each group, differing in a number of stamens from 60 to 100, having constant number of carpels set to 50, and differing in a seed for random factor from 1 to 10. In every case, the initial phylotactic pattern, in the 3rd row, starting from the end of androecium zone, and the ultimate one, in the 3rd row down from the end of gynoecium, i.e. from the top of virtual floral shoot, have been determined. This way, apart from the initial gynoecial pattern we also acquired information on pattern rearrangements in given subgroups. Patterns were identified by counting contact parastichies and recorded in a form of contact parastichy pair formula (as:bz). To process all these data we developed a small program (Counter ver. 0.1). Qualities and frequencies of patterns have been summarized for all analyzed cases (Table 1), because there was no significant difference in these parameters among three groups. The most common was the main Fibonacci pattern. The Lucas pattern was the second and bijugy the third most frequent among the patterns. We have noted extreme asymmetry of pattern chiral configurations, which in nature occur in more similar frequencies. This effect of simulations is not yet fully understood. Table 1. Quality and frequency of ultimate gynoecial patterns; F – main Fibonacci, L – Lucas, Bi – bijugy, T –tetrajugy, Tr- trijugy, P- pentajugy, irr.- irregular pattern pattern expression 3s:5z 4s:5z 4s:6z 4s:4z 3s:4z 5s:5z 5s:6z 4s:7z 3s:3z 2s:4z 2s:5z irr. No of cases 356 128 225 131 301 3 2 4 8 6 1 35 pattern type F F(Bi) F(T) L F (P) L F(Tr) F(Bi) In the next step, we analyzed the pattern rearrangements (phyllotactic transitions) in all 3 groups: S, M, L. The data for each group had been divided into 5 subgroups, according to the range of changes in the number of stamens: first one with 60 to 68 stamens, second with 69 to 76, third with 77 to 84, fourth with 85 to 92 and fifth with 93 to 100. The highest rate of phyllotactic transitions was recorded for each range in S group (Table 2). Table 2. Number of rearrangements associated with changing number of stamens in 3 groups: S, M and L range 60-68 69-76 77-84 85-92 93-100 Sum S 58 40 47 39 40 224 M 26 14 17 22 29 108 L 31 24 13 13 7 88 From the same set of data it was possible to extract the information, which pattern is developmentally the most stable. Among the 5 most common patterns, surprisingly, the most stable was the Lucas pattern (Table 3). 9 Table 3. Gynoecial pattern stability. Most stable are those where an initial pattern frequency and the frequency of cases, in which the same pattern was stable, are similar. Their ratio is given at the bottom of the table. Pattern 3s:5z 4s:5z 4s:6z 4s:4z 3s:4z initial 493 119 255 58 104 ultimate 356 128 225 131 301 stable 342 60 190 33 103 % 69,37% 50,04% 74,50% 56,89% 99,00% Finally we plotted the data about rearrangements in to a graph (Fig.2). To have a right scale we divided the number of rearrangements in each subgroup by the number of rearrangements in the whole group (S, M, L). 60-68 69-76 77-84 85-92 93-100 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 S. M. L. Fig. 2. Frequency of rearrangements depending upon the number of stamens in 3 groups: S, M and L. In the range between 77 and 92 stamens the pattern, regardless its quality, is the most stable. It has been shown already, in similar simulations, that some phyllotactic patterns in their lowest expressions are more developmentally stable than others (Szpak and Zagórska-Marek 2011). In magnolia, however, pattern expressions in gynoecium are high. Shown here clear disproportion between the number of rearrangements in S and L group of magnolia virtual floral shoots as well as pattern stability, which depends upon the number of organs generated by floral meristem, are in fact the first hints of why some magnolias may have gynoecial phyllotaxis more diverse than others. More accurate empirical data should be collected, to create a collation with the data obtained from simulations. We also feel that developing a program for analyzing the quality of phyllotactic pattern should be considered to eliminate the human error in diagnosing the effects of simulations. More research is also needed to understand fully the phenomenon of phyllotactic fingerprint – our working hypothesis that changing number of stamens may favor selection of the specific patterns has been neither falsified nor verified, yet! LITERATURE CITED Adler I. 1974. A model of contact pressure in phyllotaxis. J.Theor.Biol.45: 1-79. Erbar C, Leins P. 1982. Zur Spirale in Magnolien-Blüten. Beitr Biol Pflanzen.56:225–241. Szpak M, Zagórska-Marek B. 2011. Phyllotaxis instability – exploring the depths of first available space. Acta Soc. Bot. Pol. 80:279–284. http://dx.doi.org/10.5586/asbp.2011.043 Xu FX. 2006. Floral ontogeny of two species in Magnolia L. J. Integr. Plant Biol. 48:1197–1203. http://dx.doi.org/10.1111/j.1744-7909.2006.00341.x Xu FX, Rudall PJ. 2006. Comparative floral anatomy and ontogeny in Magnoliaceae. Plant Syst Evol. 258:1–15. http://dx.doi.org/10.1007/s00606-005-0361-1 Wiss D, Zagórska-Marek B. 2012. Geometric parameters of the apical meristem and the quality of phyllotactic patterns in Magnolia flowers. Acta Soc.Bot.Pol. 81:203-216. http://dx.doi.org/10.5586/asbp.2012.029 Zagórska-Marek B, Szpak M. 2008. Virtual phyllotaxis and real plant model cases. Funct Plant Biol. 35:1025–1033. http://dx.doi.org/10.1071/FP08076 Zagórska-Marek B. 2011. Magnolia flower - the living crystal. Magnolia. The Journal of the Magnolia Society International 89: 11-21. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 10 Modelling the spatial arrangement of vascular bundles in plants Fabrizio Cartenì1*, Francesco Giannino1, Gianni Boris Pezzatti2 and Stefano Mazzoleni1 1Dipartimento di Agraria,University of Naples Federico II, via Università 100, 80055, Portici (Na), Italy, 2Swiss Federal Institute for Forest, Snow and Landscape Research, Ecosystem Boundaries Research Unit, Via Belsoggiorno 22, CH-6500 Bellinzona, Switzerland *correspondence: fabrizio.carteni@unina.it Highlights: The spatial arrangement of vascular bundles varies between plant species and organs. A novel reaction-diffusion 2D model is presented defining a set of logical and functional rules able to simulate the differentiation of procambium, phloem and xylem. The model shows that a common mechanism, lying behind the formation of vascular tissues, is able to qualitatively reproduce most stelar structures observed. Keywords: PDE, reaction-diffusion, stele evolution, tissue differentiation INTRODUCTION Spontaneous spatial pattern formation as a result of the dynamic interactions of system components is common in nature at all scales. In plant development and morphogenesis, several regular patterns have been widely studied such as the establishment of the main axes, phyllotaxis, organ shape and venation. In the last decades, simulation models have proven to be useful tools for hypotheses testing on complex systems. Models have been often applied to unravel non-intuitive relations of local processes with the emergence of global forms and patterns. Several studies using computational modelling have been carried out on plant morphodynamics (Jönsson and Krupinski, 2010; Prusinkiewicz and Runions, 2012). Recent work (reviewed in: Jönsson et al., 2012) has focused on two topics: i) venation and phyllotaxis driven by auxin polar transport and ii) genetic regulation of stem cells in apical meristems. So far, no modeling effort has been done yet on the formation of primary vascular structures. We present a spatially explicit reaction-diffusion model defining a set of logical and functional rules able to simulate the differentiation of procambium, phloem and xylem. The model qualitatively reproduces most stelar structures observed in different plant taxa. MODEL DESCRIPTION Fig. 1. Schematic representation of vascular patterns in plants. We developed a mathematical model that simulates the development of a group of undifferentiated cells in a sub-apical transverse section of stems and roots (Fig. 1). We used the activator–inhibitor and activator- substrate modelling approaches introduced by Gierer & Meinhardt (1972), and fully developed by Meinhardt 11 (1982). The main assumptions of our model are the following: • mitotic index strongly relates to cell position within the meristem, being significantly higher in the outer zone than in the inner zone (Laufs et al., 1998); • sugar metabolism, particularly cellular sugar status (Koch, 2004; Eveland and Jackson, 2012), plays a fundamental role in plant development and definition of spatial domains within plant organs (Pien et al., 2001); • the emergence of vascular tissues depends on the juxtaposition of adaxial/central and abaxial/peripheral spatial domains which sets a cascade of species-specific and organ-specific genetic and molecular dynamic processes. We defined a system of 9 PDEs that describe the spatio-temporal dynamics of different compounds in a group of meristematic cells. A first equation describes the sugar status of the cells. A set of three equations describes the dynamics of an activator-substrate system which leads to the differentiation of procambium. Another set of 5 equations drives the emergence of phloem and xylem and describe the dynamics of two locally mutually exclusive compounds with lateral reciprocal facilitation (Meinhardt and Gierer, 1980). Meristematic cells are in a continuous state of division and the velocity of cellular division depends on their position within the organ. Sucrose cleavage to hexoses is positively correlated to the division rate, then fast dividing cells have higher hexoses concentrations. An hexose threshold value results in the activation of genes marking the cell as either adaxial or abaxial. The two newly defined cell domains start producing specific signals which are necessary to produce an autocatalytic activator responsible for the activation of procambium-fate genes. Once differentiated, provascular cells start the production of two other competing autocatalytic activators responsible for the activation of phloem-fate and xylem-fate genes respectively. According to the prevalence of either one or the other activator, procambial cells differentiate into either phloem or xylem. RESULTS AND DISCUSSION Fig. 2. Examples of simulated steles. Grey: ground tissue; Red: phloem; Blue: xylem. A) Protostele; B) Actinostele; C) Siphonostele; D) Eustele with collateral bundles; E) Eustele with bicollateral bundles. The arrangement of vascular bundles observed in plant steles, can be summed up in three basic types: i) protostele presenting a solid column of vascular tissue (Fig. 2A); ii) siphonostele characterised by an hollow cylinder of vascular tissue (Fig. 2C); iii) eustele showing separated strands of vascular tissue, usually arranged as a discontinuous cylinder (Fig. 2D) (Beck et al., 1982). Model simulations were able to effectively reproduce most stelar types observed in plants showing that different vascular patterns can be developed by similar molecular and genetic processes (Fig. 2). Model numerical analysis and simulation results of the first set of equations, show that the emergence of protostelic opposed to siphonostelic or eustelic patterns depends on domain dimension where the process occurs (Fig. 2 A,C). Varying only the domain diameter, a protostelic structure emerges in small domains, while either siphonostelic or eustelic structures are formed in larger domains. The formation of these latter spatial patterns mainly depends on the parameter controlling the autocatalytic reaction between procambium activator and its substrates. Moreover, the differentiation of both phloem and xylem occurs in consistent arrangements within the abovementioned vascular structures. The different spatial organization of phloem and xylem, e.g. collateral bundles (Fig. 2D) and bicollateral bundles (Fig. 2E), depends on levels of diffusion and reaction rates of respective activators. Future work will be focused on a better definition of sugar metabolism and on the simulation of secondary growth. 12 LITERATURE CITED Beck CB, Schmid R, Rothwell GW. 1982. Stelar morphology and the primary vascular system of seed plants. Botanical Review 48:691-815. Eveland AL, Jackson DP. 2012. Sugars, signalling, and plant development. Journal of Experimental Botany 63(9):3367-3377. Gierer A, Meinhardt H. 1972. A theory of biological pattern formation. Kybernetik 12:30-39. Jönsson H, Gruel J, Krupinski P, Troein C. 2012. On evaluating models in computational morphodynamics. Current Opinion in Plant Biology 15:103-110. Jönsson H, Krupinski P. 2010. Modeling plant growth and pattern formation. Current Opinion in Plant Biology 13:5- 11. Koch K. 2004. Sucrose metabolism: regulatory mechanisms and pivotal roles in sugar sensing and plant development. Current Opinion in Plant Biology 7:235-246. Laufs P, Grandjean O, Jonak C, Kieu K, Traas J. 1998. Cellular parameters of the shoot apical meristem in Arabidopsis. Plant Cell 10:1375-1390. Meinhardt H, Gierer A. 1980. Generation and regeneration of sequences of structures during morphogenesis. Journal of theoretical Biology 85:429-450. Meinhardt H. 1982. Models of biological pattern formation. London, UK: Academic Press. Pien S, Wyrzykowska J, Fleming AJ. 2001. Novel marker genes for early leaf development indicate spatial regulation of carbohydrate metabolism within the apical meristem. The Plant Journal 25:663-674. Prusinkiewicz P, Runions A. 2012. Computational models of plant development and form. New Phytologist 193:549- 569. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 13 Estimating the genetic value of F1 apple progenies for irregular bearing during first years of production Jean-Baptiste Durand1,2, Baptiste Guitton3, Jean Peyhardi2,4, Yan Holtz5, Yann Guédon2, Catherine Trottier4 and Evelyne Costes3 1Grenoble University, Laboratoire Jean Kuntzmann, BP53, F-38041 Grenoble Cedex 9, France, 2CIRAD/Inria, Virtual Plants Team, UMR AGAP, F-34095 Montpellier, France, 3CIRAD, UMR AGAP, F- 34398 Montpellier, France, 4Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier 2, F-34095 Montpellier, France, 5INRA, AFEF Team, UMR AGAP, F-34398 Montpellier, France *correspondence: jean-baptiste.durand@imag.fr Highlights: Flowering regularity in apple trees during the beginning of their mature phase was assessed using new descriptors based on annual yields. These descriptors were approximated using subsamples of annual shoot sequences at axis scale to allow genotype evaluation at reasonable sampling costs. The approximation provided a good discrimination between regular and alternate bearing genotypes. QTLs were detected for some descriptors. Keywords: alternation indices, biennial bearing, breeding, linear mixed model, Malus x domestica, QTL detection. INTRODUCTION Because irregular bearing generates major agronomic issues in fruit-tree species (Monselise and Goldschmidt, 1982), particularly in apple, the selection of regular cultivars is desirable. Here, we aimed at defining methods allowing an early diagnostic in populations segregating for bearing behaviour. It was shown by Guitton et al. (2012) that biennial bearing is inheritable and segregates in an apple progeny (“Starkrimson”× “Granny Smith”), suggesting that selecting new varieties with intrinsic regular bearing is a possible strategy. However, breeding programs for fruit-tree species do not consider this trait yet, because it requires flowering observations over several years before its value for a given genotype can be assessed (and the first flowering occurs two to four years after grafting). Development of methods for a faster diagnostic of the bearing tendency of a genotype during its first years of production is thus highly desirable. The Biennial Bearing Index (BBI) has been widely used to quantify biennial bearing at different scales (Wilcox, 1944): whole areas, individual trees or branches - on apple and other fruit trees. Huff (2001) highlighted that the distribution of BBI strongly depends on the mean and variance of yields, under the hypothesis that they are a random sample. Therefore, the accepted interpretation of BBI as a measure of the magnitude of irregular bearing is questionable. Moreover, it has been shown by Pearce and Dobersek-Urbane (1967) that using BBI on trended series may lead to confound alternation and trend. The observation that yield is subject to a progressive increase in the first years of tree production, motivated our research for new descriptors of alternation. With the aim to dissociate yield increase from bearing pattern, we investigated a new modelling approach incorporating a trend term for yearly yields, and terms representing dependencies and amplitudes of successive deviations from the trend. Our expectation was to distinguish the genotype bearing behaviour applying clustering methods on these new descriptors. To avoid measuring yearly numbers of flowers at tree scale, we also investigated the possibility of early discrimination between genotypes, based on the same descriptors, using samples of successive annual shoots (AS) at axis scale. Finally, from the analysis of correlations between descriptors at both tree and AS scales we explored how fruiting behaviour at tree scale may be obtained from that at axis scale. MATERIALS AND METHODS A segregating population obtained from a cross between ‘Starkrimson’ and ‘Granny Smith’ (Guitton et al., 2012), was used. One or two tree replicates were available for each of the 120 genotypes composing the population. Flowering recurrence was measured at two scales: whole tree and AS scales. The total number of inflorescences per year and tree was observed from the 2nd to the 7th year after grafting. At AS scale, the 14 succession of vegetative v. floral AS over the same consecutive years were observed along different types of axes: trunk, long and short axillary shoots. Long axes were scaffolds chosen as similar as possible along the trunks. The data consisted of 2- to 6-year sequences of AS, with 4 to 45 sequences per genotype. Let Tg,r denote the number of years of growth of tree replicate r of genotype g and Yg,r,t its number of inflorescences at year t. A Gaussian linear mixed regression model with first-order autoregressive errors (to model the serial correlations between successive residuals) was used (2).)(,(1))( ,,1,,,,,,,,,, trgtrgrggtrgtrgrgggtrg utY ++=+++++= −εγγεεξααββ Here, (1) is a trend sub-model, and the first-order autoregressive process (2) on the deviations εg,r,t between Yg,r,t and the trend (Fig. 1) quantifies the alternation through the dependencies between successive residuals (measured by γg). Their amplitudes were quantified using a BBI-like index on εg,r,t , normalized by mean yields, defined as ( ) ( ) ./ )1(/ˆˆ rmBBI_res_no ,1 ,, ,2 1,,,, , , ∑∑ ∑ ∑∑ ∑ = = − −− = r rgr T t trg r rgr T t trgtrg TY T rg rg εε A clustering of the genotypes based on BBI_res_norm and γg was obtained using a Gaussian mixture model and the Bayesian information criterion to select the number of clusters (Bishop 2006, Chap. 4 and 9). The ability to retrieve the genotype bearing behaviour (or class) from the subsample of AS sequences was assessed by approximating BBI_res_norm and γg by their values in the subsamples (leading to two indices referred to as BBI_res_norm_loc and γloc, respectively). Two other kinds of descriptors computed at AS scale were also used to predict the bearing behaviour: an index of synchronism in flowering based on entropy (Bishop, Chap. 1) and a 2nd-order Markov chain with memory × genotype and memory × year interactions. Five descriptors, namely BBI_res_norm and γg at tree scale, and BBI_res_norm_loc, γloc and entropy at AS scale, were used for QTL detection which was performed using the STK×GS consensus genetic map (Guitton et al., 2012) and MapQTL® 5.0. (Van Ooijen, 2004), with 4.0 as LOD score threshold for all traits. RESULTS AND DISCUSSION trgY ,, trg ,,ε 0 1 2 3 5t =4 Year 0 20 0 40 0 60 0 80 0 N um be ro f i nf lo re sc en ce s trend for genotype trend for replicate (with equation of trend line) measurement BBI_res_norm γ g regular biennial 0.5 1.0 1.5 -1 .0 -0 .5 0. 0 0. 5 irregular Fig. 1. Data, trend model and residuals for total yields at tree scale for a biennial bearing genotype (γg = -0.88, BBI_res_norm = 1.21) Fig. 2. Clustering obtained using a 3-component Gaussian mixture using BBI_res_norm (x-axis) and γg (y-axis). Cluster 1 can be interpreted as regular bearing genotypes, cluster 2 as biennial bearing genotypes and cluster 3 as irregular bearing genotypes. The clustering obtained using the descriptors at tree scale BBI_res_norm and γg highlighted three clusters (Fig. 2). Cluster 1 is characterized by a low BBI_res_norm (low dispersion of yields around trend) and unstructured residuals (γg ≈ 0 in (2)); thus, it is interpreted as regular genotypes. Cluster 2 is characterized by a high BBI_res_norm (high dispersion of yields around trend) and residuals with alternate signs (γg close to -1), and is interpreted as biennial bearing genotypes. The genotypes in cluster 3 have intermediate values and are interpreted as irregular. 15 The genotypes have the following behaviours at AS scale, depending on their cluster: genotypes in cluster 1 have high entropies (0.38 on average) (i.e. high uncertainty), which corresponds to asynchronous and irregular flowering at AS scale. The transition probabilities of the Markov chain highlight a higher probability of these genotypes to flower in year t after flowering in year 1−t , and a higher probability to flower in 2009, which is an “off” year for the majority of biennial bearing genotypes (even years being “on” years, on the contrary). Genotypes in cluster 2 have low entropies (0.23 on average), which corresponds to synchronous and well-predictable flowering at AS scale. An AS preceded by a flowering AS in year 1−t and a vegetative AS in year 2−t has a lower probability to flower in year t, and any AS has a lower probability to flower in 2009. Genotypes in cluster 3 have high entropies (0.38 on average), and intermediate probabilities of AS to bear flowers during successive years or in 2009. Comparison of the genotype behaviours at AS and whole tree scales highlights that in the available progeny, regularity comes from the combination of irregular axes and asynchronism, whereas alternation comes from the combination of alternate axes and synchronism. A clustering was also performed using the descriptors at AS scale, to assess whether the clusters approximate those obtained from descriptors at tree scale. Two confusions occurred between regular and alternate bearing genotypes, and 44 confusions occurred between irregular and both other clusters of genotypes. The other 69 genotypes were correctly classified. As a consequence, regular and biennial bearing genotypes are well discriminated from their behaviour at AS scale, whereas irregular genotypes are poorly discriminated. Thus, we can propose that breeders (i) progressively suppress biennial or irregular genotypes after the first observation of a large decrease in flowering during the beginning of the mature phase (ii) confirm the regular fruiting behaviour of the pre-selected genotypes during the stable mature phase. Five QTLs altogether were identified in four separated genomic regions, and explained from 13.5 to 22.5% of the genetic variability. At tree scale, two QTLs were found for BBI_res_norm on LG1 and LG8 (LOD 6.69 and 5.82, respectively) and no significant QTL was detected for genotype AR coefficient γg. At AS scale, one QTL was mapped for BBI_res_norm_loc on LG8 in the same region (LOD 5.74) than the QTL mapped for BBI_res_norm at tree scale. Two QTL were also detected for γloc on LG11 and LG14 (LOD 7.24 and 4.55, respectively). By contrast, no QTL was detected for the entropy. QTLs mapped on LG1 and LG8 corroborate zones that have been identified in a previous study (Guitton et al., 2012). The QTL cluster on LG1 seems to be linked to the antagonist relationship between fruit production and inflorescence initiation in a same year, as reported by Bangerth (2009). The two QTL revealed on LG11 and LG14 for γloc are located on zones that were not previously associated to flowering or bearing traits in this progeny. Further exploration of these genomic regions is required to interpret precisely which mechanism could underlie these associations. The absence of QTL detection for other descriptors, especially γg at tree scale and entropy at AS scale, may be due to the population size. Indeed, 120 individuals can be limiting to detect QTL with small effects (Bernardo, 2004) and only major QTLs (explaining more than 13% of the trait variance) were confirmed in the present study. However, it may be noticed that the QTLs detected in the present study do not depend on year effects but rather are associated to genotype bearing behaviour over years. LITERATURE CITED Bangerth F. 2009. Floral induction in mature, perennial angiosperm fruit trees: Similarities and discrepancies with annual/biennial plants and the involvement of plant hormones. Scientia Horticulturae 122: 153-163. Bernardo R. 2004. What proportion of declared QTL in plants are false? Theoretical and Applied Genetics 109: 419- 424. Bishop CM. 2006. Pattern Recognition and Machine Learning. Springer Verlag, 2006. Guitton B, Kelner J-J, Velasco R, Gardiner SE, Chagné D, Costes E. 2012. Genetic control of biennial bearing in apple. Journal of Experimental Botany 63: 131-149. Huff A. 2001. A significance test for biennial bearing using data resampling. Journal of Horticultural Science & Biotechnology 76: 534-535. Monselise SP, Goldschmidt EE. 1982. Alternate bearing in fruit trees. Horticultural Reviews 4: 128-173. Pearce SC, Dobersek-Urbane S. 1967. The measurement of irregularity in growth and cropping. Journal of Horticultural Science 42: 295-305. Van Ooijen JW. 2004. MapQTL® 5, Software for the mapping of quantitative trait loci in experimental populations. Wageningen, Netherlands: Kyazma B.V. Wilcox J. 1944. Some factors affecting apple yields in the Okanagan Valley: tree size, tree vigor, biennial bearing, and distance of planting. Scientific Agriculture 25: 189. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 16 Biomechanical modelation of Ravenala madagascariensis petiole Andrés Valencia-Escobar1*, M. Paulina Fernández2 and Diego J. Celentano3 1Industrial Design Faculty, Universidad Pontificia Bolivariana, Medellin, Colombia 2Faculty of Agronomy and Forest Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile 3School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile *correspondence: andres.valencia@upb.edu.co Highlights: The use of shape transformers methodology, local buckling Brazier model and finite elements analysisis to model the Ravenala madagascariensis petiole allows to discover how the relation between shape and mater gives to the plant a structural support to bear high bending and torsion loads without fail. The combination of an elliptical stiff perimeter (epidermis) reinforced with a highly ordered cellular core (aerenchyma) gives to Ravenala petiole two very efficient and secure stability mechanisms. Keywords: Ravenala madagascariensis, Petiole, Structural efficiency, biomechanics modeling INTRODUCTION Modeling of structural behavior of plants is an important step in their biomechanical analysis. It allows identifying the relationships between the morphological and anatomical features and the mechanical behavior of the structure under analysis. The models obtained are useful for three purposes basically: to understand the physics behind biological processes (Niklas and Spatz, 2012), to support the behavior of natural materials with commercial interest like wood or bamboo (Mattheck, 1998; Niklas et al., 2006; Vincent, 2012), and to bring the results of the model to the design table and translate them into objects or strategies (Vincent, 2006; Nychka and Chen, 2012). Nowadays, one of the most innovative work areas for plants biomechanical models is the design of structures based on the structural principles observed in them (Martone et al., 2010; Shimomura, 2010) in order to optimize man-made structures (Vogel, 2000). This activity, called biomimicry, uses the structural models as its main tool to mimicry the natural behavior through the design process. Petioles can be considered like cantilever beams subjected to bending and torsion (Niklas, 1992; Vogel, 1992). The combination of shape from its cross-section perimeter and the mechanical properties and distribution of tissues, are the main variables included in most of the models. This work approximates the mechanical behavior of the Ravenala madagascariensis petiole (refered as R. mad). R. mad it’s a monocotiledonean plant of the Zingiberales order and Strelizciaceae (Bird of Paradise) family, endemic of Madagascar island (Kress, Schatz, Andrianifahanana, & Morland, 1994) and is planted like ornamental tree throughout the tropics. The plant presents a set of long petioles and leaves arranged sideways in a bidimensional alternate pattern like a giant hand fan (Fig. 1a). The interest for this type of study about structural morphology lies on the remarkable formal mechanisms that this petiole presents to support all the loads imposed by self weight, wind, rain and animals, and the potential to use them like patterns for the mechanical design of artificial elements. In the modeling approach the contribution of the perimetral shape of the cross-section to the overall structural performance is considered. Moreover, we link the shape with the distribution and mechanical properties of the three main tissues present in the petiole (i.e. epidermis, the combination of parenchyma and aerenchyma and sclerenchyma) (Figure 1b), with the aim to model the efficiency of the real behavior. MATERIALS AND METHODS To model the structural behavior of R. mad petiole, 9 mature petioles were collected and analyzed microscopical and macroscopically. Cross-section cuts were prepared and microscopic images were obtained (a) (b) Figure 1: (a) Ravenala madagascariensis exemplar in the Botanical Garden of Medellín, Colombia and (b) cross section of the petiole. 17 with Computed Axial Tomography technique with a Toshiba Aquilion 64 CT Scanner, Motic SMZ 140 stereo zoom microscope and Jeol JSM-6490 SLV scanning electron microscope. From macroscopic images morphological and anatomical features were measure and described. Cantilever bending and torsion tests were developed to obtain the elastic load-displacement curves. To analyze and model the contribution of the perimetral shape in the overall behavior of the petiole, the shape transformers methodology -STM- was used. The STM proposes the mass minimization as optimization criteria in structural design (Pasini et al., 2002). The modeling of the local buckling the cross-section under bending loads uses as reference the model proposed by Brazier (Brazier, 1927). To apply FEM, a 3-D digital model of the R. mad petiole cross-section was developed based on the real distribution of tissues, shapes and dimensions. Only peripheral sclerenchyma fiber bundles were taken into account, assuming that the fibers in other locations have only physiological and not a significant structural contribution to the overall petiole mechanical behavior. The model was meshed using 2D 4-node isoparametric cuadrilateral elements and 3D 8-node isoparametric hexahedrical elements with a special interpolation of the shear component for the bending test. The calculations were made by means of finite element-based code called VULCAN (Celentano, 1999). RESULTS AND DISCUSSION The average elliptical shape obtained from the sampled petioles has a width of 36.43mm ± 2.56mm and a height of 56.80mm ± 7.11mm with a thickness of 2.50mm ±0.16mm. This shape includes the epidermis and the first part of the parenchyma tissue which is reinforced with sclerenchyma fibers. Two models of cross-section were designed and analyzed with the STM to define comparatively its structural efficiency. Fig. 2 shows the results of the computation of structural efficiency parameters proposed by STM in bending and torsion: ψA, ψI and ψJ. Closed elliptical shape allows the structural modeling of the open cross-section of R. mad petiole. The experimental calculations for the geometrical shape transformers ψA, ψI and ψJ lie over the modeled shapes curves. It means that the supposition of the closed section is valid to analyze the structural efficiency of R. mad petiole. The petiole cross-section behaves as less efficient compared to a perfect elliptical shape, at bending and torsion. Nevertheless, we have to consider that real shape is an open section probably responding to structural but also to physiological and morphological requirements. Analyzing real petioles cross-sections, it was found that the theoretical circumference of thickness of 1mm (shape marked with “b” in Figure 3) that would generate an elliptical ring with the same dimensions of those observed in the petioles (shape marked with “a” in Figure 3) would have an average radius of 22.8mm ± 2.1mm. Applying the Brazier model, the ovalized ellipse generated by local buckling process from this circular cross-section has the same dimensions of the original elliptical shape but rotated 90° (shape marked with “c” in Figure 3). If both elliptical sections, the original petiole cross-section shape and the ovalized elliptical shape, are compared with the theoretical circular shape that originate them, we see that the oval cross-sectional shape of the petiole acts as a structural security factor, with a second moment of inertia 44.8%± 9.7% higher than a circular cross-section with the same area. Besides, the ovalized elliptical shape generated from the theoretical circular cross-section modeled according to the Brazier model, has a second moment of inertia 27.8%±3.1% lower than circular section. If torsion constant of the sections are compared, the average loss of torsional stiffness of the elliptical shape with respect to the circular is just 15.8%±0.8%. Thus the use of elliptical shape with the major axis oriented with the vertical direction in cantilever beams subjected to bending and torsion Fig. 2. a: structural efficiency maps for bending stiffness; b: structural efficiency maps for torsion stiffness. Fig. 3. Dimensional analysis of the local buckling ovalization process modeling. Dimensions in mm. 18 loads seems to be an evolutional structural advance of the R. mad petioles. The petiole rotates when the wind comes in, in order to reduce its projected area. The use of less-efficient shape in torsion, but stiffer in bending than circular section, helps the species adapting to extremely windy conditions. FEM allows finding the normal and shear stress distribution over the cross-section. For this load the modeled petiole followed the behavior predicted for beam theory (Timoshenko and Goodier, 1969), where the maximum stresses are located on the points of the cross-section farther from the neutral axis. The shear stress distribution shows that modeled petiole exhibits a mechanical behavior which differs from the behavior predicted by elasticity theory. The values of stresses on the peripheral points over the minor axis of ellipse are very similar to the stresses on the peripheral points over the ellipse major axis, when the theory says that those values must differ proportionally to the ratio of the major and minor axis (Timoshenko and Goodier, 1969). For bending, the Young modulus variation shows that parenchyma is the major stiffness-related tissue. A change of four orders of magnitude in the parenchyma Young modulus value, gives a bending load four orders of magnitude higher. While the same variation in the Young modulus of the epidermis and sclerenchyma fibers doesn´t respond similarly. For torsion, a variation in four orders of magnitude in the parenchyma Young modulus gives a torsional moment increase of the same magnitude order. While the same variation in the Young modulus of the other two tissues, doesn´t implies a similar magnitude variation in moment. For each load type, the level of contribution of each tissue is different. This could mean that the high level of anisotropy of each tissue affects its mechanical behavior. The change in the stiffness of the entire system is higher with the change of the Young modulus of the parenchyma for both bending and torsion, but not in same proportion. The contribution of epidermis differs in each load type. Sclerenchyma fibers appear as a tissue useful in bending but less important in torsion. FEA of modeled petiole shows that the peripheral points of the cross-section bear similar shear stresses. It could mean that the aerenchyma tissue not only helps to stabilization of the section to resist the compression stresses due bending, but redistribute the magnitude of shear stresses to decrease the warp of the elliptical section when rotation by wind, stabilizing the section to allow high angular deformations. The almost radial configuration of the aerenchyma chambers walls (Fig. 1b) suggests a mechanical based orientation. The aerenchyma anatomy shows a grid with non-circular spaces that generate almost straight lines through which the loads may be distributed. For that reason aerenchyma can be assumed as inner reinforcing mechanism. Madagascar is an island located in the path of tropical cyclones and hurricanes with maximum wind velocity in normal weather conditions of 40km/h. This generates very complex and extreme environmental conditions to which R. mad seems to be properly adapted. A main conclusion is that the real contribution of each tissue to the mechanical resistance of the petiole depends more on form and organization than on individual mechanical properties. LITERATURE CITED Brazier LG. 1927. On the Flexure of Thin Cylindrical Shells and Other "Thin" Sections. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 116: 104-114. Celentano D. 1999. Vulcan. Martone PT, Boller M, Burgert I, Dumais J, Edwards J, Mach K, Rowe N, Rueggeberg M, Seidel R, Speck T. 2010. Mechanics without Muscle: Biomechanical Inspiration from the Plant World. Integrative and Comparative Biology 50: 888-907. Mattheck C. 1998. Design in nature: learning from tress. Springer, Berlin. Niklas KJ. 1992. Plant biomechanics. The University of Chicago Press, Chicago. Niklas KJ, Spatz HC. 2012. Plant physics. University Of Chicago Press Niklas KJ, Spatz HC, Vincent JFV. 2006. Plant biomechanics: an overview and prospectus. Am. J. Bot. 93: 1369-1378. Nychka J, Chen PY. 2012. Nature as Inspiration in Materials Science and Engineering. JOM Journal of the Minerals, Metals and Materials Society 64: 446-448. Pasini D, Burgess SC, Smith DJ. 2002. Performance indices for arbitrarily scaled rectangular cross-sections in bending stiffness design. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications 216: 101-113. Shimomura M. 2010. The New Trends in Next Generation Biomimetics Material Technology: Learning from Biodiversity. Science and Technology Trends. Quarterly Review: 53-75. Timoshenko S, Goodier JN. 1969. Theory of elasticity. McGraw-Hill. Vincent JFV. 2006. The Materials Revolution. Journal of Bionic Engineering 3: 217-234. Vincent, J.F.V., 2012. Structural Biomaterials. Princeton University Press. Vogel S. 1992. Twist-to-Bend Ratios and Cross-Sectional Shapes of Petioles and Stems. Journal of Experimental Botany 43: 1527-1532. Vogel S. 2000. Ancas y palancas: mecánica natural y mecánica humana. Tusquets editores, Barcelona. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 19 Modeling and analyzing the topology development of young Michelia chapensis Dong Li1,2, Mengzhen Kang3, Philippe de Reffye4 and Zhifu Xu1* 1 Institute of Digital Agriculture, Zhejiang Academy of Agricultural Sciences, Hangzhou, Zhejiang Province,310021, P.R. China 2 Zhejiang Tengtou Landscape CO.,LTD, Ningbo, Zhejiang Province,315100, P.R. China 3 LIAMA&NLPR, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China 4 Cirad-Amis, UMR AMAP, TA 40/01 Ave Agropolis, F-34398 Montpellier cedex 5, France *correspondence: zhifux868@163.com Key words: Michelia chapensis, plant development, topology structure, GreenLab model Highlights: Michelia chapensis is one of the most important landscape trees and it is important to study the plant topology structure. We measured the 2 years old michelia tree through one year, study the tree topology structure, well fit and simulate the tree with the new GreenLab version. INTRODUCTION Michelia chapensis is one of the most important landscape trees which are more and more broadly bred in the nursery garden in the South of China. When the plant topology structure is well studied and the dynamic plant structure model is used, the landscape designer can use the model to make the dynamic landscape design. It is important to study the plant topology structure. For many studies about the plant structural model or functional-structural model, the plant was studied with one year as the time step, such as LIGNUM (Perttunen et al., 1996, 1998) or GreenLab pine (Wang et al., 2012). It was enough to study the forestry trees, but it is not available to arrange the management strategies or landscape design for the garden trees. In this study, we measured the 2 years old michelia trees, study the tree topology structure, fit and simulate the tree with the new GreenLab version. MATERIAL AND METHODS Field experiment The field experiments were conducted in the nursery garden of Tengtou Landscape Company (29°42' N, 121°22' E) in Zhejiang province. The plant were sown in spring of 2010 by seeds and transplanted to the nursery garden in autumn. Plant grew at a spacing of 0.5 × 0.5 m. The branches which were below the 8th phytomer were pruned in the beginning of 2011. Fertilizer inputs and irrigation were conducted so as to avoid any mineral and water limitations to plant growth. From 21 April,2011 to 13 March,almost every month, 20 plants were sampled and counted the phytomer number of the main stem. And at the same time 12 plants were sampled and the topology structure were recorded, as well as the branch level and position, the phytomer number of the branches, the blade living time and expansion time. Brief description of GREENLAB model Detailed descriptions of the model were presented in some previous studies (Yan et al., 2004; Guo et al., 2006) and we just recall its main principles and the new features. In the model, the plant architecture is described hierarchically according to their physiological age (PA), as presented in a review paper by Barthélémy and Caraglio (2007). The time step, called growth cycle (GC), is the time elapsed between emergences of two successive phytomers expressed in thermal time. GL2 is a stochastic functional-structural model, where the plant topology development depends on probabilities related to bud functioning (e.g., branching probabilities, buds survival probabilities, rhythm ratio between different PAs). In the new version GL5, the topology and biomass production were fitted separately. We fitted the topology first and got the topology development for the plant. Then the biomass will be fitted for the total biomass and the allometry based on common pool and basic GreenLab principle. In this study, we just considered the following probabilities , such as the growth probabilities of all the PAs, the delay growth cycle of the PA2 and PA3, the rhythm ratio between different Pas, the delay and growth in the winter, etc. The branch death was not considered in this study. All the probabilities were 20 described with the binomial distribution and fitted and simulated in Matlab software produced by the Mathworks Inc. RESULTS Descriptions on michelia structure There was almost 1 branch, which were the 1st level branch (PA2), at each phytomer rank along the main stem (PA1). To these branches, there were about 4 growth cycles delay. The growth rate of PA2 is almost the same with PA1, sepecially for the new branches. At the beginning of the year 2011, there were about 14-19 phytomers in the michelia tree. Through the main stem there was no branch or there are little branches at the position from 15-23, maybecause the bud were dead in the winter. There were the 2nd level branches (PA3) on the 1st level branch (PA2), but the PA3 didn’t come out until the phytomer of PA2 is more than 6. And also there was 2 or 3 growth cycle delay in the PA3 compared to PA2. The plant growth fast in the summer and early autumn, there was one new phytomer about three to five days from April to Octomer in 2011 (Fig.2a), but keep almost constantly from Octomer, 2011 to March, 2012. Almost all the plants grew in the same rate and the variability is small for the main stem of all the sampled trees. Fig. 2. Total phytomer number of the main stem and branches. Fig. 2a represents the phytomer number of the main stem (PA1) changing with time, Fig. 2b denotes the phytomer number of all the first level branches (PA2) varying with time and Fig. 2c represents the phytomer number of the total PA3s in one tree. To PA2 and PA3, the total phytomer number decreased because some of the branches died in the autumn and winter. Also the variability is larger than PA1. Fitting and simulating results The phytomer number of different PAs was fitted separately and well simulated. The rhythm ratio was almost one for all PAs, that means the main stem grew one growth unit, the children branch could grew a growth unit, too. But the probability of growth for PA1 was larger than PA2 and probability of PA3 was the smallest. At the same time, the probability of branch death for PA1 was the smallest (nearly to zero) and probability of PA3 was biggest (data were not shown in this paper). The delay of year 2011 and the Inhibition control could also be modeled (Fig.3). DISCUSSION Trees can grow for many years, so many researchers study the tree growth using 1 year as the time step. Some information of the tree growth will be lost (Sievänen et al, 2000) and most of the information is very important especially for the young garden tree which grew in the nursery garden. In this study we observed, measured and simulated the young Michelia grown in one year, studied the growth rate of the main stem and 0 100 200 300 400 500 Ph yt om er n um be r 0 10 20 30 40 50 60 Day after Jan.1, 2011 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 200 400 600 800 PA1 PA2 PA3 a b c 21 branches. The gardener can decide their irrigating, fertilizing strategies and also they can deciede when to prune and transplant the plant through the model. We also found when the plants were pruned, the new branches grew in a very similar way as the young trees. And the model was also important to the big trees. So we can also use the model to show the influence of pruning and landscape design. In the future, the climate factors, the biomass production and allocation will be considered in this model, which is then more useful in the management strategies. ACKNOWLEDGEMENT The research has been supported by Zhejiang Tengtou Landscape CO.,LTD. The authors are grateful to Mr. Feng Wang, Miss Xiujuan Wang, Ms Hong Guo and Miss Yue Li for their kind help on the experiment measurements. REFERENCES Cournède PH, Mathieu A, Houllier F, Barthelemy D, de Reffye P. 2008. Computing Competition for Light in the GREENLAB Model of Plant Growth: A Contribution to the Study of the Effects of Density on Resource Acquisition and Architectural Development. Annals of Botany 101: 1207-1219. Guo Y, Ma YT, Zhan ZG, Li BG, Dingkuhn M, Luquet D, de Reffye P. 2006. Parameter Optimization and Field Validation of the Functional-Structural Model GREENLAB for Maize. Annals of Botany 97: 217-230. Kang MZ, Cournède PH, de Reffye P, Auclair D, Hu BG. 2008. Analytical study of a stochastic plant growth model: Application to the GreenLab model. Mathematics and Computers in Simulation 78: 57-75. Perttunen J, Sievänen R, Nikinmaa E, Salminen H, Saarenmaa H, Väkevä J. 1996. LIGNUM: a tree model based on simple structural units. Annals of botany 77: 87-98. Perttunen J, Sievänen R, Nikinmaa E. 1998. LIGNUM: a model combining the structure and the functioning of trees. Ecological Modelling 108: 189-198. Sievänen R, Nikinmaa E, Nygren P, Ozier-Lafontaine H, Perttunen J, Hakula H. 2000. Components of functional- structural tree models. Annals of forest science 57: 399-412. Wang F, Letort V, Lu Q, Bai X, Guo Y, de Reffye P, Li B. 2012. A Functional and Structural Mongolian Scots Pine (Pinus sylvestris var. mongolica) Model Integrating Architecture, Biomass and Effects of Precipitation. PloS one, 7: e43531. Yan HP, Kang MZ, de Reffye P, Dingkuhn M. 2004. A Dynamic, Architectural Plant Model Simulating Resource- dependent Growth. Annals of Botany 93: 591-602. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 22 Automated Parameter Estimation for a Plant Architecture Model Florian Schöler*, Jenny Balfer and Volker Steinhage Department of Computer Science III, University of Bonn, Römerstraße 164, 53117 Bonn, Germany *correspondence: schoele@iai.uni-bonn.de Highlights: We present an automated procedure for the creation of architectural plant models. It uses an algorithm for the computation of skeletons from sensor data. The skeletons are annotated with semantic labels for the extraction of architectural parameters. The values of several samples are averaged and serve as the basis for the model, which is implemented as a Relational Growth Grammar. Keywords: Architectural Modeling, Skeletonization, Relational Growth Grammar INTRODUCTION When creating a model for the architecture of a plant, questions arise, like what parameters describe the architecture, how they are captured, or how it is actually modeled. In one way or another many of those questions were already answered in previous works (Godin, 2000; Watanabe et al., 2005; Barthélémy and Caraglio, 2007; Dornbusch et al., 2007; Fourcaud et al., 2008). Almost always they contain a substantial amount of manual labor for determining parameter values, for example, for the length or the frequency of occurrence of a plant component. In this paper we show, using the example of berryless grape clusters of the grapevine plant (Vitis vinifera L.), how a large part of the process can be automated. To this end we make use of an algorithm that takes sensor data of the plant as input and computes a skeleton, which is a set of connected line segments that represents the structure of the original object. That skeleton is annotated with semantic labels like rachis or pedicel. Then, parameter values like lengths or frequency of occurrence of components are extracted from that skeleton. The values of several samples are averaged and serve as the basis for the actual model. We construct our architectural model as a Relational Growth Grammar (RGG) (Kurth et al. 2005). Figure 1 gives an overview of the process. In general, this procedure is also applicable to other plants or plant parts. To our best knowledge this is the first attempt of an automated parameter value extraction for the architectural plant modeling. Of course, the presented procedure still relies on a careful selection of plant samples and architectural parameters, but the process of extracting and averaging their values is greatly simplified. Figure 1: Overview of the procedure. From left to right: From every point cloud a skeleton is computed. The colors in the skeleton refer to the different semantic annotations (black: rachis, blue: lateral branch, green: pedicel). Based on the skeleton, values of architectural parameters are extracted and averaged. This is the basis for the RGG-model. See section MODEL CONSTRUCTION for an example of how the parameters are integrated into the model. DATA AND PARAMETERS For computing the skeletons we use the algorithm presented in (Balfer, 2012; Balfer et al., 2013). This algorithm not only computes the bare architecture but also adds semantic labels to the different parts: rachis, 23 lateral branch, and pedicel. We have gathered 20 exemplars of grape clusters of the cultivar Riesling, an example of a very popular cultivar that usually produces very compact grape clusters. The clusters were cut off the trunks of ten grapevine plants and we always took the lowest two clusters. The plants were grown in the field, not in lab- conditions. According to the extended BBCH-scale from Lorenz et al. (1994) the clusters were taken at stage BBCH 65 ''full flowering: 50% of flowerhoods fallen.'' (BBCH is short for Biological Institute of Agriculture and Forestry, Federal Office for Plant Varieties and Chemical Industry – in German: Biologische Bundesanstalt für Land- und Forstwirtschaft, Bundessortenamt und Chemische Industrie). For each of the clusters we cut off the flowers (but not the pedicels), counted the flowers and scanned the clusters with a Perceptron ScanWorks V5 laser rangefinder, resulting in 20 dense point clouds with a minimum point-to- point resolution of 12 μm. These point clouds and their ''starting points'' were used as input to the skeletonization algorithm. The starting point is where the cluster was formerly connected to the plant. The resulting semantic skeletons each produced one vector of parameter values. We then had to combine the single vectors into one vector representing the twenty clusters. For parameters with continuous values like the length of the rachis we could just compute the average and the standard deviation assuming a normal distribution. For other, non-continuous, parameters we had to do different calculations. For example, for the number of pedicels that branch from the same node we computed a relative histogram of the gathered values. In total we extracted 89 different parameters and, for now, assumed them to be independent. Some of the parameters are taken from the descriptor list of International Plant Genetic Resources Institute (IPGRI 1997), and the second edition of the descriptor list of the International Organization for Vine and Wine (OIV 2009). For example, for the number of rachises we found occurrences of 1, 2, 3, 4, 5 and corresponding occurrence probabilities of 0.05, 0.85, 0.05, 0.0, 0.05 respectively. This means that in 17 of the 20 cases we found exactly two rachises; one main rachis and one secondary rachis. MODEL CONSTRUCTION The thus gathered and averaged parameter values are the basis for the model construction. We demonstrate this by means of an example. We have several values concerning the main rachis of the grape cluster: Their lengths, number of lateral branches per node, number of secondary rachises, internode lengths, number of nodes, etc. These pieces of information are concentrated in a new module in our RGG, called MainRachis. For the main rachis module also a specific grammar rule exists. This rule demands that the first branching point on the main rachis can lead to a lateral branch or a secondary rachis. After that point only lateral branches or pedicels may emerge from nodes. In addition we know, for example, how long the rachis can be and how many nodes in what distances can be expected. Thereby we create only such rachises that are topologically and geometrically realistic, according to our model, which itself is based on real grape clusters. Likewise we create RGG-modules for secondary rachises, lateral branches and pedicels. Furthermore, this parameterized model allows setting the parameters to a different, consistent set of values to produce grape clusters of other cultivars or in other development stages. DISCUSSION AND CONCLUSION See Figure 2 for an overview of six example runs of the grape cluster model. As can be seen, lateral branches get shorter from base to tip, internode lengths vary, and sometimes there is a secondary rachis. As was shown in Steinhage et al. (2012) such a model can be used not only for virtualization or visualization purposes. Utilized for a reconstruction algorithm it helps vastly decreasing the space of possible reconstruction hypotheses. In this respect the term ‘possible’ is described in terms of the model since only such hypotheses are allowed that can be constructed by the model. In conclusion we have shown (a) how the extraction of architectural parameter values of plants can be automated by use of a skeletonization algorithm, (b) how those values can be combined to gain averages for a specific cultivar, and (c) how such a model can be used for the purpose of reconstruction from sensor data. There are several possible paths to follow from here. One could make the skeletonization algorithm more adaptable to other plants, gather more parameter values and investigate possible dependencies, and optimize the algorithm for shorter runtimes. 24 Figure 2: Six example runs of the RGG-model. For each run we show the generated grape cluster with and without flowers. One can see typical properties of grapevine grape clusters. For example, the lateral branches get shorter from base to tip, there can be secondary rachises, and from lateral branches pedicels emerge. ACKNOWLEDGEMENTS This work was supported by the Federal Ministry of Education and Research (BMBF). We thank all partners of sub-project D2 of CROP.SENSe.net for valuable discussions. Especially, we thank Reinhard Töpfer and Katja Herzog from the Julius-Kühn-Institute, Siebeldingen, Germany for providing the plant samples. We thank Heiner Kuhlmann and Stefan Paulus from the Department of Geodesy of the University of Bonn, Germany for generating the laser rangefinder measurements. LITERATURE CITED Balfer J. 2012. 3D Skeletonization for the Analysis of Grapevine Structure. Master’s Thesis, University of Bonn, Germany. Balfer J, Schöler F, Steinhage V. 2013. Semantic Skeletonization for Structural Plant Analysis. Submitted to International Conference on Functional-Structural Plant Models. Barthélémy D, Caraglio Y. 2007. Plant Architecture: A Dynamic, Multilevel and Comprehensive Approach to Plant Form, Structure and Ontogeny. Annals of Botany 99(3): 375–407. Dornbusch T, Wernecke P, Diepenbrock W. 2007. A Method to Extract Morphological Traits of Plant Organs from 3D Point Clouds as a Database for an Architectural Plant Model. Ecological Modelling 200(1-2): 119–129. Fourcaud T, Zhang X., Stokes A, Lambers H, Körner C. 2008. Plant growth modelling and applications: the increasing importance of plant architecture in growth models. Annals of Botany 101(8): 1053–1063. Godin C. 2000. Representing and Encoding Plant Architecture: A Review. Annals of Forest Science 57(5–6): 413–438. IPGRI, UPOV, and OIV. 1997. Descriptors for Grapevine (Vitis ssp.). International Union for the Protection of New Varieties of Plants, Geneva, Switzerland/Office Internationale de la Vigne et du Vin, Paris, France/International Plant Genetic Resources Institute, Rome, Italy. Kurth W, Kniemeyer O, Buck-Sorlin G. 2005. Relational Growth Grammars – A Graph Rewriting Approach to Dynamical Systems with a Dynamical Structure. J.-P. Banâtre, P. Fradet, J.-L. Giavitto, O. Michel (eds.): UPP 2004, LNCS 3566, pp. 56 – 72, Springer. Lorenz DH, Eichhorn KW, Bleiholder H, Klose R, Meier U, Weber E. 1994. Phänologische Entwicklungsstadien der Weinrebe (Vitis vinifera L. ssp. Vinifera). – Codierung und Beschreibung nach der erweiterten BBCH-Skala – Phenological growth stages of the grapevine (Vitis vinifery L. Ssp. Vinifera). Vitic. Enol. Sci. 49(2):66-70 Organisation Internationale de la Vigne et du Vin (OIV). 2009. 2nd Edition of the OIV Descriptor List for Grape Varieties and Vitis Species. Organisation Intergouvernementale crée par l’Accord International du 3 Avril 2001. Steinhage V, Schöler F, Balfer J. 2012. A Model-Based Approach to High Performance Phenotyping. Proceedings of the International Conference on Informatics for Environmental Protection, 303-310. Watanabe T, Hanan JS, Room PM, Hasegawa T, Nakagawa H, Takahashi W. 2005., Rice Morphogenesis and Plant Architecture: Measurement, Specification and the Reconstruction of Structural Development by 3D Architectural Modelling. Annals of Botany 95(7): 1131–1143. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 25 Modeling the blade shape of landscape trees Fuping Lin1, Xiujuan Wang2, Haoyu Wang2, Xueqiang Shi3, Dong Li1,4* 1 Zhejiang Tengtou Landscape Co., Ltd, Ningbo, Zhejiang Province,315100, P.R. China,2 LIAMA&NLPR, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China, 3 Northwest A & F University, Yangling, Shanxi Province, 712100, China, 4 Institute of Digital Agriculture, Zhejiang Academy of Agricultural Sciences, Hangzhou, Zhejiang Province,310021, P.R. China *correspondence: lidong808@163.com Keywords: garden tree, blade modeling, 3D digitizing Blade is very important organ which is not only for the physiology process but for the appearance structure of the plants, especially landscape plants. So it is necessary to make a library of blades for the plant 3D visualization. The 3D digitizing instruments were used in some researches to build the blade model (Loch, et al., 2005). This blade model was made up of a lot of facets and it is time-consuming to visualize the plants using this model, espe- cially for visualization of the dynamic growth of trees. In this study, a 3D blade library was built for more than twenty kinds of landscape trees, which were measured with 3D digitizing method. The data of these blades were transformed into horizontal coordinates and the leaf shapes of these plants were modeled by simple function mod- els. Blades from 22 kinds of plants were selected in the nursery garden of Tengtou Company (29°42' N, 121°22' E) in Zhejiang province. All the blades were either fusiform shape blade or lanceolate blade. 5 blades for each kind of tree were sampled and measured with a 3D digitizer (FastSCAN Scorpion, Polhemus, USA). The 3D blade models were built. A mouse interaction program was developed to obtain the coordinate data of blade margins by reading the scanned file, and then the coordinates were transformed into 2D data. These data was normalized to obtain the blade shape. Furthermore, the data of blade margins were computed with a quadratic function c x x 2 ++= bay , which is often used to describe blade shape (Stewart and Dwyer, 1999), as well as the new composite func- tion ) sin( exy π= . The parameters a, b, c and e of the two model were estimated with the Least Square methods and the similar and simple blade model was built. All the sampled blades were measured and the blade models were built using the 3D digitizer (pictures not shown). The normalized blade shape was simulated using both quadratic function and the composite function. The parameters for 10 kinds of blades were given in Table1 (Others not shown here). For most of the blades, the results obtained with the composite function were better than the quadratic function. Moreover, only 1 parameter was used for the composite function. It was simple and useful for modeling the tree growth. By using these parameters, as well as the length and the largest width of blade, the simulated blade can be used to build the plant model. The parameters for the blade shape were similar for some different kinds of plant. Thus, we can conclude that it is not enough to identify the tree only by using the parameters of leaf shape. Table1. The parameters for the blade shape fitted by the two functions Plant Names a b c e Magnolia denudata -4.048 3.987 0.017 0.994 Malus halliana -3.748 3.482 0.216 0.723 Elaeocarpus decipiens -4.105 4.143 -0.048 1.045 Michelia chapensis -4.063 3.959 0.068 0.904 Cinnamomum camphora -3.752 3.441 0.127 0.749 Myrica rubra -3.523 3.916 -0.191 1.509 Prunus serrulata -3.761 3.353 0.215 0.681 Koelreuteria paniculata -3.846 3.478 0.178 0.729 Zelkova serrata -3.526 3.048 0.252 0.626 Sapindus mukurossi -3.814 3.574 0.148 0.765 Note: a,b, c were the parameters for the quadratic function model and e for the composite function REFERENCES Loch B, Belward JA, Hanan JS. 2005. Application of surface fitting techniques for the representation of leaf surfaces. MODSIM05: International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making. Melbourne, Australia, Modeling and Simulation Society of Australia and New Zealand Inc. 1272-1278. Stewart D, Dwyer L. 1999. Mathematical characterization of leaf shape and area of maize hybrids. Crop Science 39: 422-427. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 26 Biomass-based rapeseed (Brassica napus L.) leaf geometric parameter model Hongxin Cao 1,,Wenyu Zhang 1, Weixing Zhang 1, Yan Liu 1, Yongxia Liu 1, Jim Hanan2, Yuli Chen1, Yanbin Yue,3, Zhiyou Zhang4, Daokuo Ge1 1 Institute of Agricultural Economics and Information ; Engineering Research Center for Digital Agriculture, Jiangsu Academy of Agricultural Sciences, Nanjing 210014, Jiangsu Province, P.R. China, 2The University of Queensland, Centre for Biological Information Technology, Brisbane, Queensland 4068, Australia, 3Institute of Agricultural Sci-tech Information, Guizhou Academy of Agricultural Sciences, Guiyang 550000,Guizhou, P.R. China, 4Institute of Agricultural Sci-tech Information, Hunan Academy of Agricultural Sciences, Changsha 410000, Hunan, P.R. China Highlights: A biomass-based model of leaf geometric parameters of rapeseed was developed, and the effects of cultivars and environmental conditions on rapeseed leaf morphogenesis were considered through the connection to rapeseed growth model via biomass. Keywords: biomass, leaf geometric parameter, model, rapeseed (Brassica napus L.). To quantify the relationships between rapeseed leaf geometric parameters and the corresponding leaf biomass, this paper presents a biomass-based model of leaf geometric parameters of rapeseed (Brassica napus L.) in the seedling stage, including Biomass-base leaf blade length model LLj(i) = CPLBj(i) · DWSP(i)· RLWj(i), blade length-based leaf blade width model , leaf sheath length model , leaf blade bowstring length model , and leaf blade angle models TAj(i) = CPLBj(i) · DWSP(i)·RTWj(i), BAj(i)= CPLBj(i) · DWSP(i)· RBWj(i) , designed to explain effects of genotypes and environmental conditions on rapeseed leaf morphogenesis at the individual leaf level. Various model variables, including biomass of blade, and blade length, were parameterized for rapeseed based on data derived from an outdoor experiment with rapeseed cv. Ningyou18, Ningyou16, and Ningza19. The leaf dimensions of rapeseed are modelled taking corresponding leaf biomass as an independent variable. Various variables in rapeseed showed marked consistency in observation and simulation, suggesting possibilities for a general rapeseed leaf geometric parameter model in the seedling stage. Our descriptive model is suitable for our objective. However, they can set the stage for connection to physiological model via biomass and development of Functional Structural Rapeseed Models (FSRM), and start with the localized production and partitioning of assimilates as affected by abiotic growth factors. The finding of biomass-based rapeseed leaf geometric parameter models also can be used in morphological models of internode, ramification, anthotaxy, and root of the other stages in rapeseed life. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 27 Optimize Tree Shape: Targeting for Best Light Interception Jing Hua and Mengzhen Kang State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, China *correspondence: mengzhen.kang@ia.ac.cn Highlights: It is assumed that plants have a certain kind of fitness so they can optimize their behaviors to maintain a specific target. Optimization algorithm is used to find tree shape that can maximize the light interception. The shape we got is reasonable and looks like a real tree, which proves partly the fitness of plants. Keywords: Optimization, Tree Shape, GreenLab model, Fitness, Light interception INTRODUCTION It is observed that plants have some adaptively variable behaviors during their growth (Trewavas 2003), such as changing branch numbers and shape to intercept more light, transmitting biomass internally to guarantee growth of fruits, and reducing leaf area to preserve water in the arid environment, etc. From these phenomena, it is reasonable for us to assume that plants have a certain kind of fitness so they can change their behaviors in order to maintain a specific target. Trying to simulate and analyze this kind of fitness with virtual plants is an interesting and challenging work. Functional-structural plant models (FSPMs), originated by combining Process-Based Models and plant structure, can be used to simulate plants fitness. In general, the simulation process in FSPM begins from a parametric setting, computes plant development (organ formation) and plant growth (biomass pruduction and partitioning) cycle by cycle, and finally gets some results such as organ biomass, organ number, 3D shape, etc. If this simulation process is regarded as a function whose inputs are model parameters and outputs are simulation results, it is possible for us to use some optimization algorithms to find parameters that can maximize or minimize some outputs. It is a feasible way to simulate the fitness of plants. As light environment plays a key role for plant growth and development, light interception is a key topic in plant growth modeling. Tree shape, which is mainly decided by phyllotaxy, branching angle and bending, will greatly affect the light interception of a tree. Given the topological connections and organ sizes of a tree, there is an optimized tree shape that can maximize the light interception. In this work, we aimed to use some heuristic algorithms to find this optimized shape. Although it is just a simulation and needs further calibration, the result is interesting because the tree shape we got looks very similar to the real tree shape. METHODS We used GreenLab model to simulate growth of the tree. Detailed computation process can be referred to Yan HP et al. (2004) and Kang MZ et al. (2008). Once the simulation ended, we got topological connection of branches and size of all organs, based on which the 3D shape can be constructed. Our object is to find a tree shape that can maximize the light interception of this tree. Next we will describe briefly model parameters controlling tree shape, light distribution algorithm and optimization methods. 1. Parameters controlling tree shape There are three important aspects that can affect tree shape: phyllotaxy, branching and bending. Firstly, phyllotaxy is the arrangement of leaves on a plant stem. As branches develop from axillary buds, phyllotaxy also decides the direction of branches. GreenLab model uses a parameter 𝜙 (ranging from 0 to 360 degree), which is defined as rotate angle between two adjacent internodes, to describe phyllotaxy, as shown in Fig.1. Secondly, branching angle is the angle between a branch and its mother stem. As it is assumed that branching angle increases along the main stem from top to bottom, GreenLab model uses a parameter 𝜃 (ranging from 0 to 180 degree) to describe the maximum branching angle, i.e., angle between the lowest branch and main stem, as shown in Fig.2. Other branching angles are calculated using linear interpolation. Finally, branches are seldom straight completely. They bend downward according to the gravity and upward according to the phototropism. As a result, branches are represented as many kinds of shapes. We use a method which originated from mechanical calculation to compute the branch bending. After simplification, 28 there are two parameters 𝐾 (larger than zero) and 𝑝 (ranging from 0.0 to 1.0) that control respectively the degree of bending and the position where the branch begins to fold upward. The effect of these two parameters is illustrated in Fig.3. Fig. 1. Phyllotaxy angle 𝜙 , which is defined as rotate angle between two adjacent internodes Fig. 2. Maximum branch angle 𝜃 Fig.3. The effect of two parameters controlling the branch bending. Parameter values from left to right are: (1) 𝐾 = 0.02,𝑝 = 1.0, (2) 𝐾 = 0.05,𝑝 = 1.0 and (3) 𝐾 = 0.05,𝑝 = 0.4 2. Light interception computation In plant growth modeling, light interception is computed either by an empirical Beer-Law approach using leaf area index, or by summing up the light interception from individual organs. Since our object is to optimize the tree shape, we choose the latter method because it takes into account the detailed description of plant structure. There are several works concerning the light distribution in crop canopy (Wang XP et al. 2006, Zheng BY et al. 2011). Unfortunately, these methods can be hardly used in tree canopy because firstly there are more organs in trees than in a crop and secondly the ratio of single leaf size to the whole tree size is too small. A simple light model is implemented in our system. Since leaf is represented as a mesh object in computer memory, several rays were emitted evenly into sky sphere from each point of the leaf mesh. For each ray, we counted leaves that this ray encounters (assuming 𝑛). The visibility of this ray is calculated as 𝑡𝑛, where 𝑡 is the light transmittance of leaf. Finally, the visibility of a leaf is estimated using the mean value of visibility of all rays emitted from this leaf mesh. We use the sum of visiblity of all leaves (denoted by 𝑉) to measure the light interception of the tree. 3. Optimization algorithm Given branch connections and sizes of all organs, the visibility 𝑉 can be written as a function of four parameters described in part 1, 𝑉 = 𝑓(𝜙,𝜃,𝐾,𝑝) . It is a typical optimization problem to find a set of parameters to maximize 𝑉. As the function is non-derivative or even discontinuous, heuristic algorithms are more suitable for this problem. We used PSO (Particle Swarm Optimization) algorithm (Shi et al. 1998). As 𝑉 has different sensitivities to different parameters, we used three steps to optimize. In each step, we fixed some parameters and optimize others. The order of optimized parameters is: firstly phyllotaxy, secondly branching angle and finally bending parameters. 29 RESULTS AND DISCUSSION The simulation result is illustrated in Fig.4. All leaves are removed for showing more clearly the structure of the tree. We chose a relatively simple tree whose structure is shown in the left. The initial parameter values are: 𝜙 = 180,𝜃 = 25,𝐾 = 0.0,𝑝 = 1.0, which means that all branches are straight and in a vertical plane, and all branching angle are the same. After optimization, we got the tree shape in the right, whose parameter values are 𝜙 = 48.52,𝜃 = 102,𝐾 = 0.0555,𝑝 = 0.21. It is very intersting that the shape looks like a real tree. This result shows that it is possible to use optimization algorithm to get reasonable tree shape, and then proves partly the assumption that plants have a certain kind of fitness so they can optimize their behavior in a specific environment. Fig. 4. Simulation result. Left is the topological structure of a tree and right is the optimized tree shape we got. We choose a simple tree in this work just because of the computing efficiency, as both calculation of light distribution and the optimization algorithm are very time-consuming. There are no substantial difficulties to generalize this method to more complex trees because the computing time is proportional to the number of organs. What we need are just more powerful computers. This method can also be used in crop fields to optimize phyllotaxy, leaf angle, and so on. It will be very useful if we could find the good crop shape in some conditions such as given planting density. It is challenging but deserves hard working. LITERATURE CITED Kang MZ, Cournede PH, de Reffye P, Auclair D, Hu BG. 2008. Analytical study of a stochastic plant growth model: Application to the GreenLab model. Mathematics and Computers in Simulation 78:57-75.. Shi Y, Eberhart RC. 1998. A modified particle swarm optimizer. Proceedings of IEEE International Conference on Evolutionary Computation 69-73. Trewavas A. 2003. Aspects of Plant Intelligence. Annals of Botany 92:1-20. Wang XP, Guo Y, Li BG, Wang XY, Ma YT. 2006. Evaluating a three dimensional model of diffuse photosynthetically active radiation in maize canopies. International Journal of Biometeoroloy 50:349-357. Yan HP, Kang MZ, de Reffye P, Dingkuhn M. 2004. A dynamic, architectural plant model simulating resource- dependent growth. Annals of Botany 93:591-602. Zheng BY, Ma YT, Li BG, Guo Y, Deng Q. 2011. Assessment of the influence of global dimming on the photosynthetic production of rice based on three-dimensional modeling. Science China Earth Sciences 54:290-297. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 30 A novel plant cell division algorithm based on ellipse/ellipsoid fitting Metadel K. Abera, Pieter Verboven, Thijs Defraeye, Maarten L.A.T.M. Hertog, Bart M. Nicolai Flanders Centre of Postharvest Technology / BIOSYST-MeBios, University of Leuven, Willem de Croylaan 42, B-3001, Leuven, Belgium *correspondence: metadel.abera@biw.kuleuven.be Highlights: A novel plant cell division algorithm is presented for both 2D and 3D representation of cells. The position and orientation of the dividing cell wall were determined by fitting ellipse/ellipsoid to the cell vertices. The new wall is then inserted along the minor diameter of the fitted ellipse/ellipsoid perpendicular to the major diameter of the fitted ellipse/ellipsoid. Keywords: cell division, biomechanics, turgor pressure, thin-walled structure, Hooke's law, Newton's law, ellipse fitting, ellipsoid fitting INTRODUCTION Cellular pattern studies and simulation of higher level processes such as phyllotaxis and vascular patterning calls for models of the division and arrangement of cells into tissues (Smith et al., 2006). Many biophysiological processes in plant organs, such as gas transport, are strong functions of the microstructural geometry of the tissue (Ho et al., 2011) which is in turn dependent on the cell division and arrangement of cells. In contrast to animal cells, plant cell walls are relatively rigid. The walls of the neighbouring cells are joined by the middle lamellas, which are composed mainly of pectins. Moreover, the walls are traversed by plasmodesmata (thin, intercellular, plasmic channels) (Romberger et al., 1993). Unless the cell is in the division phase, or pores are generated by separation of cells or death of cells, the contiguous walls of the neighbouring cells do not slide or slip with respect to each other, thus the cell topology is maintained. These aspects should be taken into account when considering cell division and expansive growth. Cell division rules that were proposed by Hofmeister (1863), Sachs (1878) and Errera (1886) are still the most prominent works which are the basis for modern thoughts. According to Hofmeister, the dividing wall is inserted at right angle to the longitudinal axis of the mother cell; while Sachs suggested that the new wall intersects the side walls at right angles. Errera’s rule states that the dividing wall should be the shortest wall that partitions the mother cell into two equal daughter cells (reviewed by Prusinkiewicz & Runions, 2012). Besson and Dumais (2011) have developed a rule for symmetric division of plant cells based on probabilistic selection of division planes. According to their work, the Errera’s rule of cell division failed to account for the variability observed in symmetric cell divisions, in particular, the fact that cells of identical shape do not necessarily adopt the same division plane. The variability in symmetric cell division is accounted for by introducing the concept of local minima rather than global minima. The division planes are then selected based on a probability which scales inversely to the difference between a candidate plane and a plane which is the global minima. In our model we have achieved this using the random selection of the minor diameter when the fitted ellipse/ellipsoid is a circle/sphere which will result in infinitely many possible candidates for the dividing wall. Robinson et al. (2011) introduced an asymmetric cell division algorithm in which the division wall is chosen as the shortest wall which passes through the nucleus of the mother cell. In their model, the asymmetric cell division is achieved by displacing the nucleus of the mother cell from the centroid of the cell in a random direction. In our model we have achieved this by randomly moving the position of dividing wall along the major diameter of the fitted ellipse/ellipsoid. The dynamic pattern of cell arrangement is a function of not only the position and orientation of division walls but also the timing of cell division and growth of the tissue. The early work of Korn (1969) reintroduced by Merks and Glazier (2005) represents cells as a set of points, and growth is achieved by the addition of new points to a cell. Cell division is carried out according to Errera’s rule. Cell mechanics based models for 2D cell growth were developed by different researchers (Dupuy et al., 2010; Sahilin and Jönson, 2010 & Abera et al., 2012a ‘in press’). The 2D cell growth model developed by Abera et al. (2012) has recently been extended to a 3D cell growth model (Abera et al. 2012b). 31 Based on the literatures detailed above, there is no single generic model. Some models are intended either for symmetric or asymmetric cell division. Some of them are focused merely on the division rules, without paying attention to the timing of cell division and the actual expansive growth and others are not accounting for cell mechanics when modeling cell growth. To our knowledge, 3D plant cell division models are scarce. Knowledge on the 3D arrangement of plant cells and their growth in tissues is however of high importance to our understanding of biophysiological processes. The objective of this paper is to develop both 2D and 3D plant cell division algorithms that are generic and based on cell growth mechanics. METHODOLOGY In our model, the cell is considered as a closed thin walled structure, maintained in tension by turgor pressure. The cell walls of adjacent cells are modeled as parallel, linear elastic elements which obey Hooke's law. Cell expansion then results from turgor pressure acting on the yielding cell wall material. To find the sequence of positions of each vertex and thus the shape of the tissue with time, a system of differential equations for the positions and velocities of each vertex is established and solved using a Matlab ordinary differential equation solver (For details, see Abera et al., 2012a ‘in press’). The cell division algorithm calculates the area/volume of the cells and checks if there are cells which exceed a predefined cell area/volume. The readiness of the cell to divide was determined based on cell size which is a function of time. A dividing wall is inserted whenever a cell exceeds its predefined size. In order to determine the position and orientation of the new wall that divides the cell, an ellipse/ellipsoid fitting algorithm is implemented, based on the cell vertices. The new wall is then inserted along the shortest diameter of the fitted ellipse/ellipsoid perpendicular to the longest diameter of the fitted ellipse/ellipsoid (see Fig. 1). The cell vertices, walls and edges are then updated and the cell expansion resumes. By moving the position of the dividing wall in either direction along the major axis based on a random factor chosen between -1 and 1 a switch between symmetric and asymmetric division is possible. Fig. 1. Demonstration of the cell division algorithm: a) 2D cell division where blue lines are boundaries of the mother cell; green line is the fitted ellipse and red line is the new wall dividing the cell; b) 3D cell division where i) is the mother cell; ii) is the fitted ellipsoid (the red plane shows the orientation and position of the new wall); iii) shows the two daughter cells with distinct colors. RESULTS AND DISCUSSION We have developed a generic algorithm, based on cell wall mechanics, that is capable of producing variety of cell and tissue types. The algorithm can produce the variability observed in symmetric cell division without introducing the concept of local minima but sticking to the Errera’s rule of global minima (Besson and Dumais, 2011). In our model, an ellipse/ellipsoid is fitted to the vertices of the mother cell. The position and orientation of the minor diameter of the ellipse/ellipsoid is used as the position and orientation of the dividing wall. If the fitted ellipse/ellipsoid is a circle/sphere, we have infinitely many possible orientations for the candidate dividing wall. The random selection of one of them made it possible to produce the variability observed in symmetric cell division (see Fig. 2). Fig. 2. Symmetric 2D cell division (a) and symmetric 3D cell division (b). 32 The asymmetric cell division (Robinson et al., 2011) is achieved by random displacement of the dividing wall along the major diameter of the fitted ellipse/ellipsoid. By making the mechanical properties and the maximum resting length of the walls/edges global direction dependent, the model allows both isotropic and anisotropic cell growth which leads to different tissue types. The cell division algorithms can be coupled to the 2D expansive plant cell growth model (Abera et al., 2012a, ‘in press’) and the 3D expansive plant cell growth model (Abera et al., 2012b) which were initiated from a 2D and 3D Voronoi tessellations respectively. In conclusion, the main merits of the algorithm are: 1) both cell shape and topology are taken care of; 2) it is based on physics; 3) the equations for the actual growth of the cell walls (change in resting length of the walls) and cell division are solved continuously; 4) it is generic in that a switch between isotropic growth and anisotropic growth as well as between symmetric cell division and asymmetric cell division is automatic and easy; 5) there is no need for an iterative procedure to find the shortest wall for cell division. In our algorithm, the division wall is inserted along the minor diameter of the ellipse/ellipsoid. To our knowledge, the 3D cell division and cell growth algorithm presented here is the first one based on cell wall mechanics introduced to the literature. LITERATURE CITED Abera MK., Fanta SW, Verboven P, Ho QT, Carmeliet J, Nicolai BM. 2012a. Virtual Fruit Tissue Generation based on Cell Growth Modeling. Journal of Food and Bioprocess Technology, in press. DOI: 10.1007/s11947-011-0775- 4. Abera MK., Verboven P, Herremans E. et al. 2012b. 3D virtual pome fruit tissue generation based on cell growth modeling. Submitted. Besson S, Dumais J. 2011. A universal rule for the symmetric division of plant cells. Proceedings of the National Academy of Sciences, USA, 108: 6294–6299. Dupuy L, Mackenzie J, Haseloff J. 2010. Coordination of plant cell division and expansion in a simple morphogenetic system. Proceedings of the National Academy of Sciences, USA, 107: 2711–2716. Errera L. 1886. Sur une condition fondamentale d’équilibre des cellules vivantes. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, 103: 822–824. Hofmeister W. 1863. Zusatze und berichtigungen zu den 1851 veröffentlichen untersuchungen der entwicklung höherer kryptogamen. Jahrbucher für Wissenschaft und Botanik, 3: 259–293. Ho Q, Verboven P, Verlinden B. et al. 2011. A 3-D multiscale model for gas exchange in fruit. Plant Physiology, 155 (3), 1158-1168. Korn RW, 1969. A stochastic approach to the development of Coleocheate. Journal of Theoretical Biology, 24:147– 158. Merks RMH, Glazier JA. 2005. A cell-centered approach to developmental biology. Physica A, 352: 113–130. Prusinkiewicz P, Runions A, 2012. Computational models of plant development and form. New Phytologist, 193: 549- 569. Robinson S, Barbier de Reuille P, Chan J, Bergmann D, Prusinkiewicz P, Coen E. 2011. Generation of spatial patterns through cell polarity switching. Science, 333: 1436–1440. Romberger, JA., Hejnowicz, Z., Hill, J.F. 1993. Plant Structure: Function and development. Springer, Berlin Heidelberg. Sachs J. 1878. Über die anordnung der zellen in jüngsten pflanzentheilen. Arbeiten des botanischen Instituts in Würzburg, 2: 46–104. Sahlin P, Jönsson H. 2010. A modeling study on how cell division affects properties of epithelial tissues under isotropic growth. PLoS One, 5: e11750., doi:10.1371/journal.pone.0011750. Smith RS, Guyomarc’h S, Mandel T, Reinhardt D, Kuhlemeier C, Prusinkiewicz P. 2006. A plausible model of phyllotaxis. Proceedings of the National Academy of Sciences, USA 103: 1301–1306. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 33 Modeling Cucumber leaf orientation as growing in heterogeneous canopy Tingting Qian1,2, Chunjiang Zhao1,2*, Xinyu Guo1, Shenglian Lu1 1Beijing Research Center for Information Technology in Agriculture, Beijing 100097, China 2Shanghai Jiaotong University, Shanghai, 200240, China *correspondence: zhaocj@nercita.org.cn Highlights: The change of leaf azimuth during cucumber growth was analyzed. Five plant density treatments were conducted to analyze the relationship between light environment and leaf azimuth. There is significant evidence shown in the results that leaf distribution frequency changed as the influence of heterogeneous light conditions. Key words: LAI, Leaf azimuth, Sunlit greenhouse, Cucumber, Heterogeneity INTRODUCTION In cucumber canopy, it can be observed that cucumber leaves adjust the orientation into the direction of the incoming radiation to improve light interception (Kahlen et al. 2008). The study of Chen et al. (1994) shows that leaf orientation has much greater effects on canopy photosynthesis than spatial distribution of leaf area density. Leaf azimuth should be explicitly described as it has a big impact both on light distribution and photosynthesis (Sarlikioti 2011). Kahlen et al. (2008) have done some remarkable research on leaf phototropism in a cucumber canopy. A model was developed by considering leaf reorientation as triggered by the gradient in the R: FR ratio between left and right half of one leaf. Some of our early results show that cucumber leaves in a sunlit greenhouse usually reoriented their azimuth, especially, the leaves oriented to north as influenced by the north wall of the greenhouse which blocks most of the light. The leaf orientation was affected by not only the shade caused by leaf blocked but also the environment heterogeneous in sunlit greenhouse. The objective of this work is to analyze the changes of leaf azimuth during cucumber growth and describe the relationship between light environment and leaf azimuth character using a simplified model. MATERIALS AND METHODS Experiments Four experiments were conducted in autumn 2012 in experimental sunlit greenhouse at Beijing Academy of Agriculture and Forestry Sciences (39º26´ N, 116 º 19´ E). The experiments had 5 density treatments, the planting spacing of treatments (row × plant) were: 30×40cm, 35×40cm, 40×40cm, 45×40cm, 50×40cm. Every two rows in one ridge, the distance between ridges was 70cm. Eight neighboring plants per treatment were selected to measure leaf azimuth, leaf length and leaf width at 2012-10-11, 2012-10-18, 2012-10-29 and 2012-11-8, respectively, as cucumber growing. Leaf distribution statistics Leaf distribution in canopy was separated into 8 orientation class. The frequency of leaf distribution in each class and in each canopy was counted. The data of leaf distribution frequency in 30×40cm, 40×40cm, 50×40cm canopies of four experiments were used to analyze the changes of leaf azimuth during cucumber growth and describe the relationship between light environment and leaf azimuth character. The data of 35×40cm and 45×40cm treatments were used to evaluate the accuracy of the model. Due to the heterogeneous characteristics of light distribution in sunlit greenhouse, light environment is difficult to measure directly. Following the Beer-lambert law, light intensity in the canopy is directly impacted by LAI. Therefore, we use LAI to indicate the light condition in the canopy based on the theory that as LAI increased the light transmittance decreased. In order to study the leaf distribution in detailed, the leaf azimuth distribution range from 0º to 359º in a clockwise direction was separated into 8 orientation classes named in capital letters respectively (from I to VIII) and each class contains 45º angle ranges. RESULTS The data of leaf distribution frequency in each class as cucumber growing are shown in figure 1. Leaf distribution was uniform at an early stage in which the leaf number per plant was 8, but it became 34 non-uniform at late stage in which the leaf number per plant was more than 18. The azimuth of most leaves at late stage reoriented to south. Leaf frequency in class I and VIII decreased from nearly 12.5% to 5% while leaf frequency in leaf azimuth distribution classes IV and V increased from nearly 12.5% to 20%, and leaf frequency in II, III, VI and VII fluctuated during cucumber growing in different planting density treatments. The LAI increased with the increase of leaf number and leaf area; at the same time, planting density also changes leaf area index. With the aim to simplify the relationship between leaf orientation and LAI, the orientation class was integrated into 4 classes which were north (316º-45º), east (46º-135º), south (136º-225º) and west (226º-315º). The leaf distribution frequency changing was different between 4 classes (Fig. 2). A linear function was used to describe the relationship between LAI and leaf distribution frequency in different classes. The regression function and determination coefficient are showed in table 1. The leaf distribution frequency in 316º-45º decreased as LAI increased while the opposite situation was found in the southern direction (136º-225º). There was no significant increase or decrease of frequency in east and west range. The regression functions also show that at the beginning of cucumber growth, the leaf distribution in 4 ranges is uniform (nearly 25%) which match the result in Fig. 1(A) very well. The function accuracy was tested using data measured in 35×40cm and 45×40cm treatments. The data are shown in Fig. 3, and the RMSE is 6.46. DISCUSSION The aim of this study was to analyze the changes in leaf azimuth during cucumber growth and describe the relationship between the light environment and leaf azimuth character using the regression functions (Table 1). There was a significant change in leaf orientation distribution during cucumber growth. The results shown in Fig.1 B exhibited a great fluctuation between different orientation classes and we considered that it might be because of insufficient data. The determination coefficient for LAI dependent leaf distribution changes was low in the eastern and western azimuth classes. We considered that even the slope of the regression functions of this two distribution ranges was very small which means that the leaf distribution frequency changed little with LAI increased, but the frequency of leaf distribution was not constant, since the orientation of most leaves deviated from initial direction were restricted by maximum rotation angle, so some leaves re-orientated the direction from north to east or west. We considered that the frequency in eastern and western classes was affected by the two other ranges. The accuracy of the regression function of north and south distributions was higher than east and west. In the future we need more detailed experiments to refine the relationship between leaf distribution and LAI. The leaf distribution character will be used as parameter in cucumber canopy structural modeling which will be used in light interception calculation, so we also need to evaluate the accuracy of leaf distribution character using canopy light interception results. Fig. 1 leaf distribution frequency in each class of 3 treatments (30×40cm, 40×40cm, 50×40cm canopy density) at 4 times. Eight neighboring plants per treatment were selected and average leaf numbers per plant of 4 times were 8, 12, 0 5 10 15 20 25 30 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Fr eq ue nc y Leaf orientation class A. 2012-10-11 30c m 40c m 0 5 10 15 20 25 30 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Fr eq ue nc y Leaf orientation class B. 2012-10-18 30cm 40cm 50cm 0 5 10 15 20 25 30 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Fr eq ue nc y Leaf orientation class C. 2012-10-29 30cm 40cm 50cm 0 5 10 15 20 25 30 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Fr eq ue nc y Leaf orientation class D. 2012-11-8 30cm 40cm 50cm 35 18, 22, respectively. Fig. 2 Leaf distribution as LAI changes. Table 1. Regression function and determination coefficient (R2) for LAI dependent leaf distribution changes Distribution Regression function R2 316º-45º y = -4.3061*L AI+ 22.598 0.5878 46º -135º y = -0.7943*L AI + 30.341 0.0246 136º -225º y = 4.461*L AI + 21.565 0.6187 226º -315º y = 0.227*L AI + 26.885 0.012 Fig. 3. Comparison between the simulated and measured leaf distribution frequency LITERATURE CITED Chen SG, Shao BY, Impens I, Ceulemans R. 1994. Effects of plant canopy structure on light interception and photosynthesis. Journal of Quantitative Spectroscopy and Radiative Transfer 52: 115-123. Kahlen K, Wiechers D, Stützel H. 2008. Modelling leaf phototropism in a cucumber canopy. Funct Plant Biol 35: 876-884. Sarlikioti V, de Visser PHB, Marcelis LFM. 2011. Exploring the spatial distribution of light interception and photosynthesis of canopies by means of a functional-structural plant model. Ann Bot-London 107: 875-883. 0 5 10 15 20 25 30 35 40 45 0 1 2 3 4 Fr eq ue nc y leaf area index North (316º-45º) East (46º -135º) South (136º -225º) West (226º -315º) 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 si m ul at ed fr eq ue nc y measured frequency simulated value RECONSTRUCTING AND OBSERVING PLANT STRUCTURE Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 39 A combined method for quantifying 3D root architecture of field-grown maize Jie Wu, Bo Yang and Yan Guo* Key Laboratory of Arable Land Conservation (North China), Ministry of Agriculture, College of Resources and Environment, China Agricultural University, Beijing 100193, China *correspondence: yan.guo@cau.edu.cn Highlights: A new method for reconstructing 3D root architecture of field-grown maize was developed through integrating the spatial deployment of maize axile roots determined by digitizing in situ in the field with geometrical and topological information of scanned lateral roots. Spatial root length density and other root traits of maize can be estimated basing on this integrated method. Keywords: root system architecture, topological structure, maize, root traits, model INTRODUCTION Root system architecture (RSA), refers to the topological arrangement of root segments and their geometrical characteristics (Fitter 1987; Danjon and Reubens 2008), has high capacity of plasticity responding to its rooting environment (Hodge 2004; Pagès et al. 2004). Camera and 3D laser scanner have been applied to non-invasively measure 3D dynamic RSA traits of young crop plants grown in transparent gel media (Fang et al. 2009; Clark et al. 2011). However, the root traits screens from non-soil media could be significantly different from or even reversed to those obtained from soil media (Gregory et al. 2009; Clark et al. 2011). To image and quantify 3D RSA in soil media, X-ray micro-computer tomography (CT) and neutron tomography have been utilized (Moradi et al. 2011; Mairhofer et al. 2012). However, high cost, restricted container size and limit of environmental factors restricts their applications in the field. The objective of this study is to develop a combined method for quantifying 3D RSA of field-grown maize. We utilize digitizer to measure axile roots of individual plants in situ in the field, and develop a method to sample and collect topological and geometrical information of lateral roots using a software for root image analysis. We match the lateral root information with the axile roots to reconstruct and visualize the entire root system of individual plants. Different types of 2D and 3D root traits can be estimated based on the developed root model. MATERIALS AND METHODS Maize hybrids ZD958 (Zea mays L.) was seeded with row and plant spacing of 0.6 m and 0.3 m respectively on May 6, 2011 at the Shangzhuang experimental farm (40°08’ N, 116°10’ E) of the China Agricultural University. For lateral roots measurement, three plants were selected at 75 days after sowing (10 days after silking). A self-made root auger (55 cm high, 50 cm diameter), composed by two half hollow cylinders, was put on soil surface with one sample plant at the center of the root auger. The root auger was hammered into the soil 50 cm in depth. A self-manufactured lift system was used to lift the root auger with sampled root system. Adjustable hydraulic nozzles were used to wash away soil with a disc kept at the base of the sampled root system to avoid root broken during washing. Then the root system was stored in a freezer with temperature kept 3 ℃. Two roots from the 4th to 8th nodal root whorls were selected for scanning. Branched zone of axile roots was cut into 5 cm segments from the base and first-order lateral roots along each axile root segment were cut. Axile root segment and its cut lateral roots were placed in a rectangular glass dish (25 cm × 20 cm) with water. Lateral roots were untangled carefully to minimize root overlap and then scanned using a scanner (ScanMaker i800 plus, Microtek, China). The eraser tool of WinRHIZO Pro 2009 software (Régent Instruments, Canada) was used to separate the overlapping of root segments in the images and remove noise. The developmental analysis function and Largard algorithm of the software were adopted to analyze the root developmental order, length and diameter of lateral roots while the former was also used to estimate the length and diameter of axile roots. Visual Basic Application embedded in Microsoft Excel 2007 was programmed to extract topological and geometrical information of lateral roots, length and diameter distribution of non-branched axile roots, and diameter of each 5 cm axile root segment. Axile roots of two neighboring maize plants in a row were digitized in situ in the field using 3Space 40 Fastrak (Polhemus, USA) at 90 days after sowing (grain-filling stage). The axile roots were cut immediately after digitization and stored in a freezer for scanning to determine diameter and length of axile root segments. 3D RSA model of individual maize plant was built through matching measured lateral roots on the digitized axile roots using C++ language, boost library, SQLite and Visualization Toolkit. Model visualization was realized using ParaView software. RESULTS AND DISCUSSION The spatial deployment of axile roots of two neighboring maize plants at grain-filling stage was illustrated based on the dataset digitized in situ in the field (Fig.1A). Through matching measured lateral roots (Fig.1B) with digitized axile roots, the complete 3D RSA of an individual maize plant was reconstructed (Fig. 1C). Fig. 1. A. 3D visualization of axile roots of two neighboring maize plants in a row, different colors indicate distinct root types. B. A sample of lateral root system output from WinRHIZO software, light blue, dark blue and green indicate first, secondary and tertiary order lateral roots. C. Visualization of the complete root architecture of an individual maize plant, red, yellow and green segments were first, secondary and tertiary order lateral roots, respectively. Different root traits can be extracted based on the constructed RSA model. 2D root traits include the branching number and length density, the highest order of lateral roots, and the total length of each order lateral root on each 5 cm axile root segment of different root types. 3D RSA traits include angle and horizontal trajectory of different types of axile roots, and root length distribution of different orders of lateral roots and types of axile roots in each soil cell. The distribution of lateral root length density of two neighboring maize plants at different soil depth was presented (Fig. 2). More than 70% of the lateral root length of the 0-40 cm soil profile was distributed in the 0-20 cm soil horizon. Significant variation of lateral root length density occurred in distinct soil horizons. For the top 10 cm soil horizon, most of root length concentrated around the plant base. In contrast, the distribution of root length density is much lower and more homogeneous at 20-40 cm soil horizon. Fig. 2. The distribution of lateral root length density of maize at different soil horizons. The origin of the horizontal and vertical axis indicates the centre between two neighboring plants in a row and the vertical axis is perpendicular to 0 - 5 cm 5 - 10 cm 10 - 15 cm 15 - 20 cm 20 - 25 cm 25 - 30 cm 30 - 35 cm 35 - 40 cm -30 -15 0 15 30 -30 -15 0 15 30 -45 -30 -15 0 15 30 45 -45 -30 -15 0 15 30 45 -45 -30 -15 0 15 30 45 -45 -30 -15 0 15 30 45 Parallels to the row (cm) D ep th (c m ) 0.0001 0.001 0.01 0.1 1 3 10 25 RLD (cm cm3) A C B 41 the row direction. The color mapping the values of root length density (RLD) in the legend is under logarithmic transformation. ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (41071205) and National Scientific and Technological Support Plan (2012BAD35B02). LITERATURE CITED Clark RT, MacCurdy RB, Jung JK, Shaff JE, McCouch SR, Aneshansley DJ, Kochian LV. 2011. Three-dimensional root phenotyping with a novel Imaging and software platform. Plant Physiology 156: 455 –465. Danjon F, Reubens B. 2008. Assessing and analyzing 3D architecture of woody root systems, a review of methods and applications in tree and soil stability, resource acquisition and allocation. Plant and Soil 303: 1–34. Fang S, Yan X, Liao H. 2009. 3D reconstruction and dynamic modeling of root architecture in situ and its application to crop phosphorus research. The Plant Journal 60: 1096–1108. Fitter AH. 1987. An architectural approach to the comparative ecology of plant root systems. New Phytologist 106: 61– 77. Gregory PJ, Bengough AG, Grinev D, Schmidt S, Thomas WTB, Wojciechowski T, Young IM. 2009. Root phenomics of crops: opportunities and challenges. Functional Plant Biology 36: 922–929. Hodge A. 2004. The plastic plant: root responses to heterogeneous supplies of nutrients. New Phytologist 162: 9–24. Iyer-Pascuzzi AS, Symonova O, Mileyko Y, Hao Y, Belcher H, Harer J, Weitz JS, Benfey PN. 2010. Imaging and Analysis Platform for Automatic Phenotyping and Trait Ranking of Plant Root Systems. Plant Physiology 152: 1148 –1157. Mairhofer S, Zappala S, Tracy SR, Sturrock C, Bennett M, Mooney SJ, Pridmore T. 2012. RooTrak: Automated Recovery of Three-Dimensional Plant Root Architecture in Soil from X-Ray Microcomputed Tomography Images Using Visual Tracking. Plant Physiology 158: 561 –569. Moradi AB, Carminati A, Vetterlein D, Vontobel P, Lehmann E, Weller U, Hopmans JW, Vogel H-J, Oswald SE. 2011. Three-dimensional visualization and quantification of water content in the rhizosphere. New Phytologist 192: 653–663. Pagès L, Vercambre G, Drouet J-L, Lecompte F, Collet C, Le Bot J. 2004. Root Typ: a generic model to depict and analyse the root system architecture. Plant and Soil 258: 103–119. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 42 Semantic Skeletonization for Structural Plant Analysis Jenny Balfer, Florian Schöler* and Volker Steinhage Department of Computer Science III, University of Bonn, Römerstraße 164, 53117 Bonn, Germany *correspondence: schoele@iai.uni-bonn.de Highlights: Computational plant modeling from 3D sensor data is crucial for the early assessment of plant traits. Semantic modeling enables the incorporation of knowledge about the plant species, leading to an improvement of purely geometrical skeletonization approaches. Structural plant features can thereby robustly be extracted from the sensor data. Keywords: Plant modeling, Structural plant analysis, 3D skeletonization, Feature extraction INTRODUCTION Structural plant analysis can help plant breeders to detect, e.g., a susceptibility of a new breed to a certain disease. Currently, the phenotyping bottleneck limits the throughput of automated plant trait assessment. In this work, we are interested in the automated extraction of structural features of plants, in particular grapevine, from 3D laser range data. We employ a skeletonization algorithm, which reduces the structure of an object represented by a point cloud to a vectorized representation in the form of a set of connected line segments, whilst preserving its topology and geometry. But for our purpose, structural preservation alone is not sufficient. We also need to know what part of the curve skeleton refers to what part of the original plant. Therefore we propose to add a further layer to the skeletonization, namely semantics. Our goal is to automatically identify curve skeleton components as plant components. In order to achieve this we include a biological model into the skeletonization algorithm. This model enables a semantic annotation of the plant components, which in general allows us to extract the structural features. RELATED WORK Owing to an extensive survey by Cornea et al., it is widely accepted that curve skeletons should fulfill certain properties such as homotopy, thinness, centeredness, reliability, component-wise differentiation, smoothness, and hierarchy (Cornea et al., 2005; Cornea et al., 2007). Some of these properties may contradict each other, and especially for point cloud data with irregular sampling, some properties can be hard to achieve and evaluate. This is why many methods for the skeletonization of plants from 3D point clouds additionally incorporate model knowledge. One common prerequisite is to have the root point of the plant structure identified (Livny et al., 2010; Preuksakarn et al., 2010; Verroust and Lazarus, 2000; Xu et al., 2007). Other approaches try to fit cylindrical structures (Pfeifer et al., 2004; Runions et al., 2007) into the point cloud, thus implicitly simulating the geometric properties of branches. Our work is based on a skeletonization method that follows a global optimization approach (Livny et al., 2010). This approach is specifically designed for the skeletonization and reconstruction of tree structures. SEMANTIC MODELING, ANNOTATION, AND GEOMETRY CORRECTION We exemplify our method on the berryless grape cluster, in the following termed grapevine stem system. This choice is motivated by two main reasons: First, stem systems determine the overall structure and geometry of the grape cluster. Second, they show typical characteristics that are generally challenging in plant analysis, namely self-occlusion, self-touching, and very fine structures. The knowledge incorporated into the algorithm arises from a number of observations about the biological structure of the plant to model. To formalize these inherently informal observations, we utilize the implicit graph structure of the curve skeletons. We define the structural depth d of a vertex v in a curve skeleton as shown in equation 1, where p denotes the parent of vertex v, J denotes the set of junctions, i.e., vertices with more than one child, and l(v) the Euclidean length of the longest edge chain in v’s subgraph. The proposed semantic annotation algorithm utilizes this definition of depth to annotate each vertex according to the structural plant part it belongs to. Figure 3 visualizes this semantic annotation with different colors, where each edge is assumed to have the label of its end vertex. 43 𝑑(𝑣): = �0 if 𝑝 = ∅𝑑(𝑝) if 𝑝 ∉ 𝐽 ∨ 𝑙(𝑣) = 𝑙(𝑝) − ‖𝑣 − 𝑝‖ 𝑑(𝑝) + 1 otherwise (1) The curve skeletons obtained by the method of Livny et al. (Livny et al., 2010) contain a number of erroneous edges for our data. Therefore, the approach presented herein aims at the automated identification and removal of these unnecessary edges. The semantic annotation described before is employed to assign each edge one of the labels ”rachis”, ”lateral branch”, ”pedicel”, or ”vascular remains of berries”. Edges that contradict biological constraints, e.g. by representing decreasingly long lateral branches in basipetal direction, are removed. Furthermore, all edge segments classified as vascular remains of berries are contracted. Figure 3 shows one remaining curve skeleton, which constitutes our final result. Fig. 1: Point cloud of a stem system. Fig. 2: Semantic annotation Fig. 3: Corrected curve skeleton. FEATURE EXTRACTION The semantic model and its implementation are designed to remove all edges from the curve skeleton that do not reflect branches in the grape cluster. This removal is crucial for the derivation of phenotypic characteristics for grapevine breeding. We will show how the semantically labeled and corrected curve skeletons can be used for the extraction of a formal grapevine descriptor from sensor data. To identify possible features of grapevine, existing descriptor lists can be consulted. (IPGRI, 1997; OIV, 2009). The list of phenotypic features we compute include, amongst others, the existence of secondary bunches, the size of branching angles, or the length and thickness of branches and internodes. Several of these features refer to the growth direction of the stem system or the number of internodes in one branch. In order to encode the growth direction and identify the number of vertices (and thus internodes) in one structural component, a unique numbering scheme for vertices is introduced. As a consequence, the formal features can be easily derived and used in a statistical analysis. The resulting statistical model can be used to infer knowledge about hidden object parts in the grape cluster including berries, and can furthermore serve as parameters for plant reconstruction (Schöler et al., 2013). EXPERIMENTAL RESULTS To quantitatively evaluate the obtained curve skeletons, we compare them to manually created reference skeletons. To operationalize the comparison of two curve skeletons, we formulate the given task as an assignment problem (Munkres, 1957) and match the number of skeletal junctions in both skeletons to each other. Then we compute precision and recall as performance measure for the number of skeletal junctions that are part of the assignment A (cf. Equation 2). Here, the precision P is given as the fraction of junctions JS in the obtained curve skeleton that are part of the assignment, and therefore measures correctness of junctions. The recall R is the fraction of junctions in the reference skeleton JR that are part of the assignment, and measures completeness of the obtained curve skeleton. Our evaluations show that we are able to significantly improve the skeletons' precision by semantic geometry correction. Furthermore, we were able to keep high recall due to the deletion of erroneous edge segments, thus enabling a robust feature extraction. Figures 5 and 6 report the precision and recall values for a curve skeleton before and after semantic-driven geometry correction. 44 𝑃 ∶= |𝐽𝑅 ∩ 𝐴||𝐽𝑆| , 𝑅 ∶= |𝐽𝑅 ∩ 𝐴||𝐽𝑅| (2) For the evaluation of structural plant features, we compare the automatically computed values to those given by the manually created reference skeletons. We found that the errors of these feature values in the semantically corrected curve skeletons are significantly smaller than in the uncorrected ones. One example is the length of the peduncle, i.e., the “distance from insertion point on the shoot to the 1st ramification of primary bunch” (OIV, 2009). Due to erroneous edges in the curve skeletons before the semantic geometry correction, the first ramification of the primary bunch is detected too early, resulting in a very short peduncle. After semantic geometry correction, its length can be robustly measured (cf. figures 5 and 6). CONCLUSION In conclusion, we have shown how the skeletonization of 3D point clouds of grapevine stem systems can be enhanced by the introduction of a biological model. By means of this model, we can add semantic annotations to curve skeleton components. These annotations are used to correct the computed curve skeletons and to improve on the extraction of structural features. We performed an extensive evaluation of our approach and were able to show that both skeletonization and feature extraction could be significantly improved. Moreover, first investigations on whether the structural features can be used to distinguish different cultivars have shown to be beneficial for plant reconstruction results (Steinhage et al., 2012). Fig. 4: Point cloud of a stem system (29,922 points). Fig. 5: Curve skeleton before geometry correction (P = 0.29, R = 1.0). Fig. 6: Curve skeleton after geometry correction (P = 0.55, R = 1.0). LITERATURE CITED Cornea N, Silver D, Min P. 2005. Curve-Skeleton Applications. Proceedings of the IEEE Visualization Conference 2005:95-102. Cornea N, Silver D, Min P. 2007. Curve-Skeleton Properties, Applications, and Algorithms. IEEE Transactions on Visualization and Computer Graphics 13:530-548. IPGRI, UPOV, OIV. 1997. Descriptors for Grapevine (Vitis spp.). International Union for the Protection of New Varieties of Plants, Geneva, Switzerland/Office International de la Vigne et du Vin, Paris, France/International Plant Genetic Resources Institute, Rome, Italy. Livny Y, Yan F, Olson M, Chen B, Zhang H, El-Sana J. 2010. Automatic Reconstruction of Tree Skeletal Structures from Point Clouds. ACM Transactions on Graphics 29:151:1-151:8. Munkres J. 1957. Algorithms for the Assignment and Transportation Problems. Journal of the Society for Industrial and Applied Mathematics 5:32-38. Organisation Internationale de la Vigne et du Vin. 2009. 2nd Edition of the OIV Descriptor List for Grape Varieties and Vitis Species. Organisation Intergouvernementale crée par l'Accord International du 3 Avril 2001. Pfeifer N, Gorte B, Winterhalder D. 2004. Automatic Reconstruction of Single Trees from Terrestrial Laser Scanner Data. Proceedings of the 20th ISPRS Congress 114-119. Preuksakarn C, Boudon F, Ferraro P, Durand J-B, Nikinmaa E, Godin C. 2010. Reconstructing Plant Architecture from 3D Laser Scanner Data. Proceedings of the 6th International Workshop on Functional-Structural Plant Models 16-18. Runions A, Lane B, Prusinkiewicz P. 2007. Modeling Trees with a Space Colonization Algorithm. Proceedings of the Eurographics Workshop on Natural Phenomena 63-70. Schöler F, Balfer J, Steinhage V. 2013. Automated Parameter Estimation for a Plant Architecture Model. Submitted to the International Conference on Functional-Structural Plant Models. Steinhage V, Schöler F, Balfer J. 2012. A Model-Based Approach to High Performance Phenotyping. Proceedings of the 26th International Conference on Informatics for Environmental Protection 1:303-310. Verroust A, Lazarus F. 2000. Extracting Skeletal Curves from 3D Scattered Data. The Visual Computer 16:15-25. Xu H, Gossett N, Chen B. 2007. Knowledge and Heuristic-based Modeling of Laser-Scanned Trees. ACM Transactions on Graphics 26:19:1-19:13. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 45 PlantScan™: a three-dimensional phenotyping platform for capturing the structural dynamic of plant development and growth Xavier Sirault1, Jurgen Fripp2, Anthony Paproki2,Peter Kuffner1, Chuong Nguyen3, Rongxin Li4, Helen Daily1, Jianming Guo1, Robert Furbank1 1High Resolution Plant Phenomics Centre, CSIRO Plant Industry, Cnr Clunies Ross St and Barry dr, Canberra ACT 2601, Australia, 2Australian e-Health Research Centre, CSIRO ICT Centre, Brisbane, Australia, 3CSIRO CMIS, ANU, 4CSIRO ICT Centre, Sydney *correspondence: xavier.sirault@csiro.au Highlights: PlantScanTM is an integrated analysis pipeline, seamlessly integrating hardware and software tools, to provide automated, non-invasive analyses of plant structure (topology, surface orientation, number of leaves, internode length...), morphology (leaf size, shape, area, volume...) and function (conductance,…). By utilising cutting edge information technology to automatically digitise plants in three-dimensions, it enables plant scientists to better understand the complex interactions involved in plant growth, i.e., the plant's genetic make-up, its physical characteristics and the environment in which it grows, thus, providing essential information to populate functional structural plant models. Keywords: Plant architecture, transformational technology, automated feature extraction, quantification INTRODUCTION Plant architecture is of major importance for agricultural production. It is a major determining factor for yield potential as evidenced by the first green revolution, which resulted in a doubling of global cereal production worldwide. This was achieved by the breeding of high yielding cultivars with reduced plant stature (Hedden, 2003). Because plant architecture also determines the physical, chemical and biotic factors to which a plant is exposed (Wilson and Chakraborty, 1998), plant breeders and geneticists have been actively selecting for plant architecture and have been exploiting natural genetic variation in canopy architecture for centuries. Nevertheless, the genetic control of plant architectural characteristics still remains today largely unknown due to the complexity and challenges in accurately and rapidly quantifying plant structure and geometry. This difficulty of measuring plant structure is compounded when studying plant architecture dynamically and its impact on physiological traits (conductance, light interception…) across a large number of genotypes. Indeed, not only does it require determination of plant topology and quantification of shape and size of each organ in high throughput but it also requires capturing and tracking organ expansion and growth over time under various environmental conditions. Despite the technological challenge, exploiting the dynamic nature of plant architecture and its influence on physiological traits within breeding programs represents a window of opportunities for improving yield potential in response to changing climatic conditions. Analysis of digital representation of individual plants in three dimensions, in combination with proxy- sensing technologies (hyperspectral, infrared, visible imaging) is one way to determine plant topology, quantify plant geometry and assess simultaneously their impact on plant function. In this manuscript, we introduce an advanced automated phenotyping platform, PlantScanTM, which combines the advantages of stereo-optical cameras and laser ranging sensors for faithfully digitising plants in three dimensions. Combining these two technologies is particularly valuable for digitising thin structures such as leaves and stems (Li et al, in prep.). To provide a link between plant structure and function, colour and thermal infrared images are projected onto these 3D structural representations. These digital objects are then fed to a generalised analysis processing pipeline that automatically derives structural (e.g. topology, surface orientation, number of leaves…), morphological (e.g. leaf size, shape, area, volume…) and functional information (conductance, photosynthesis...) at the whole organ or plant level (Paproki et al, 2012). Although the platform has been tested on a range of plant species (rice, wheat, canola, eucalyptus, tobacco, millet and tomato), we illustrate our results using mainly corn and cotton; nonetheless we will discuss the inherent difficulties at applying these in-silico methods to complex cereals such as rice or wheat. 46 THE DIGITISATION PLATFORM PlantScanTM is a custom-built imaging chamber integrating multi-wavelength, optical-imaging sensors and Light Detection and Ranging (LiDAR) systems, which are arranged in a multi stereo configuration (Fig 1). Two microbolometer sensors (model A645, FLIR systems Inc, MA, USA) collect thermal information with temperature resolution of 0.045°K in the waveband 7.5 to 14 µm, while three JAI 3-CCD optical sensors (model AT-200GE) and one JAI 4-CCD RGB/NIR optical line scanner (model LQ-200 CL), equipped with Fujinon zoom lenses (model C22x17R2D-ZP1) collect information in the visible and near infrared spectra. In addition, two synchronised light detection and ranging (LiDAR) sensors (SICK LMS400) operating at a wavelength of 650nm with a 70° sweep collect time of flight data and reflectance data at a rate of 270Hz. Fig. 1.The PlantScanTM phenotyping platform The light spectrum in the chamber is generated by fluorescent light run on a 75 kHz electrical signal to avoid noise in the acquired images. The light is diffused to approximate Lambertian conditions using Y20 Miniprism diffuser panels within the imaging chamber (York precision panels, Sydney, Australia). The platform is composed of a double conveyor belt, manually loaded, with plants held in position on pot carriers. Individual plants are identified by 2D bar codes. A first transfer station diverts the plant to a split conveyor belt which accurately positions the plant for imaging using laser proximity sensors. A rotating turntable, fitted with an incremental encoder with up to 2.5 million counts per revolution and mounted on a scissor-lift platform (10µm linear accuracy), ensures the plant is scanned from every angle in a 360° rotation. After imaging, the plant is conveyed to a second transfer station before being ejected by an actuator onto a double gravity belt. Plants are then manually unloaded and transported back to their growing environments. All motion control and image acquisition was realised utilising the graphical programming environment LabVIEW (National Instrument). The platform is able to scan very small seedlings or plants from a few centimetres to a couple of metres in height and up to a metre thick. Image and LiDAR data are captured simultaneously in 50 seconds (one image every 3° from all cameras, while LiDAR is continuously acquiring) with their contextual information and collated into one multi-layer data file before being stored in a purpose-built database. THE SOFTWARE PIPELINE To obtain 3D architectural representations of crops, trees and/or model species, overlayed with spectral information, a number of computer vision techniques have been simultaneously integrated in a reconstruction scheme running on a computer cluster, thus combining the respective advantage of each technique: • Stereo-techniques using silhouette-based (Visual hull) and Embedded Voxel Colouring (Leung et al, 2012) (Fig 2A) and textural methods (Patch based Multi-view Stereo - PMVS) (Furukawa and Ponce, 2010)(Fig 2B); 47 • Fusion of LiDAR Point cloud to mesh results using Random sampling and Consensus (RANSAC) approaches associated with iterative closest point (ICP) algorithms (Fig 2C); • Fusion of spectral signals onto 3D structural representations: only colour and thermal infrared images close to the surface normal (within 30°) of each mesh polygon are averaged and projected, thus taking into account the influence of plant geometry on data collected by proxi-sensing technologies (Guo et al, in prep) (Fig 2D). To achieve higher reconstruction accuracy, we designed a new calibration algorithm, which estimates camera parameters (including geometric distortion) from all camera positions at once around a rotating axis (Chuong et al, in prep.). The results are high-resolution 3D plant meshes with sub-millimetre resolutions, which are then automatically segmented in order to semantically identify the different parts of the plants as detailed in Paproki et al. 2012. Figure 2E shows a maize mesh automatically segmented and Fig 2F shows the fitting of spline function to the midrib of two leaves from the corn plants in Fig 1E. A longitudinal 3D matching pipeline for plant mesh parts can also be used to evaluate temporal changes at the whole plant and/or organ level. RESULTS AND DISCUSSION A) B) C) D) E) F) Fig. 2.Automated reconstruction of Gossypium species by A) Visual hull methods, and B) Patch-based Multi-view stereo. C) fusion of LiDAR and mesh information for wheat species (the mesh has been deleted to show the co- registration of LiDAR information), and D) 3D data fusion of Infrared information for Zea mays (false colour imaging of leaf temperature). E) False colour imaging of mesh segmentation for Zea mays: green identifying each leaf and brown identifying the stem, F) automated margin extraction and spline fitting of the midrib for two of the maize leaves in E) 48 Currently, there are a few limits to our methods, in particular when trying to reconstruct complex cereals like wheat or rice as our algorithms do not cope well with overlapping structures and concave surfaces when using visual hull-based methods alone. To address this issue, we are looking at integrating prior-knowledge of geometric structures by using x-ray geometric datasets, parametric models and statistical shape models as well as prior-knowledge of plant development in our reconstruction scheme. For PMVS methods, the accuracy relies on texture quality. Plants are known to lack surface texture. Improving results from PMVS can be addressed by using higher resolution images. Today, our system can resolve structures as small as 0.5mm. This is suitable for monitoring organ development or overall plant growth but not enough to resolve leaf thickness. Another area of improvement is on the calibration of our optical system. Currently our calibration algorithm does not work at sub-pixel resolution, thus limiting our ability to achieve higher accuracy. By providing an integrated multi-sensing platform relying on a range of imaging sensors, PlantScan increases scientists’ capacity to precisely and accurately quantify the biological processes involved in the development and functioning of plants and this with greater detail, frequency and objectivity than traditional methods. We point to the prospect that outputs from such a platform, which was developed for phenomics applications, i.e. measurement of correlated phenotypes in high-throughput, could provide a suite of new tools for populating functional structural plant models (FSPM) assuming that these outputs can be transformed into model parameters (Vos et al, 2010). These 3D models of plants with metadata will be made available via an on-line data repositories in self-contained collections (e.g. Data Access Portal - https://data.csiro.au/dap/), along with the means to handle, test, measure and interrogate them, allowing empirical research on these virtual models of crop plants. We are hoping that the information deposited on this repository will provide the necessary data for developing a predictive framework for enabling in-silico physiological breeding in the future. LITERATURE CITED Furukawa Y and Ponce J 2010 Accurate, dense and robust multiview stereopsis. IEEE Transaction on Pattern Analysis and Machine Intelligence, 32(8): 1362-1376. Hedden, P. 2003 The genes of the Green Revolution. Trends Genet. 19: 5–9 Leung Carlos, Ben Appleton, Mitchell Buckley and Changming Sun 2012 Embedded Voxel Colouring with Adaptive Threshold Selection Using Globally Minimal Surfaces. International Journal of Computer Vision 99(2): 215-231 (2012) Paproki Anthony. Xavier Sirault, Scott Berry Robert Furbank and Jurgen Fripp 2012. A novel mesh processing based technique for 3D plant analysis.. BMC Plant Biology 12(1): 63. Peng SB, Laza R, Visperas RM, Khush GS, Virk PS, Zhu DF 2004. Rice: progress in breaking the yield ceiling. In “proceedings of the 4th international cro science congress” (eds T Fisher, N Turner, J Angus, L McIntyre, M Robertson, A Borrell, D Lloyd) (The regional institute Ltd: Brisbane). Vos J, J. B. Evers, G. H. Buck-Sorlin, B. Andrieu, M. Chelle, and P. H. B. de Visser 2010 Functional–structural plant modelling: a new versatile tool in crop science J. Exp. Bot. 61(8): 2101-2115 Wilson P and Chakraborty S 1998. The virtual plant: a new tool for the study and management of plant diseases. Crop Protection. 17: 231–239. Zheng Bangyou, Shi Lijuan, Ma Yuntao, Deng Qiyun, Li Baoguo and Guo Yan 2008. Comparison of architecture among different cultivars of hybrid rice using a spatial light model based on 3D digitising. Functional Plant Biology 35: 900-910 Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 49 Improving branch distribution models in trees using X-ray computed tomography Emmanuel Duchateau1*, David Auty1, Frédéric Mothe2 and Alexis Achim1 1Faculté de foresterie, géographie et géomatiques, Université Laval, 2405 rue de la Terrasse, Québec G1V 0A6, QC, Canada 2INRA, UMR1092 LERFoB, 54280 Champenoux, France *correspondence: emmanuel.duchateau.1@ulaval.ca Highlights: The use of external measurements to describe the distribution of branches on tree stems can induce imprecision and bias in estimates of both the number of annual growth units and the azimuthal distribution of branches. The scanning of logs using X-ray computed tomography yielded knot data that enabled more accurate identification of the limits of each growth unit. Such information, in conjunction with current models of tree architecture, can be incorporated into functional-structural models describing relationships between tree morphology and biological processes. Keywords: X-ray computed tomography, tree architecture, black spruce, branch distribution INTRODUCTION Computer-based systems capable of simulating the 3D structure of plants, their metabolic processes and environmental interactions are increasingly being developed to increase our understanding of how plant architecture and biological processes interact (Fourcaud et al. 2008). In trees, such functional-structural models can be useful tools for understanding and predicting important wood quality attributes such as branch morphology and distribution. An underlying principle of these models is that plant structure can be described in terms of a hierarchical system of replicating ‘architectural units’ (Barthélémy et al. 1989). In temperate tree species, the ‘growth unit’ (GU) i.e. the annual elongation of the terminal shoot from the apical meristem (De Reffye et al. 1995), is the single most important component of existing branch distribution models (e.g. Colin and Houllier 1991). Such models are normally parameterized using data from external measurements. This has the advantage that data collection is relatively straightforward and can be accomplished with limited equipment. However, this simplicity may come at the expense of accuracy for certain measurements, such as branch inclination and azimuthal orientation. More recently, X-ray computed tomography techniques have been developed that can generate high-precision internal information, which could lead to improved model accuracy. Black spruce (Picea mariana (Mill.) BSP) is the dominant conifer in the North American boreal forest. It develops according to Rauh’s model of monopodial, rhythmic growth and attains its final developmental stage after 10-15 years (Bégin and Filion, 1999). After this, the basic structure of first and second order axes (trunk and branches, respectively) and third and fourth order axes (twigs) is duplicated through a process known as reiteration. The high reiterative capacity of black spruce accounts for its characteristically high phenotypic plasticity. This leads to a complex and apparently disorganised branching structure that complicates the development of functional-structural models, since the precise delineation of annual growth units can be difficult. The objectives of this study were: 1) to develop a method based on selective filters to locate annual growth units on black spruce logs using data derived from X-ray computed tomography and 2) to examine the distribution of branches around black spruce stems at the stem and growth unit levels. MATERIALS AND METHODS Measurements were taken on 33 black spruce trees from unmanaged stands in Québec, Canada. First, branch and tree characteristics were recorded following the protocol established by Colin and Houllier (1991). Sample trees were then cut into successive 2.5 m logs for X-ray scanning. Each of the resulting 107 logs were scanned at 2 mm intervals along the longitudinal axis with a 2-mm-wide X-ray beam, so that the scanned segments were contiguous. This provided accurate internal profiles for 23,040 knots (Duchateau et al. 2013). 50 The total number of growth units in each 2.5-m section was determined from the difference in the number of annual growth rings between discs cut from each end of the log. However, the precise limits of each annual shoot were difficult to determine, even using the X-ray data (Fig. 1). We developed an empirical method based on two filters to select the most likely location of the limits of each GU, which should correspond to the location of nodal branches produced from subterminal buds. First, the basal area of each branch (i.e. cross-sectional surface at the bark) was calculated and summed when branches originated from the same point at the stem’s pith. We then applied a series of thresholds to select basal area peaks along the main stem. Secondly, we tested thresholds of minimum GU lengths, as some of the identified peaks occurred in close proximity, presumably as a result of reiteration (Bégin and Filion, 1999). Once each GU was located, we analyzed the circular branch distribution at the scale of both the tree and the growth unit. This was carried out using circular statistics and a Rayleigh test (Jammalamadaka and Sengupta 2001). RESULTS AND DISCUSSION The number of GUs along the stem was significantly underestimated when only external branch measurements were used. On average, the underestimation was 2.4 GUs per 2.5-m log (SD=3.7), or around 15% of the total. For a mature tree, this would represent approximately 16 GUs, which is unsatisfactory for the development of accurate models. One possible explanation is that black spruce contains a relatively large number of branches along each growth unit, but the diameter ranges of nodal (terminal) and internodal (median) branches overlap, so the delineation of GUs based on branch basal area might be problematic. Fig. 1. Distribution of branch basal area along the stem from data extracted using the ImageJ Java plug-in ‘Gourmand’. Fig. 2. Distribution of the branch basal areas along the stem and delineation of the separate growth units using our two-filter method. For the identification of GUs using internal data, best results were obtained when 1) a GU limit was placed when the sum of branch basal areas initiating from the same point was above the 75th percentile for all branch initiation points within the log and 2) the next limit was located at a minimum distance of 7.5 cm along the main stem (Fig. 2). The utilization of the CT images coupled with this two-step method allowed us to significantly increase the accuracy of GU identification. The resulting mean bias in the number of GUs per log approached 0 (0.195). This represented a significant improvement compared to external assessment, although some variation remained (SD=2.8). The ability to identify branch initiation points at the pith of the main stem therefore allowed us to differentiate between nodal and internodal branches more accurately. 51 Fig.3. Distribution of branches around the stem by diameter (in red) and by number (in blue) for A) all branches, B) the largest diameter branch per GU and C) the largest diameter branch per tree. Once we had obtained the best GU selection, we studied the circular distribution of the branches at the tree and the GU levels. For all branches on one tree, the distribution was uniform (Fig. 3A). However, the largest branch per GU had a preferential orientation of 194° (SD = 65°) and the distribution was non-uniform for 18 out of 33 sample trees (Fig 3B). The largest diameter branch in each tree had a similar mean orientation of 200° (Fig 3C). Future work will focus on 1) the influence of inter-tree competition on branch distribution around the stem, 2) testing the applicability of the two-filter method to other species and growing conditions, and 3) increasing data processing speed using automated knot detection and measurement algorithms (Longuetaud et al. 2012). LITERATURE CITED Barthélémy D, Édelin C, Hallé F. 1989. Architectural concepts for tropical trees. In Tropical forest. Botanical dynamics, speciation and diversity. Edited by L.B. Holm-Nielsen, I.C. Nielsen, and H. Balslev. Academic Press, London. pp. 89–100. Bégin C, Filion L. 1999. Black spruce (Picea mariana) architecture. Botany 77: 664–672. Colin F, Houllier F. 1991. Branchiness of Norway spruce in north-eastern France - Modeling vertical trends in maximum nodal branch size. Ann For Sci 48: 679–693. De Reffye P, Houllier F, Blaise F, Barthelemy D, Dauzat J, Auclair D. 1995. A model simulating above-and below- ground tree architecture with agroforestry applications. Agroforest Syst 30: 175–197. Duchateau E, Longuetaud F, Mothe F, Ung C-H, Auty D, Achim A. 2013. Modelling knot morphology as a function of external tree and branch attributes. Can J For Res 10.1139/cjfr-2012-0365. Fourcaud T, Zhang X, Stokes A, Lambers H, Körner C. 2008. Plant growth modelling and applications: the increasing importance of plant architecture in growth models. Ann Bot-London 101: 1053-1063. Jammalamadaka SR, Sengupta A 2001. Topics in circular statistics. World Scientific Pub Co Inc. Longuetaud, F., Mothe, F., Kerautret, B., Krähenbühl, A., Hory, L., Leban, J.M., and Debled-Rennesson, I. 2012. Automatic knot detection and measurements from X-ray CT images of wood: A review and validation of an improved algorithm on softwood samples. Comput Electron Agr 85: 77-89. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 52 tLiDAR methodologies can overcome limitations in estimating forest canopy LAI from conventional hemispherical photograph analyses Eric Casella1, Mat Disney2, James Morison1 & Helen McKay1 1Centre for Sustainable Forestry and Climate Change, Forest Research, Farnham, Surrey, GU10 4LH, UK 2Department of Geography, University College London, London, WC1E 6BT, UK Correspondence: Eric.Casella@forestry.gsi.gov.uk Highlights: The hemispherical photography technique has been widely used to assess the three-dimensional reconstruction quality of virtual plant canopy architectures (Casella & Sinoquet 2003). High-resolution terrestrial Light Detection And Ranging (tLiDAR) has recently been applied for measuring the 3-D characteristics of forest vegetation (Omasa et al. 2006.) and specifically the extraction of canopy directional gap fraction (Danson et al. 2007). In contrast with the digital hemispherical photography method, sky conditions appear to have little influence on the quality of the data collected by the tLiDAR technique. This study considers the resolution used during both point cloud data acquisition and the computation of equiangular hemispherical images, which may influence the resolving power of this technique in estimating gaps in a forest environment. Keywords: TLS, laser, point cloud, gap fraction, equiangular projection, composite hemispherical picture, resolution INTRODUCTION Leaf area index (LAI) is defined as the one-sided leaf blade area per unit ground area. It is a key parameter in ecophysiology for scaling-up from leaf to canopy level gas exchange and energy fluxes between the vegetation and the atmosphere. LAI is one of the most difficult parameter to quantify in situ although many non- destructive methods have been proposed (Bréda 2003). The upward-looking hemispherical photography technique has been used extensively to map and quantify canopy gaps for LAI computation. However, photographs must be taken under uniform overcast sky conditions and image analyses involve complex and critical steps for pixel classification between sky and canopy components despite recent increases in the resolution of digital cameras. Terrestrial laser scanners (TLS) have the potential to provide detailed information about forest canopy architecture by collecting 3-D point clouds of several million data points (Tab. 1) that can be transformed into hemispherical images by an equiangular projection procedure (Steyn 1980). However, the resolving power of this technique in estimating gaps in a forest environment may be affected by the resolution used during both point cloud data acquisition and the computation of hemispherical images as shown in Figure 1. Fig. 1. Modelled mean number of laser return hits per pixel in each 5o zenith band from hemispherical images generated by an equiangular transform projection procedure (Fig. 2.) of a x, y, z coordinate data set computed from an opaque hemisphere for the Low (), Medium (), High () and Ultra-high () TLS resolution levels (Tab.1). METHODS The TLS used was the pulsed time-of-flight HDS 6100 (Leica Geosystems Ltd.) which has a rotating mirror system that covers a 360º (horizontal) x 310º (vertical) field of view with a range of about 79 m at 90% albedo (Tab. 1). The laser beam wavelength is 670 nm with a 3 mm spot size at its source and a 0.22 mrad beam divergence. Hemispherical photographs were taken using a Nikon Coolpix 995 camera (2.25 M pixel) with the Nikon FC-E8 hemispherical lens. Spatially and temporally coincident point-cloud data and digital hemispherical photographs were collected in a six-year-old stand of Eucalyptus spp. in southeast England. The stem density was 700 trees ha- 1, with an average tree height of 11±3 m. For each position (n=8) and for scan zenith angles of 0-90º, one point-cloud was recorded at each of the four predefined resolution levels of the TLS (Tab. 1). 53 Tab. 1. Characteristics of the Leica HDS-6100 TLS used in this study for point cloud acquisitions. Pre-set scanner resolution levels Low (L) Medium (M) High (H) Ultra-high (U) Angular sampling resolution (º) 0.072 0.036 0.018 0.009 Point spacing at 50 m (m) 0.063 0.032 0.016 0.008 Maximum point cloud size (M points) 6.255 25.01 100.02 400.04 Acquisition time (minute) 3.6 6.8 13.4 25.2 An equiangular projection procedure (Fig. 2) was used to transform each point cloud into 2.25, 9, 36 or 144 M pixel hemispherical images. Hemispherical photographs and images were processed with the HemiView program. Lens correction factors were applied after classifying the photographs using the CANEYE software. For each image, sky-maps were constructed by dividing the sky into an array of 18 annuli of equal zenith angle. Fig. 2. Illustration of the Cartesian-spherical (top) and spherical-planar (bottom) equiangular transform projection procedures used to generate hemispherical images from the x, y, z coordinate TLS data. O is the TLS location and d is the distances from the laser beam source to a plant component hit. ϕ is the elevation angle and r = 2ro(90-ϕ)/π. Fig. 3. Examples of computer-generated hemispherical images at 2.25 M pixel from the x, y, z coordinate TLS data (position #1) for the Low (L), Medium (M), High (H) and Ultra-high (U) TLS resolution levels. Colours represent the distance from the laser source to a plant component hit. RESULTS AND DISCUSSION Neither the range of the TLS, nor the sky conditions have any influence on the quality of the data collected (results not shown), but the quality of the reconstructed hemispherical images was gradually improved with: i) increasing levels in TLS resolution (Figs. 3 & 4); ii) increasing the resolution of the hemispherical image (Fig. 4). Alterations in the shape of the gap fraction distributions were explained by gradual increases in levels of non-return signal from the vegetation with increases in zenith angle values (Fig. 5). This loss of return signal was mainly explained by the effect of laser beam scattering around the edges of plant components (results not shown). Therefore, the reconstruction method of the hemispherical images has been modified by taking into account this limitation in the resolving power of the technique as presented in Fig. 1. As a result, composite hemispherical images have been recomputed from the Ultra-high x, y, z coordinate data, showing gradual decreases in their resolution i.e., from 144 M pixel at the zenith to 2.25 M pixel at the horizon (Fig. 6). 54 Fig. 4. Estimated gap fraction values in each 5o zenith band from hemispherical images (2.25, 9, 36 or 144 M pixel) generated by the equiangular transform projection procedures of the x, y, z coordinate TLS data for position #1. Same symbols as in Fig. 1. Fig. 5. Mean relative numbers of missing pixels per image and missing laser return hits per pixel in each 5o zenith band. Fig. 6. Example of a composite hemispherical image computer-generated from the x, y, z coordinate TLS data for position #1. Computed at the entire sky-map level, estimated gap fraction and plant area index (PAI) values from the hemispherical photographs were close to those estimated from the images (Fig. 7), especially when using the composite method (Fig. 6). Fig. 7. Comparison between gap fraction values and plant area index (PAI) estimated from the hemispherical images (, 2.25 M pixel for the Ultra-high TLS resolution level; , using the composite method) and the photographs over the entire sky-map. Each data point represents a different location within the stand. CONCLUSION The tLiDAR technique will be central to developments in acquiring canopy geometric characteristics in the future, especially for computations of solar radiation indices. Avoiding the problem of loss of return signal, the technique explained here shows promise in overcoming the discrepancies in cross-validation between direct and indirect methods for assessing canopy LAI (Bréda 2003). No effects of laser beam divergence on gap detection have been detected in this study, but further experimentation will be required to assess the influence of wind on the quality of the data collected as high scanning resolutions take longer. Casella E, Sinoquet H. 2003. A method for describing the canopy architecture of coppice poplar with allometric relationships. Tree Physiology 23:1153-1170. Omasa K, Hosoi F, Konishi A. 2006. 3D lidar imaging for detecting and understanding plant responses and canopy structure. Journal of Experimental Botany 58:881-898. Danson FM, Hetherington D, Morsdorf F, Koetz B, Allgöwer B. 2007. Forest canopy gap fraction from terrestrial laser scanning. IEEE Geosciences and Remote Sensing Letters 4. Bréda NJJ. 2003. Ground-based measurements of leaf area index: a review of methods, instruments and current controversies. Journal of Experimental Botany 54:2403-2417. Steyn DG. 1980. The calculation of view factors from fisheye-lens photographs: Research note. Atmosphere-Ocean 18:254- 258. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 55 Shape reconstruction of fruit tree from colored 3D point cloud Shenglian Lu, Xinyu Guo, Chunjiang Zhao, Weiliang Wen, Jianjun Du Beijing Research Center for Information Technology in Agriculture, Beijing 100097, China *correspondence: lusl@nercita.org.cn Highlights: An automatic and accurate method was presented for structure reconstruction of fruit tree from laser scanner measured colored point cloud. The color characteristics of different organs were selected as rules to segment point cloud into small point cloud. A skeleton of the tree was then extracted from some small point clouds, and final 3D reconstruction was achieved by combining some distribution model of leaf and shoot. Key words: 3D Reconstruction, fruit tree, 3D point cloud, modeling plant structure INTRODUCTION Rapid and automatic reconstruction of plant structure is an interesting and challenging topic both in computer graphics and agronomic research. In most applications of 3D modeling for fruit tree, an entire and detailed mesh model is expected to enable potentially further application (e.g. calculating light intersection of canopy, demonstrating the difference between varieties and outside appearance). As such popular methods for modeling plant structure (e.g., L-systems, functional-structural model and interactive design method) will meet difficulties in reconstructing a 3D model of fruit tree with a satisfying accuracy for these kind applications, recently digitizing data from real objects have been used extensively for creating 3D models, and more methods reproduce virtual 3D plant models from real measured data. Electromagnetic digitizers were used earlier to measure the spatial position and orientation of stems and leaves for giving a quantitative assessment to the tree geometry (Sinoquet and Rivet, 1997; Sonohat et al., 2006) However, it is a tedious and time-consuming job in digitizing tree structure by using electromagnetic digitizers, and often not precise enough for accurately capture the detailed organ geometry. Recently non-contact laser scanners have been used for various plant measurement and reconstruction (Kaminuma, et al., 2004; Dornbusch, et al., 2007). Laser scanners enable us to rapidly quantify the surface of an object as a dense set of points. But if an organ or part of the plant is invisible to the scanner, its information will be missed in the captured point cloud. The missing information can be estimated by using existing or statistic knowledge about morphological structure of plants (Xu, et al., 2007). But this will lose accuracy for the measured plant. So these methods are more suitable for digital entertainment rather than agronomic research. In this paper, we aim to provide a method for automatic and accurate reconstructing the structure of fruit tree from laser scanner measured colored point cloud, and demonstrate some experimental results. MATERIALS AND METHODS A 10-year-old pear tree was chosen for data measurement at its fruiting stage. And a large range laser scanner (Focus3D 120, FARO Technologies, Inc.) was used to finish the measurement. Three stations scanning around the tree were made to obtain enough points for later reconstruction (see Fig. 1. left). Fig. 1. Scanning pear tree by using FARO Laser Scanner Focus3D(left:); the measured colored point cloud(right). 56 Software FARO SCENE 5.0 (www.faro.com) was used to process the multi-station scanned data, which produce the 3D point cloud of the tree from these measured data. Each point also brings a RGB color as such we get a colored point cloud (see Fig. 1. right). We also use this software to remove noise points manually (coming from the ground and other trees) in the colored point cloud interactively. SHAPE RECONSTRUCTION The shape reconstruction process includes five steps. Firstly a pre-process was done to the point cloud because there are too many points in the origin scanned points (especially coming from leaves, see Fig.1 Right). A distance based noise points deleting method was used to remove noise points, and this could result in a simplified point cloud. The second step was to segment the point cloud into several small organ point clouds. In other words we wish to separate different organs from the point cloud of the canned tree. We found that the color of each organ in pear tree is very different to other organs’ , as such we can distinguish each organ from the point cloud by using its color feature. Firstly organs of pear tree were classified three categories (leaf, fruit, trunk and branch respectively). Then we calculated the color character of each category by selecting manually 20 points from the point cloud of this kind organ and computing average color value (RGB) of these selected points. The resulted average color value was used as the color character of this kind organ. After all color character of were calculated, a checking process was conducted to the simplified point cloud to check the nearest color character for each point basing on its color. The point cloud was then segment into three small organ point clouds. Fig.2 (left) shows the trunk and branch point cloud. A lot of data-missing could be found resulted from shelter of leaves. In the next step we target to extract a skeleton of the tree directly from the trunk and branch point cloud. A constrained Laplacian smoothing method (Su et al., 2011) was used to extract the skeleton. Then we generated a skeleton model (see Fig.2 right) from the extracted . Some knowledge about the morphological structure of pear tree were used in this step to improve the skeleton because there are many discontinuous branches in the extracted skeleton. For example, some branches may be apart from the trunk, and one branch may be divided into several segments in the initial extracted skeleton, and these branches need to be connected to form a smooth skeleton of tree. Fig. 2. The trunk and branch point cloud (left); projection vector of internodes (right). The fourth step was to calculate the information of fruits from the fruit point cloud. A distance-based cluster algorithm was used to further divide the fruit point cloud into small point clouds. And each small point cloud represents a fruit and all points in this point cloud coming from the same fruit. Then the center coordinate of a fruit point cloud was calculated, which would be used as the position of the fruit in the final reconstruction step. The radius of a fruit was also calculated from its point cloud data. Based on the extracted skeleton and fruit information, we finished the entire reconstruction of the scanned tree. But the little shoots and leaves were still missing in the extracted skeleton, which need to be restored for a complete reconstruction. Currently we addressed this problem by using a knowledge-driven strategy which could repair the missing little shoots and leaves. Concretely, we used distribution models about shoots and leaves based on how locating on different types of branches, which supplys little shoots and leaf model for the extracted skeleton model. In which a leaf model was a mesh surface measured from the real fruit tree by using a hand-held laser scanner. 57 RESULTS AND DISCUSSION A pear tree has been reconstructed by proposed method, in which the number of fruit, the conposition and radius of each fruit all were calculated at the fourth step. Five leaf models (with texture mapping) were used in the reconstruction to achieve a more realistic results(see Fig.3). The automatic 3D reconstruction of a whole plant from laser scanned data points is presently still an open problem.Currently we just use some knowledge about leaf distribution on the canopy to orient the reconstruction, instead of using the scanned leaf point cloud, since it is a very difficult task to restore the 3D surface of leaves directly from the scanned leaf point cloud. And our further study expect to remove errors which may be caused by knowledge-oriented method. Fig. 3. The shape reconstructed result of the pear tree Acknowledgments. This work is supported by China National Science and Technology Support Program (No. 2012BAD35B01) and Beijing Science and Technology Project of China (No. D111100001011002). LITERATURE CITED Sinoquet H, Rivet P. 1997. Measurement and visualisation of the architecture of an adult tree based on a three- dimensional digitising device, Trees: Structure and Function. 11,265-270. Sonohat G, Sinoquet H, Kulandaivelu V, Combes D, Lescourret F. 2006. Three-dimensional reconstruction of partially 3D digitised peach tree canopies, Tree Physiology. 26:337-351. Kaminuma E, Heida N, Tsumoto Y, Yamamoto N, Goto N. 2004. Automatic quantification of morphological traits via three-dimensional measurement of Arabidopsis. The Plant Journal. 38:358–365 Dornbusch T, Wernecke P, Diepenbrock W. 2007. A method to extract morphological traits of plant organs from 3D point clouds as a database for an architectural plant model. Ecological Modelling. 200: 119–129. Xu H, Gossett N, Chen B. 2007. Knowledge and heuristic-based modeling of laser-scanned trees. ACM Transaction On Graphic. 26(4):19 Su Z, Zhao Y, Zhao C, Guo X, Li Z. 2011 Skeleton extraction for tree models. Mathematical and Computer Modelling，54: 1115–1120. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 58 Optimal 3D reconstruction of plants canopy from terrestrial laser scanner data by fusion of the 3D point information and the intensity value Mathilde Balduzzi1*, Frédéric Boudon2 and Christophe Godin1 1INRIA/2CIRAD, Virtual Plants INRIA Team, UMR AGAP, 95 rue la Galéra, 34095 Montpellier, France *correspondence: mathilde.balduzzi@inria.fr Highlights: We develop an algorithm to digitize in situ canopy and to tag automatically each of its leaves. This algorithm fuses the distance information and the intensity values of a terrestrial LiDAR scanner. Keywords: Terrestrial LiDAR, leaves geometry, LiDAR intensity, shape-from-shading, Kalman filter INTRODUCTION Terrestrial LiDAR scanner (TLS) provides a novel tool for generating in a high measurement rate an accurate and comprehensive 3D geometrical description of the canopy. This device sends a laser beam and gives a precise estimation of the distance to the object surface with which it interacts. Combined with a zenithal and an azimuth rotation, it creates a virtual scene of its surrounding in the form of a TLS point cloud. It became a common metrology tool in several domains and draw itself plant scientists’ attention. Despite the good accuracy of the measurement (estimation errors less than a few millimeters for most TLS in the measured range), only general indicators such as LAI, vertical plant profile and vegetative volume have been extracted (e.g. Rossel et al., 2009). These indicators are frequently used in physical models for canopy/environment interaction, such as light interception models (Sinoquet et al. 2005). However, these models rely on constraining hypothesis such as homogeneous distribution of leaves, infinitely small leaf elements, etc. In many applications, these assumptions simply do not hold and the condition of use of these models is therefore invalid. As an alternative, TLS can be used to reconstruct realistic foliage geometry that can be subsequently used in realistic physic-based models. Several techniques based on surface fitting have been developed to digitized isolated leaves (Loch et al. 2005, Quan et al. 2006, Chambelland et al. 2008). They rely on user intervention and remain tedious for entire canopy reconstruction. In addition, they do not deal with outliers points present on leaves edges (Hebert & Krotkov 1992) and they suppose a high signal-to-noise ratio (i.e. variability due to the size of the object vs. variability of the noise), which is not always possible for field measurements. The goal of this study is to digitize an entire canopy from laser TLS data so that the noise impact on the leaves reconstruction and segmentation is minimized. For this, we exploit the intensity information provided by the TLS. This information depends on the local inclination of the measured surface and thus provides complementary information to the distance measured by the scanner. Thanks to this information we could design a method for segmenting and reconstructing leaves geometry accurately from canopy scans. Leaf segmentation combines the intensity and distance information to detect outliers point, while leaf 3D reconstruction is made from intensity information using a propagation approach based on Shape-From- Shading (Durou et al. 2004). This reconstruction is progressively fused with the distance information using a Kalman filter to optimally merge both information from both sources (intensity and distance). METHODS In general, the intensity of pixels in an image is correlated to incidence angle of the light beam with the surface of the object at that point. Based on this information it is thus possible to design methods to reconstruct the local geometry of the scanned objects, i.e. the leaves. However, we have to face two main issues: i) the distance has an effect on the intensity amplitude and must be corrected; ii) The algorithm to reconstruct surfaces from the intensity must be able to integrate distance information. To solve i), Balduzzi et al. (2011) have proven that the distance effect on intensity could be corrected and that a relationship between the incidence angle α and the intensity I can be built for a given leaf material. To 59 solve point ii), an algorithm of shape-from-shading (Durou et al. 2004) is developed. This algorithm proceeds by spatial propagation of an initial surface solution patch. Decisions to segment the reconstructed surface (here leaves) are taken during the reconstruction propagation. To set it up, we proved several mathematical properties, in particular that: 1) the propagation can be done along the greatest slope direction on an iso-intensity region; 2) those directions can be computed from any 3D curves belonging on the surface when the incidence angle information is provided; and 3) the surfaces generated by those greatest slope line are specific surfaces called the sand-pile surfaces. Fig 1. Algorithm flowchart for the surface reconstruction. Thanks to those previous properties, the following pipeline has been set up (figure 1): a) After the correction of the distance effect and the initialization of the I to α relationship, the intensity picture is smoothed out to make iso-intensity contours apparent. b) Those contours are hierarchized to drive the propagation: the iso-intensity contours of highest value (maxima) will be the seeds of the propagation carried out along the iso-intensity contour hierarchy. c) 1: The distance values of the seeds are initialized thanks to the point cloud. It is the initial boundary of the reconstructed surface. 2: At the same time, the analysis of these boundary geometries (e.g. sink or saddle case) makes it possible to disambiguate the positive (up) or negative (down) local orientation of the surface. d) 1: The greatest slope directions are computed along the boundary of the reconstructed surface to start or to continue the propagation. 2: Simultaneously, we estimate the greatest slopes direction thanks to the point cloud. 3: The comparison of the two greatest slope calculations gives estimation on the confidence we can have on both. A Kalman filter is used to fuse them depending on this confidence. e) 1: Sand-pile surfaces fill the space in between two isophotes, i.e. the surface portion that corresponds to iso-intensity region; and between two consecutive greatest slopes. 2: The incidence angle α is estimated on the corresponding point cloud portion. 3: As for d.2), we obtain an indication on the confidence we can have on both calculation. This indicator is used to make decision on the segmentation. f) Finally, the propagation continues on the new reconstructed surface boundary (step d1) until the surface is entirely segmented. Our algorithm is able to reconstruct and to segment step by step a surface from its intensity picture and its 3D point cloud. The uncertainties on distance and intensity are minimized using a Kalman filter. PRELIMINARY RESULTS To test the algorithm, we have generated several virtual surfaces. The greatest slope retrieving and the propagation are robust even if we can note that the accuracy of the reconstruction is a function of the 60 intensity and may be significant as the incidence angle approaches 90°. Figure 2 iii) shows the reconstruction of a virtual ellipsoid when both of its picture and point cloud are given (fig 2. i and ii). In this talk, we will present leaves reconstruction and segmentation in the case of real scans (figure 3). ACKNOWLEDGEMENT This work is supported by the Labex NUMEV and the project Plantscan3D from the Agropolis Foundation. Fig 2. Reconstruction of a virtual ellipsoid. i) Its intensity picture and the iso-intensity curves (colored); ii) the initial 3D point cloud; iii) the reconstruction. Fig 3. Illustration of the reconstruction algorithm. a) We focus on a single leaf of a pear tree canopy; b) the intensity picture is smoothed to make the iso-intensity region appearing; c) the iso-intensity contour are extracted and hierarchized; d) the iso-intensity region of maximal value is taken as the propagation seed; f) the greatest slope are propagated and the leaf is segmented. LITERATURE CITED Rossel JR, Sanz R, Llorenz J, Arno J, Escola A, Ribes-Dasi M, Masip J, Camp F, Gracia F, Solanelles F, Palleja T, Val L, Planas S, Gil E, Palacin J. 2009. A tractor-mounted scanning LiDAR for the non-destructive measurement of vegetative volume and surface area of tree-row plantations: A comparison with conventional destructive measurements. Biosyst. Eng.102: 128-134. Sinoquet H, Sonohat G, Phattaralerphong J, Godin C. 2005. Foliage randomness and light interception in 3D digitized trees: an analysis from multiscale discretization of the canopy. Plant, Cell and Env. 28: 1158-1170 Chambelland JC, Dassot M, Adam B, Donès N, Balandier P, Marquier A, Saudreau M, Sonohat G, Sinoquet H. 2008. A double-digitizing method for building 3D virtual trees with non-planar leaves: Application to the morphology and light-capture properties of young beech trees (Fagus sylvatica). Funct. Plant Biol. 35: 1059-1069. Loch, B. I. and Belward, J. A. and Hanan, J. S. 2005. Application of surface fitting techniques for the representation of leaf surfaces. In: MODSIM05: International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, 12-15 Dec 2005, Melbourne, Australia. Quan, L., Tan, P., Zeng, G., Yuan, L., Wang, J., & Kang, S. B. 2006. Image-based plant modeling. ACM Transactions on Graphics (TOG). 25-3: 599-604. Hebert M, Krotkov E. 1992. 3D measurements from imaging laser radars: How good are they? Image Vision Comput. 10: 170-178. Balduzzi MAF, Van der Zande D, Stuckens J, Verstraeten WW, Coppin P. 2011. The properties of terrestrial laser system intensity for measuring leaf geometries: a case study with conference pear trees (Pyrus Communis). Sensors 11: 1657-1681. Durou JD, Falcone M, Sagona M. 2004. A survey of numerical methods for shape from shading. Rapport de recherche IRIT N°2004-2-R. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 61 Bayes trees and forests: combining precise empirical and theoretical tree models Mikko Kaasalainen1*, Ilya Potapov1, Pasi Raumonen1, Markku Åkerblom1, Risto Sievänen2 and Sanna Kaasalainen3 1Department of Mathematics, Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland 2Finnish Forest Research Institute, Vantaa Research Unit, PL 18, FI-01301, Vantaa, Finland 3Department of Remote Sensing and Photogrammetry, Finnish Geodetic Institute, Geodeetinrinne 2, FI- 02431 Masala, Finland *correspondence: mikko.kaasalainen [at] tut.fi Highlights: With the new analysis methods for TLS scans, there will be a growing and improving database of 3D descriptions of trees and forest stands. The attributes determining these descriptions can be represented as Bayesian probability distributions, with functional-structural models providing the prior information. These distributions can then be used to create versions of new realistic Bayes forests, where none of the trees are copied from data, but the structure of each is drawn from the data-based distributions. Repeated TLS measurements add a fourth dimension, time, to the mathematical modelling; in this way, we can simulate functional 4D Bayes forests. As in the modelling of the 3D structure, forest models and regularities of growth and mortality are used as prior information; conversely, the accumulating data and modelling results improve the theoretical models. Keywords: Tree models: empirical, tree models: theoretical, TLS, Bayesian inference INTRODUCTION A general method, based on terrestrial laser scanning (TLS) data, has recently been developed for producing precise 3D tree surface models that are automatic and fast to compute and record the topological and geometric properties of the tree (Raumonen et al. 2013 and this meeting). One of the core ideas behind the method is that practically any external attribute of a tree can be approximated accurately at will from a compact surface model of this type. Once we have determined the models of a representative number of trees at different sites, we can construct well-defined statistical attributes from these as functions of species, age, etc. On forest stand level, we record the typical distribution of trees. Once the distribution functions (DFs) of tapering, branching frequency, branching angles, branch curving, tree positions, etc. have been defined, we can carry out a reversed process. Now we can draw new samples from these DFs and use them to construct new trees and forests with similar statistics; i.e., 3D and 4D Bayes forests. In this process, we can use our prior knowledge of functional-structural (FS) tree models to ensure biological consistency. This can be carried out via the Bayesian approach to obtain a posterior distribution. The process can also be used to improve the theoretical models by detailed, precise, and comprehensive measurements. PROBABILISTIC TREE MODELS In the broadest sense, a tree (or, ultimately, a forest) can be described as a probabilistic entity. Its form and structure, specified by some parameters x=(x1,...,xN), has a probability p(x;u) in some measurement space spanned by u. Some components of u might describe, e.g., the local width h of a branch and its 3D direction d along its length s, resulting in a four-dimensional subspace (h,d,s) of the u-space. From a large number of scanned and analyzed trees, we can determine an experimental pS(x) for a given species (possibly with different p-functions for different age groups or other identifiers, or by including them as components of x). On the other hand, we can determine a theoretical pM(x) from a large ensemble of functional-structural models. In our representation, two trees that are not clones of each other but have the same p (i.e., x) are identical in the mathematical sense. We note here that, formally, two isolated stochastic FS models that have the same initial parameters do not necessarily produce identical 3D DFs at later stages due to self-shadowing that takes different evolutionary routes depending on the random choices during growth. In practice, identical environmental factors mostly produce statistically similar trees of the same species. 62 The tree probability p(x) can comprise a number of sub-probabilities. A probability may be a product of independent, lower-dimensional probability functions. These can be purely morphological; e.g., of the form 𝑝({𝑥𝑖};𝒅,ℎ, 𝑠) = 𝑝[{𝑥𝑖}; {𝒅𝑖(𝑠)}, {ℎ𝑖(𝑠)}, 𝑠] , where {di(s)} and {hi(s)} are sets of some basis functions modified by the set of parameters {xi}. On the other hand, the sub-probabilities can describe stochastic processes, which is the natural way of describing the growth of a tree. The sub-probabilities are then Markovian in character, specifying the probability of a length element to differ from the previous one in various ways (with either independent or joint attributes; i.e., one- or multidimensional probabilities). The elements are similar in both the observational and theoretical models; e.g., cylindrical in our basic laser- scanning model and the LIGNUM FS model (Sievänen et al. 2008). For example, ∆d can be taken to describe the difference between d of two adjacent elements. Then the probability distribution of this difference would be given by a p(∆d). A model for p linear in some parameters (xi,...,xj) is of the form 𝑝�𝑥𝑖 , … , 𝑥𝑗;∆𝒅� = � 𝑥𝑘𝑓𝑘(∆𝒅)𝑗 𝑘=𝑖 , where fk(∆d) are some given basis functions. Another linear possibility is to discretize the ∆d-space into bins whose occupation probabilities are given by xk. The problem of determining the probabilities or statistical profiles p(x) from either empirical data or synthetic models is that of determing the underlying distribution function from a set of samples (Kaasalainen 2008). This can be carried out, in the sense of the Radon transform, by least-squares fitting the parameters x such that the cumulative marginal distributions (CDFs) of p(x;u) in various directions in the measurement space of u best match the corresponding CDF values y defined by the given set of sampled u. In the case of linear models such as the p(∆d) above, this is a linear least-squares problem of the matrix form y=Ax. Once we have determined a DF, we can resample it to create statistically equivalent new trees at will (Fig. 1). This is simple for the one-dimensional case via its cumulative DF; for multi-dimensional DFs we can use sprinkle algorithms (Kaasalainen 2008) or Markov Chain Monte Carlo methods. BAYESIAN MODELS Next, we introduce the concept of a Bayesian tree (or forest). To make the experimental and theoretical tree statistics pS and pM compatible in the Bayesian sense, we write a probability distribution that can smoothly incorporate any given degree of prior information from pM. The desired posterior distribution can be obtained by a metaprobabilistic approach: we define the probability P of a tree to have a certain kind of statistical profile p represented by the parameters x. Thus, the Bayesian principle yields 𝑃(𝒙) ∝ 𝑃𝑆(𝒙)𝑃𝑀(𝒙) (without normalization as we are only interested in the shape of P(x) in x-space). The role of PM(x) is defined by some "tightening" or weight parameters that can be separate for each xi. For zero weights, PM(x) is unity; i.e., a uniform distribution without any prior preferences for x. For weights approaching infinity, PM(x) approaches the Dirac-delta distribution around its centre point x0. If the models describing the DFs are linear in the parameters x in the form y=Ax above, we obtain a simple formula for the centre point or the maximum a posteriori estimate 𝒙� of the final distribution P(x), if it as well as the distributions PM(x) and PS(x) are taken to be Gaussian: 𝒙� = 𝑄−1(𝐸0−1𝒙0 + 𝐴𝑇𝐸1−1𝒚); 𝑄 = (𝐸0−1 + 𝐴𝑇𝐸1−1𝐴), where E0 and E1 are, respectively, the covariance matrices of PM(x) and PS(x). The smaller their (diagonal) elements are, the more tightly the marginal probabilities of the components of x are constrained. We can describe the probabilities in both 3D and 4D. In the 3D-case, we consider a snapshot of a tree, specifying its momentary form. The straightforward DF product approach above is then simplest to apply to essentially isolated trees. In the time-dependent 4D-case, we examine the history of trees; i.e., the shape probability as a function of time. The probabilities are then determined by a number of stochastic as well as deterministic processes. This is necessary especially for Bayes forests, where the collective history (competition etc.) should be taken into account. The growth rules of FS models, for example, are then rendered as prior DFs. The theoretical FS models not only serve as prior probabilities in the Bayesian sense; they also help to design the parameter space in which we describe the probabilities. To create prior DFs from 63 FS models, we can use stochastic FS processes and deterministic FS models with stochastic conditions initially and during the growth. The Bayesian approach stabilizes the synthetic realizations of TLS-based DFs by, e.g., removing unrealistic outliers or biases due to selection effects in data. The FS models are also used to determine the best ways to select and express the actual tree attributes we should use in our virtual modelling. On the other hand, experimental data help to improve theoretical models. Figure 1. Left: a 2D-plot of the measured second-order branch statistics of one tree. Right: a closeup of the basic geometry (location, direction, and width) of synthetic branch generation by drawing samples from DFs corresponding to the data. MEASUREMENTS The development of a Bayes forest model requires continuous assimilation of measured data to the system. We measure and collect new TLS and other information from forests, including hyperspectral lidar (HSL) data for augmenting the structure data by information on source material and condition (Hakala et al. 2012). The sample sites and trees are chosen to acquire representative quantities, and to test a number of statistical hypotheses. For example, to which degree do the parameters x of presumably similar trees correlate? What are the typical deviations given by the experimental covariance matrix E1? How much prior information needs to be introduced in practice? FS models and observations are used to determine the most appropriate parameter space for x and the measurement space for u best representing the various attributes of trees, including branch hierarchies. The preliminary results are reported in this meeting. In 4D Bayes forest modelling, the DFs of the 3D Bayes forest have the additional dimension of time, based on the repeated observations of sample trees. Consequently, the realizations of these DFs for each Bayes forest include behaviour in time: litter production, growth, etc. As in the 3D Bayes forest, the prior constraints from the process-based studies (incorporated in LIGNUM) are important. A number of process descriptions are used as prior information sources taking into account the effects of, e.g., the competition for light, space, and resources. This information can be incorporated into the Bayes-forest model as, e.g., spatial competition indices and simple carbon-balance rules of foliage. With the biologically consistent prior components, the end product is a statistically and biologically realistic model of a forest and its processes in time. LITERATURE CITED Hakala T, Suomalainen J, Kaasalainen S, Chen Y. 2012. Full Waveform Hyperspectral LiDAR for Terrestrial Laser Scanning. Optics Express. 20: 7119-7127. Kaasalainen M. 2008. Dynamical tomography of gravitationally bound systems. Inverse Problems and Imaging. 2: 527-549. Raumonen P, Kaasalainen M, Åkerblom M, Kaasalainen S, Kaartinen H, Vastaranta M, Holopainen M, Disney M, Lewis P. 2013. Fast Automatic Precision Tree Models from Terrestrial Laser Scanner Data. Remote Sensing. 5: 491-520. Sievänen R, Perttunen J, Nikinmaa E, Kaitaniemi P. 2008. Toward extension of a single tree functional structural model of Scots pine to stand level: effect of the canopy of randomly distributed, identical trees on development of tree structure. Functional Plant Biology. 35: 964-975. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 64 Quantitative assessment of automatic reconstructions of branching systems Frédéric Boudon1, Chakkrit Preuksakarn2,4, Pascal Ferraro5, Julien Diener3, Eero Nikinmaa6 and Christophe Godin2 1CIRAD/2INRIA/3INRA Virtual Plants Team, UMR AGAP, C.C. 06002, 95 rue de la Galera,34095 Montpellier, France, 4Kasetsart University, Kamphaeng Saen Campus, Thailand, 5CNRS LABRI, University of Bordeaux, France, 6University of Helsinki, Finland *correspondence: frederic.boudon@cirad.fr Highlights: In this work, we propose a method to evaluate and compare different reconstruction methods from laser data using expert reconstruction and a new structural distance. Keywords: Structural comparison, plant architecture, laser data INTRODUCTION In the context of biology and agronomy, acquisition of accurate models of real plants is still a tedious task and a major bottleneck for the construction of quantitative models of plant development. Recently, 3D laser scanners have made it possible to acquire 3D images representing a sampling of the surfaces of objects. To process such new type of data, dedicated reconstruction methods were developed. Although successful in most applications such as urban geometry, these methods fail on plants structures as they usually contain a complex set of irregular and branching surfaces distributed in space with varying orientations. A number of specific methods have been proposed to reconstruct plausible branching structures from laser data. The first noticeable method was proposed by Xu et al. (2007) that extends the approach of Verroust and Lazarus (2000) to reconstruct branching structures. In their approach, points from the scans are first connected to their k closest neighbours to form a graph. The distance between any points can then be defined as the length of the shortest path between these points on the graph. The graph is then segmented into clusters of points according to the distance to a root point. The centres of clusters are then used to generate the skeleton of the tree. Alternatively, Livny et al. (2010) proposed to use a series of global optimisations to reconstruct major skeletal branches. Starting from the graph of shortest paths, long paths are favoured and used to align and prune the points. Remaining paths form the skeleton of the tree. Finally, the concept of space colonisation was introduced by Runions et al. (2007) and consists of guiding a simulated growing tree process with a set of points that represent the volume of the plant. It was first exploited by Coté et al. (2009) to generate realistic foliage of a tree from laser scans. Preuksakarn et al. (2010) extend this idea to follow precisely the point patterns of the scans to reconstruct the skeleton of trees. While these methods produce realistic structures as shown by Fig. 1, no method to compare them quantitatively or evaluate their respective accuracy has been proposed so far. Such evaluation is of major importance for further exploitation of reconstructed models in biological applications. In this work, we address the problem of evaluating the accuracy of reconstructed structures from laser scanner data. For this, we first present a software tool that allows experts to define reconstruction from the point cloud. Using these expert-defined structures that will be considered as reference, we then propose different indices and algorithmic methods to quantify the similarities and differences between automatically reconstructed and reference structures. Such indices make it possible to compare the reconstructions made with the different methods proposed in the literature. MATERIALS In this study, we use laser scans from city trees growing in the streets of Helsinki, Finland, which were scanned with a Leica Geosystems HDS 2500 laser scanner. We also use a scan of a Cherry tree near Clermont- Ferrand, France, which was scanned with a Leica Geosystems HDS 6200 laser scanner. Trees were scanned Fig. 1. Example of a lime tree reconstruction with the method of Preuksakarn et al. (2010). Left: an original picture of the tree. Right: the reconstructed virtual model inserted into same background. 65 from 3 to 4 positions to reduce occlusion. The scanner specification gives a range of accuracy of 4 mm for the position of a point in space. To assess more precisely the effect of the resolution and the quality of the scans on the accuracy of the reconstruction, we also use a virtual model of a Walnut tree (Sinoquet et al. 97), whose structure was first manually digitized from a real tree. This mock-up was virtually scanned and different levels of noise are introduced by removing a number of points. On these data, reconstructions are performed using our implementation of methods of Xu et al. (2007), Preuksakan et al. (2010) and Livny et al. (2010). These procedures are now part of the PlantGL open source library (Pradal et al. 2009) of the OpenAlea platform. For scanned trees, reference 3D models were built by editing the skeleton resulting from an automatic tree reconstruction. For this, we designed a visual tool and asked experts to correct the automatically reconstructed structure. Experts can edit the skeletal structure of each tree by adding, deleting, repositioning or reorganizing segments in the structure. Different visualisation tools of the software make it possible to focus display of the laser points on a specific location making it possible to identify clearly the local branching configuration. The results are tree-like structures, whose nodes are associated with branch segments, and that represent the skeleton of the tree branching structure. A database of such expert-defined structures has been established. METHODS Two classes of quantitative evaluation tests can be made. The first one consists of summarizing an individual tree by a small number of global variables such as wood content, crown volume, amount of intercepted light from several directions, etc. The similarity of the models is then measured by the distance between these synthetic variables. As a first approach, the different reconstructions are compared to the reference trees with such global indices. We also compare the reconstructions with the original point sets by estimating the mean distance of the point set to the reconstructed models. While this gives a general assessment of the reconstruction quality, these indices give no information on the quality of the topology. A second class of tests consists of comparing in more detail the three-dimensional structure of the models. For this, more structural comparison tools are required. As a first test, we experimented with the edit distance proposed by Ferraro and Godin (2000). The computation of this distance consists in determining a sequence of edit operations of minimum cost which transform an initial tree T1 into a target tree T2. Three edit operations are usually considered: substituting a vertex i of T1 with a vertex j of T1, deleting a vertex i in T1 and inserting a vertex j in T2. Each operation is associated with a cost that we parameterized according to geometrical similarities between nodes. As a side-product, the set of substitutions gives a mapping between elements of T1 and T2. However, only mappings that preserve the ancestor relationship between elements of the two trees are considered by the method. As a result, a simple inversion in the branching position of elements can create important differences with this comparison method. To overcome the previous limitation, we designed a more flexible comparison pipeline that makes it possible to detect similarities between structures even in the case when connections mismatch. For this a number of algorithmic steps are performed to finally estimate two indices that reflect geometrical and structural similarities. Three main steps compose our pipeline: first, a homogenization of the scales of the tree T1 and T2 is made; second, a mapping of their nodes is determined, and finally a mapping of their edges. From these mappings, two indices are estimated. A more precise description of these different steps follows. Before comparing a test reconstruction against the reference (expert) reconstruction, a homogenization procedure has to be carried out. Indeed, the two compared tree-like skeletal structures are in general composed of different types of segments with different sizes. To address this issue, we homogenized both skeletal Fig. 2. The software tool used to create expert-defined structures from laser data. Red spheres represent nodes of the structure. Sliders make it possible to control the location and size of the laser points displayed. The user can edit the plant structure by adding, deleting, moving or changing properties of nodes. 66 structures by re-segmenting both trees in terms of inter-ramification branch segments, i.e. one-piece segments connecting two branching points. Based on the homogenized structures, the comparison of the test and reference structures could then be carried out. In 3D space, these two structures correspond to two sets of segments that may overlap partially making it difficult to find exact correspondence from the test reconstruction to the reference one. This association is often ambiguous and for each segment of the test (resp. reference) structure, one can associate a list of candidate segments in the reference (resp. test) structure. We formalize this matching as an optimization problem. Let us call T1 and T2 the reference and test tree skeletons respectively. For any two segments that can possibly be associated in T1 and T2, we quantify the distance between these two segments as the Hausdorff distance between their skeleton curves that intuitively represents the maximal deviation between the curves. During the mapping between the two structures, some element in the reference skeleton may have no counterpart in the test skeleton, and reciprocally. In this case, we say that we have respectively a deletion or an insertion with respect to the reference structure. A mapping has a cost that is defined as the sum of the costs of each individual mapping and of the deletions and insertions of nodes. The comparison of our two skeletal structures thus comes down to finding the mapping M that minimizes the cost of the mapping. To solve this assignment problem, we use an optimal flow formulation which is solved using Tarjan’s (1983) extension of Edmonds and Karp’s algorithm. In the resulting optimal mapping M*, some elements may be deleted or inserted. However, some of these insertions/deletions may simply result from the fact that several segments in one tree altogether cover a single segment in the other tree. To take this into account, a post processing step refines the mapping produced from the previous step by testing and adding mapping configurations that include multiple segments. As a result of this mapping procedure, a geometrical correspondence between elements is defined and can be quantified with the index DG= |M*| / (|T1|+|T2|). Finally, to evaluate the difference of topology between the two structures, we then inspect whether elements are connected in a similar way in their respective structures. We quantify the topological matching between the two structures with the index DT = 2* |MT| / (|E1|+|E2|), where MT is the set of preserved relationships between T1 and T2, and E1 and E2 is the set of relationships of T1 and T2, respectively. RESULTS AND DISCUSSION A comparative evaluation of tree reconstruction using different methods from the literature was performed. An illustration of such an evaluation is given in Fig. 3. A more detailed comparison will be given in the presentation, such as the performance of each method with different levels of noise in the scan. Application of our method to the evaluation of automatic reconstruction of root architecture from images will also be presented. LITERATURE CITED Xu H., Gosset N., Chen B. 2007. Knowledge and heuristic-based modeling of laser-scanned trees. ACM Transaction on Graphics 26(4) , 19. Verroust A., Lazarus F., 2000. Extracting skeletal curves from 3d scattered data. Visual Computer 16, 15–25. Livny Y., Yan F., Olson M., Chen B., Zhang H., El-Sana J. 2010. Automatic reconstruction of tree skeletal structures from point clouds. ACM Transaction on Graphics 29(6), 151. Runions A., Lane B., Prusinkiewicz P., 2007. Modeling trees with a space colonization algorithm. Proccedings of Eurographics Workshop on Natural Phenomena 2007. 63–70. Côté J.-F., Widlowski J.-L., Fournier R. A., Verstraete M. M., 2009. The structural and radiative consistency of three- dimensional tree reconstructions from terrestrial lidar. Remote Sensing of Environment 113(5), 1067 – 1081. Preuksakarn, C., Boudon, F., Ferraro, P., Durand, J.-B., Nikinmaa, E., Godin, C., 2010. Reconstructing plant architecture from 3D laser scanner data. Proceedings of the 6th International Workshop on Functional-Structural Plant Models,16-18. Sinoquet H., Rivet P., Godin C., 1997. Assessment of the three-dimensional architecture of walnut trees using digitising. Silva Fennica 31(3), 265–273. Pradal C., Boudon F., Nouguier C., Chopard J., Godin C., 2009. PlantGL: a Python-based geometric library for 3D plant modelling at different scales. Graphical Models, 71(1), 1-21. Ferraro P., Godin C., 2000. A distance measure between plant architectures. Annals of Forest Science, 57, 445-461. Method Mean Point Distance (mm) Volume (Ref: 13.17m²) DG DT Xu et al. (2007) 12.55 12.76 0.81 0.87 Livny et al. (2010) 6.49 12.7 0.69 0.65 Preuksakarn et al. (2010) 7.26 13.3 0.90 0.72 Fig. 3. Results of our comparison for lime tree reconstructions with different methods from the literature. Global indices and geometrical and structural accuracy indices are used. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 67 Rank distributions and biomass partitioning of plants Alexander Komarov1, Elena Zubkova1, Maija Salemaa2 and Raisa Mäkipää2 1Institute of Physicochemical and Biological Problems in Soil Science, Russian Academy of Sciences, 142290, Pushchino, Moscow Region, Russian Federation; 2Finnish Forest Research Institute, PO Box 18, 01301 Vantaa, Finland *correspondence: as_komarov@rambler.ru Highlights: We study how well biomass partitioning patterns of plant compartments (organs) follow mathematical rank distributions using empirical data from the tree and dwarf shrub species in temperate- boreal zone as a test material. The simplest form of a rank distribution (Zipf’s law) shows a good statistical fit to the data and its semi-empirical dependencies can successfully be applied also in a complex ecosystem models. Keywords: Zipf’s law, optimal plant organs partitioning, dwarf shrubs, trees, ranks and classification INTRODUCTION Certain statistical regularities as attributes of complex systems in the form of power laws are observed everywhere (Clause et al. 2009): these include many social and economic effects, and some applications in different branches of biology (Furusawa and Kaneko, 2003). One of the earliest applications of power laws are modelling the numbers of species in biological taxa (Willis and Jule, 1922). These regularities have common mathematical structure and can be formulated as some properties of statistical rank distributions known as Zipf’s, Pareto’s, Heaps’ and some other laws. Soukhovolsky (1996) applied Zipf-Pareto distribution for description of plant biomass partitioning. He used this distribution for evaluating the root biomass of trees. Consider Zipf-Pareto law as the simplest example of a power rank distribution (Mandelbrot, 1969). It can be written for a ranked data in a form x(i) = A/ib, where i denotes rank, A and b are parameters, maximal rank is set to 1, next ranks in size are increasing consequently. A and b can be easily evaluated after simple log-log transformation by least-squares method. Main conditions for applying the rank distributions are as follows. Assume that available resource for total unit is distributed among its parts proportionally to its rank, i.e. to the ordered sequence of distributed resource, then distribution of resource parts has the form of Zipf’s law. Accordingly, many mechanisms have been presented to explain the emergence of the Zipf’s law (Newman 2005). We analyzed partitioning of biomass to the main plant compartments of vascular plants (trees and dwarf shrub species in ground vegetation) using empirical data from the taiga zone in Russian North-West and Finland. MATERIALS AND METHODS We analyzed two data sets, one representing a deciduous tree (Betula pendula) and another deciduous dwarf shrub (Vaccinium myrtillus) biomass data, as a test material. The tree-wise data consists of measured biomass compartments (kg dry weight) of nine different-sized trees from a 38-years-old birch stand (Oxalis forest type) in Karelia (Kazimirov et al., 1978). For each tree we calculated the proportions (%) of the following biomass compartments: stem, (coarse) roots, branches, and leaves (Table 1). The biomass data of Vaccinium myrtillus (kg dry weight/ha) is from 12 intensively monitored forest plots in Finland. Both in South and North Finland there were three Norway spruce and three Scots pine plots. The spruce plots represented mesic and moist site types whereas the pine plots represented poor and dry site types. The data of 28 small sample units (30x30 cm) have been joined for accurate description of the total biomass of V. myrtillus at each plot. We calculated the proportions (%) of the biomass compartments (rhizomes, living shoots and branches, fine roots, leaves and flowers) to normalize the heterogeneous data. The averages of the three plots in the same site type (separately in north and south) are given in Table 2. 68 Table 1. Proportion (%) of biomass compartments (out of the total biomass) for Vaccinium myrtillus. Averages and standard deviations (sd) for southern and northern pine and spruce plots (n=3 plots) given Rhizomes (diameter > 2 mm) Living shoots and branches Fine roots (diameter < 2 mm) Leaves Flowers and flower buds South pine stand Average 70.09 22.80 4.80 2.08 0.045 sd. 6.31 4.81 0.9 0.69 0.016 South spruce stand Average 55.87 31.89 6.77 5.37 0.1 sd. 8.73 12.03 4.38 2.46 0.12 North pine stand Average 67.22 22.92 7.79 2.03 0.47 sd. 3.10 5.13 3.37 1.24 0.42 North spruce stand Average 75.86 17.02 4.41 2.62 0.87 sd. 4.80 4.12 0.65 1.32 0.88 Table 2. Proportions (%) of biomass compartments (out of the total biomass) for nine Betula pendula trees. Av. – averages, sd. – standard deviation. 1 2 3 4 5 6 7 8 9 Av. sd. Stem 65.62 67.0 68.03 67.87 69.97 69.31 70.93 71.73 72.86 69.26 1.867 Roots 22.92 18.78 18.03 18.12 17.71 17.76 17.15 16.25 16.34 18.12 1.867 Branches 8.33 8.63 7.82 8.21 7.81 7.63 7.27 8.03 7.22 7.88 0.445 Leaves 3.12 5.58 6.12 5.80 4.51 5.29 4.65 3.99 3.58 4.74 0.979 RESULTS AND DISCUSSION Biomass compartments (%) of V. myrtillus and B. pendula in relation to ranks with fitted power equations are presented in Figs. 1 and 2, respectively. South pine stand. Power equation y=ax^b, coefficient data: a = 70.64; b = -1.97. R= 0.9929. South spruce stand. Power equation y=ax^b, coefficient data: a = 57.66; b = -1.42. R= 0.9588. North pine stand. Power equation y=ax^b, coefficient data: a = 67.78; b = -1.85. R= 0.9935. North spruce stand. Power equation y=ax^b, coefficient data: a = 76.04; b = -2.34. R= 0.9986. Fig. 1. Dependency between ranks and corresponding averages of biomass compartments (%) of Vaccinium myrtillus in different sites (Table 1). Quadrats are empirical data 0 20 40 60 80 1 2 3 4 5 6 % ranks Calculated Measured 0 20 40 60 80 1 2 3 4 5 6 % ranks Calculated Measured 0 20 40 60 80 1 2 3 4 5 6 % ranks Calculated Measured 0 20 40 60 80 1 2 3 4 5 6 % ranks Calculated 69 . Fig. 2. Dependency between ranks and corresponding averages of biomass compartments (%) at a 38-year- old birch stand (Table 2). Line is power equation y=ax^b, coefficient data: a = 69.27; b = -1.95. R= 0.999980. Quadrats are empirical data. Both V. myrtillus and B. pendula biomass data showed persistently good fit to power equations, which is equivalent to Zipf law. In all cases the shape of the power dependency stayed the same. We found that for the same species ranks correspond to the same biomass compartments in different climatic and edaphic conditions. However, coefficients of the power distributions can be different for the same species and reflect different response of the species to changed conditions. Thus, in Fig. 1 we clearly see that for V. myrtillus in spruce stands the portion of rhizomes (1st rank) is larger in northern conditions than in south. An interesting question is whether ranks change along plant development stage and changing site conditions. In general, they can change as a result of long-term local unstable conditions (MacArthur, 1955). It seems that the populations of V. myrtillus in spruce stands with dense canopy (Fig.1, southern spruce stands) are more unstable. This question claims further studies for establishing of limits of applicability of the approach. Our biomass distributions were close to the results of Enquist and Niklas (2002) on the log-log relationship between above- and belowground biomasses of tree stands. They averaged world wide dataset from stand characteristics and found pairwise linear allometric relationships among standing leaf, stem, and root biomass basing on general allometric model. Power-law rank distributions allow for obtaining more general relationships between plant organs linking all main biomass compartments together. Additionally, power-law dependencies can also be applied for descripting of organs’ increment. Further, it would be interesting to compare the sequence of ranks between different functional plant groups for better understanding their role in carbon cycling in ground vegetation. The study of power-law distributions is an area in which there is considerable current research interest. From a mathematical point of view, these dependencies are similar to first integral in complicated systems of differential equations. Usually knowledge of such links between variables helps to find solutions in these systems. Such dependencies will help to obtain rules needed for development of the forest simulation models. While the examples presented here certainly offer some insight, there is much work to be done both experimentally and theoretically before we can say we really understand the main processes driving these systems. LITERATURE CITED Clauset A,, Shalizi C,R,, Newman M.E.J. 2009. Power-law distributions in empirical data. SIAM Rev 51: 661–703. Enquist B.J., Niklas K.J. 2002. Global Allocation Rules for Patterns of Biomass Partitioning in Seed Plants. Scienc295:1517-1520. Furusawa C, Kaneko K. 2003. Zipf’s Law in Gene Expression. Phys Rev Lett 90: 88-102. Kazimirov, N.I., Morozova, R.M. and Kulikova, V.K. 1978. Organic Matter Pools and Flows in Pendula Birch stands of Middle Taiga. Nauka, Leningrad. 216 pp. (in Russian). MacArthur R.H. 1955. Fluctuations of animal populations and measure of community stability // Ecology. V. 36. ¹7. Pp. 533-536. Mandelbrot B. 1969. Final notes on a class of skew distribution function. Inform. and Contr. 36: 394-419. Newman M.E.J. 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics 46: 323–351. Soukhovolsky V.G. 1996. Fractional structure and phytomass production in trees and stands, Lesovedenie (Russian Forest Science) 1: 30-40 (In Russian). Willis J.C. Yule G.U. 1922..Some statistics of evolution and geographical distribution in plants and animals, and their significance. Nature 109: 177- 179. 0 50 100 1 2 3 4 5 % ranks Measured Calculated Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 70 Inference of structural plant growth from discrete samples Christoph Stocker, Franz Uhrmann and Oliver Scholz Fraunhofer Institute for Integrated Circuits, Department Contactless Test and Measuring Systems, Erlangen, Germany *correspondence: stockech@iis.fraunhofer.de, franz.uhrmann@iis.fraunhofer.de, oliver.scholz@iis.fraunhofer.de Highlights: We present an approach for the rapid generation of plant growth models from a series of explicit growth stages. Multiple structural plant descriptions, which can be gained from 3D scans, are automatically inferred to an L-system grammar. Morphological leaf features are incorporated into this model by parameterization of the structural description. Keywords: grammar inference, L-systems, plant growth modeling Modern phenotyping systems like sheet-of-light scanners allow the accurate acquisition of plant geometry, from which a description of the branching structure can be extracted (see Bucksch et al. 2010). An explicit description of the structural development over time can be gained by measuring a plant at different growth stages. L-systems are commonly used to formally describe plant structure and its development during growth (Prusinkiewicz et al. 1990). However, the development of a growth model recreating specific plant structures requires expert knowledge and is often accomplished by time-consuming trial-and-error. We present an approach to computationally infer an L-system from feature vectors describing the structure of plants at successive growing stages. The aim of our approach is to close the gap between measured data and the plant growth model. The approach consists of an inference step to model structural plant growth, which is amended by leaf morphology features in a parameterization step. The plant structure is derived from linear sequences of feature vectors (e.g. extracted from 3D scans) using a variation of the SEQUITUR-algorithm as introduced by Nevill-Manning (1996). In the course of this derivation, the inferred rules are unified to an L-System grammar with only a small set of rules. In order to incorporate leaves into the branching structure the L- system is parameterized with morphological leaf features, which can be imported from real measurement data. Intermediate plant growth stages can be created by parameter interpolation. The generated parameterized L-system can be used as a basis for more sophisticated functional-structural plant models. Furthermore, the growth model can directly be used as input for system design tools in order to minimize occluded parts in the measurement data (Uhrmann et al. 2011). LITERATURE CITED Bucksch A, Lindenbergh R, Menenti M. 2010. SkelTre. The Visual Computer 26: 1283-1300, Springer Nevill-Manning, CG. 1996. Inferring Sequential Structure. Ph.D. Thesis, University of Waikato, New Zealand. 55 p. Prusinkiewicz P, Lindenmayer A. 1990. The Algorithmic Beauty of Plants. Springer 40 p. Uhrmann F, Seifert S, Scholz O, Schmitt P, Greiner G. 2011. Improving Sheet-of-Light Based Plant Phenotyping with Advanced 3-D Simulation, Microelectronic Systems, Springer. 247-258 Fig. 1. Overview of the approach: a) Acquiring structual and morphological input e.g. by measurements. b) Result of the inference step (grammar and 3D-visualization). c) Final result: Parameterized plant model at one growth stage. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 71 A spectral clustering approach of vegetation components for describing plant topology and geometry from terrestrial waveform LiDAR data Dobrina Boltcheva1, Eric Casella2, Rémy Cumont3 and Franck Hétroy3 1Université de Nancy & Inria, LORIA, 54506 Nancy, France, 2Forest Research, Centre for Forestry and Climate Change, Farnham, Surrey, GU10 4LH, UK, 3Université de Grenoble & Inria, Laboratoire Jean Kuntzmann, 38334 Grenoble, France Correspondence:Franck.Hetroy@grenoble-inp.fr Computer models that treat plant architectures as a collection of interconnected elementary units (internode, petiole, leaf lamina), which are spatially distributed within the above- and/or the below-ground space, have become increasingly popular in the FSPM scientific community (DeJong et al. 2011). The core of such 3-D plant architecture models deal with contrasting reconstruction methods generally based on stochastic, fractal or L-system approaches, or by describing accurately the geometry of each plant component in situ using 3-D digitizing technology. These methods can approximate the geometry of many species for understanding and integrating plant development and ecophysiology, but have generally been applied at a small scale. High-resolution terrestrial Light Detection And Ranging (tLiDAR), a 3-D remote sensing technique, has recently been applied for measuring the 3-D characteristics of vegetation from grass to forest plant species (Dassot et al. 2011). The resulting data are known as a point cloud which shows the 3-D position of all the hits by the laser beam giving a raw sketch of the spatial distribution of plant elements in 3-D, but without explicit information on their geometry and connectivity. In this study we propose a new approach based on a delineation algorithm (Fig. 1) that clusters a point cloud into elementary plant units. The algorithm creates a graph (points + edges) to recover plausible neighbouring relationships between the points and embed this graph in a spectral space in order to segment the point-cloud into meaningful elementary plant units (Fig. 2). Our approach is robust to inherent geometric outliers and/or noisy points and only considers the x, y, z coordinate tLiDAR data as an input. Fig. 1. Pipeline of the segmentation method proposed in this study. Dassot M, Constant T, Fournier M. 2011. The use of terrestrial LiDAR technology in forest science: application fields, benefits and challenges. Annals of Forest Science 68: 959-974. DeJong TM, Da Silva D, Vos J, Escobar-Gutiérrez AJ. 2011. Using functional–structural plant models to study, understand and integrate plant development and ecophysiology. Annals of Botany 108: 987-989. Fig. 2. Comparison of raw (a, c) and segmented (b, d) point clouds for a 0.4 m height poplar seedling (a, b) and a 3.7 m height eucalyptus tree. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 72 Modeling and analyzing rice canopies of different cultivars and densities by 3D digitizing method Dong Li1, Zhifu Xu1, Shihua Cheng2 and Liyong Cao2,* 1 Institute of Digital Agriculture, Zhejiang Academy of Agricultural Sciences, Hangzhou, Zhejiang Province,310021, P.R. China 2 China National Rice Research Institute, Chinese National Center for Rice Improvement, Hangzhou, Zhejiang Province,310005 P.R. China *correspondence: caolycgf@mail.hz.zj.cn Key words: rice canopy, 3D digitizing, rice structural model, Oryza sativa L, model application, potential photosynthesis INTRODUCTION Rice is one of the most important crops in the world and it is the main crop in Zhejiang Province, China. It is important for breeding high yield cultivars and improving rice cultivation level to quantify rice spatial architecture. Studies on morphogenesis and development of rice plant structure have been carried out (Watanabe et al., 2005; Zheng et al., 2008, 2011). In the 3D model (Zheng et al., 2008), rice canopies were measured in the field using a 3D digitizer and reconstructed. Light distribution in the canopy and the photosynthesis capacity could be computed. The model seemed useful to evaluate the rice cultivars and to design the cultivating strategies, but the measuring work was huge. In this study, we did the experiments with different cultivars and densities, computed blade area and light distribution of rice canopies with the 3D model and analyzed the influence of cultivars and densities with the structural model. Also we wanted to study the advantages and disadvantages of the model if it was used to evaluate rice breeding and cultivation. MATERIAL AND METHODS Field experiment Field experiment was conducted in 2012 at the experimental station of Xiaoshan Institute of Agricultural sciences in Hangzhou, Zhejiang province, southeast of China (30°19' N, 120°30' E). Three cultivars of hybrid rice (Oryza sativa L.) were planted. They were “Nei2You6”, “Nei5You8015”, “Liangyoupeijiu”, and we noted the cultivars as G6, G7 and LY for simple in this study. All these cultivars were newly-bred, high- yield and broadly planted in China for the recent years. For each cultivar, the rice was planted with three densities, which were high density (HD, the space was 16.7 × 14.3 cm), middle density (MD, 16.7 × 23.3 cm) and low density (LD, 30 × 23.3 cm), respectively. The experiment was determined by the randomized blocks design of three replications. The tiller number was dynamically recorded for each treatment through the growth period and the sampling number is 12 in each replication. The length and largest width of blade at different rank for each treatment were measured. Nine plants (3 rows × 3 columns) for each treatment were chosen as the canopy at the dough stage (Oct.11-18). The plant organs, such as leaves, stems, and panicles, were measured by collecting their coordinates with a 3D digitizer (FastCAN Scorpion, Polhemus, USA). The blade length and width towards midrib were measured and the blade shape was modeled. The diameters of stems and the shape of rice spikes were measured after digitizing. With the data being checked, interpolated and modeled, the 3D canopies of these 5 treatments were reconstructed in Matlab software produced by the Mathworks Inc ( Fig.1). Each blade was divided into 200 triangles (see Wang et al., 2006; Zheng et al., 2008). The area of each triangle, as well as its inclination angle and azimuth angle, was calculated according to the 3D coordinates of the facet. Canopies were vertically divided into several layers with 5 cm interval. We calculated the leaf area distribution in the vertical profile. Also the leaf distribution in different inclination angle and azimuth angle was computed. In this study, the volume of stems and spikes were ignored. 73 Fig 1. The visualization of the 5 treatments with blade midrib and stems and each organ were divided into 5 cm long sections. G6, G7, LY represented different cultivars and HD, MD and LD denoted different densities. Before 3D digitizing measurement, light response curve (Pn-PFD ) of different position leaves for all the treatments were measured using CIRAS-2 instrument (PP Systems, USA). Results During the late growth stages, the tiller number was great influenced by rice density. The density was higher, and the tillers for each plant were fewer. For all these cultivars, the difference between densities was significant (Fig.1). For the three cultivars, at the heading stage, the tiller number of LY cultivar was much larger than other cultivars, which has no significant difference from each other. However at the dough stage, there was no significant difference between the three cultivars (Fig.1). There was no significant difference in the SPAD value for all the treatments. The net assimilation rate of LY at the measuring time was larger than the other cultivars for the flag leaf (Blade1 from up to bottom). The value was quite stable between densities with the same cultivars (Fig.2a). At the same time, the net rate was quite different for blades on different position in the same stem (Fig.2b). The difference between blades on different position was much larger than in different cultivars. Fig. 2. Tiller number of the 3 cultivars and 3 densities of different stages. The canopies for different treatments were reconstructed and visualize (Fig.1 show just stem and the midrib of blade). Based on the 3D model, the distributions of leaf inclination angle, azimuth angle and leaf area in the vertical profile were computed for different treatments. For the MD treatment, the blades of G6 were more concentrated and the total blade area was larger than the other cultivars. LY had a few more erect blades Different treatments G6 G7 LY N um be r o f t ill er s 0 10 20 30 40 50 Different treatments G6 G7 LY N um be r o f t ill er s 0 10 20 30 40 50 LD MD HD Filling stage Dough stage 74 Fig. 3 Net assimilation rate for different treatments (a, blade1) and for blades on different positions (b). DISCUSSION Based on 3D digitizing, the rice canopies of different treatments were 3D visualized. And the vertical profile for leaf inclination angle, azimuth angle and leaf area distribution could be calculated and the difference between treatments could be analyzed by this model. Zheng compared the difference with three cultivars, one was bred 30 years before and the other two were bred recently. The light distribution was similar of the two modern high yield cultivars (Zheng et al., 2008). In this study, all the three cultivars were modern rice cultivars and the difference is not significant, just as the modern cultivars used in the previous study. In this study the net assimilation rate of the canopy could not tell the difference of the plant yield because the light would distribute in a different way if the solar altitude (time) changed even if the canopies kept stable for all the time. Moreover, the canopies changed a lot irregularly for different cultivars because tillers changed in the different way between LY and G6/G7. Also in the field experiment, the plant cannot be planted in a precise density and grow uniformly, especially for rice, whose tillers vary a lot between plants. And the total growth periods for the three cultivars were different (G6 138 days, G7 133 days and LY 145 days). They were not in the exactly the same stage. We also cannot make the statistical analysis of the potential photosynthesis because the measuring work is huge and there cannot be many replications of the digitizing plant canopies. In the future, we will consider the diffuse radiation and improving the calculation of net assimilation by using the Farquhar model (Farquhar et al., 1980). But we think the 3D model will not be broadly used in rice breeding and cultivating until all these disadvantages were considered and solved. Acknowledgments: This research has been supported by State Key Laboratory of Rice Biology. The authors are grateful to Yue Li, Qingsong Xu and Dinghua Mao for their kind help on the experiment measurements and to Dr. Bangyou Zheng and Dr. Zhigang Zhan for the help on the modeling and computer programming. REFERENCES Farquhar G, Caemmerer S, Berry J. 1980. A biochemical model of photosynthetic CO 2 assimilation in leaves of C 3 species. Planta 149: 78-90. Wang X, Guo Y, Li B, Ma Y. 2006. Evaluating a three dimensional model of diffuse photosynthetically active radiation in maize canopies. International journal of biometeorology 50: 349-357. Watanabe T, Hanan JS, Room PM, Hasegawa T, Nakagawa H, Takahashi W. 2005. Rice morphogenesis and plant architecture: measurement, specification and the reconstruction of structural development by 3D architectural modelling. Annals of botany 95: 1131-1143. Zheng B, Shi L, Ma Y, Deng Q, Li B, Guo Y. 2008. Comparison of architecture among different cultivars of hybrid rice using a spatial light model based on 3-D digitising. Functional Plant Biology 35: 900-910. Zheng BY, Ma YT, Li BG, Guo Y, Deng QY. 2011. Assessment of the influence of global dimming on the photosynthetic production of rice based on three-dimensional modeling. Science China Earth Sciences 54: 290-297. Rank along the stem (from up to bottom) 1 2 3 4 N et p ho to sy nt he si s r at e 0 5 10 15 20 Different treatments G6 G7 LY N et p ho to sy nt he si s r at e 0 5 10 15 20 LD MD HD Cultivar: LY a b Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 75 Figure 1: Digitized, three- dimentional corn stalk model. The use of x-ray computed tomography for creating computational models of corn stalks and other plants: advantages, benefits, and common challenges. Douglas Cook1 and Margaret Julias2 1Division of Engineering, PO Box 129188, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates *correspondence: douglascook@nyu.edu Highlights: X-ray computed tomography (CT scanning) is a powerful tool for evaluating plant tissue, and is commonly applied in the field of biomechanics to obtain 3D representations of bone, arteries, and other anatomical data. We have applied this technique to the development of computational models of corn stalks and bamboo culms. While CT scanning has many advantages, the process of creating parsimonious models based on CT data is often challenging since this technique often produces several gigabytes of data for each scan. This paper provides an overview of the advantages, benefits, and common challenges associated with the use of computed tomography in plant modeling in the context of modeling corn stalks. Keywords: computed tomography, CT, data, 3D modeling, corn INTRODUCTION Corn (Zea mays L., Figure 1) is the leading grain crop globally. In the US, over 300 million tons of corn are harvested annually from 80 million acres (135,000 mi2) (Hondroyianni et al. 2000). Only 4 US states (Alaska, Texas, Montana, and California), have a greater land area than that devoted to corn production. Corn is susceptible to late season crop failure (called stalk lodging), with yield losses due to stalk lodging range from 5 to 25% (Nielsen and Colville 1988). These losses affect the productivity of farms, negatively impact individual farmers, and may eventually affect the overall crop supply, thus affecting commodities trading and even the broader economy (Hagenbauch 2007). Reasons for crop failure have been challenging for plant geneticists to identify, measure, and control (Esechie et al. 1977, Loesch et al. 1963), largely because most plant research focuses on biology, not structural mechanics. From an evolutionary perspective, the purpose of grain kernels is to propagate the species. The species known as Zea mays resulted from millions of years of optimization for this purpose. But humans have adopted corn for an entirely different purpose than nature intended. In the last 100 years, aggressive breeding programs have increased corn yields by over 400% (Gardunia, private communication). As a result, the highest-yield varieties currently suffer from persistent stalk failure, and further increases in crop yield are limited by the ability of the stalk structure to support such large kernels. This proposal is based on the concept that an understanding of the biomechanics of corn stalks can be used by plant breeders to develop breeding strategies that will produce stronger stalks, thus enabling further advances which would not otherwise be possible without the application of biomechanical principles. The objective of this research project is the identification of key geometric and material properties that influence structural attributes of corn stalk. Once these factors have been identified, plant breeders can use this information to develop varieties exhibiting stronger stalks. As a first step toward this long term objective, we require detailed 3D descriptions of corn stalk geometry. This paper desribes our efforts to develop a method for obtaining this information in an efficient manner using computed tomography to produce detailed digital models of corn stalks (see Figure 1). SCAN METHODOLOGY CT scanning was performed on multiple corn stalk samples using an X-5000 scanner from NorthStar Imaging (Rogers MN, USA). This scanner is capable of producing CT reconstructions ranging from 10µm 76 Figure 2: Process utilized in creating digital stalk models. Note that the relevant geometric data requires only 60KB of the original 10GB data set. to 127µm. All CT scanners operate on a principle of combining a number of 2D x-ray to mathematically reconstruct a 3D representation of the scanned object. Typically, between one and two thousand images are required for an high quality scan. The quality of CT reconstruction depends upon many factors, including x-ray intensity, frame-rate of data acquisition, rigidity of the holding fixture, the number of 2D radiographs, density variation within the object, and scan type (continuous or intermittent). We constructed a holding fixture which consists of a central post, around which 5 corn stalks were arranged, attached by inserting the ends of each stalk into lightweight foam (first image in Figure 2). Scans were conducted using from 1000 to 2500 2D radiographs. To determine the effect that number of radiographs has on reconstruction quality, we have conducted an experiment involving 2400 scans. These scans were combined to create a 3D reconstruction. Half of the same set of radiographs were then used to create a second 3D reconstruction. SEGMENTATION While there are many software programs which utilize high-power computing resources to automatically generate 3D models based on CT data, there are several practical problems with this approach. First, these software are not affordable, especially for those just starting to explore this technology. Second, the models produced by such software are often highly complex, and require a great deal of computational resources (CAD, meshing, and finite element software) to fully utilize. Our institution recently purchased Simpleware, one of the leading software products in this category. This software cost approximately $20k. In using this software, we realized that it was not optimized for the extraction of the relatively simple shapes of corn stalks. Although the software is relatively easy to use, the models produced in this way required a great deal of computer memory to manipulate. Over the course of one week, we were able to develop a segmentation process based on freely available MATLAB routines. Our approach involved much less computational power and resources, and successfully extracted relevant data regarding the corn stalk geometry. This process is outlined below. RESULTS AND DISCUSSION One of the challenges associated with corn and other plant stalks is their inherent aspect ratio. The corn rind is approximately 1mm in thickness. Adequate resolution of the wall structure therefore requires a scan resolution of approximately 100µm, which provides approximately 10 pixels across the rind thickness. The stalk diameter is usually an order of magnitude larger, typically 15-23mm. Individual nodes are 10-20 cm in length and the entire stalk is around 1 meter in length. Thus, the data set required for CT reconstruction of a single stalk will consist of approximately 3.2 billion voxels. Of these 3.2 billion, perhaps 5%-10% are corn stalk, while the rest are background data. The first challenge is to segment the images, selecting only those portions that are relevant. Of the many segmentation algorithms, we have found good success with a technique called the level set 77 method (Li et al. 2001). While many other methods will split each image into two regions (corn tissue and air), the level-set technique is particularly useful for identifying the boundary between regions, which is our primary interest. The drawback is that this method is computationally intensive, usually taking approximately 10 seconds per analyzed 2D image. However, because the corn stalk (and many other plants) have a relatively constant geometry and structure along the length of the stalk, we can attempt to reduce the number of 2D images that are analyzed. One nodal section of corn stalk may consist of around 1500 axial CT images, but not all need be analyzed. We developed an algorithm that uses a relatively crude thresholding measurement to estimate the number of pixels in each 2D image that represent corn tissue. Since the nodes contain more stalk tissue than the internode regions, this data allows us to infer the locations of the nodes. A sampling scheme is then derived which determines the number, spacing, and location of sample images. This approach requires that edge detection be performed on a small subset of all axial CT images. In our experience, a set of 1500-1800 axial slices can be adequately approximated using 50-100 judiciously chosen images. This process results in a dramatic reduction in the amount of data (data reduced by a factor of 14,000), while successfully extracting the most important data (geometric boundaries), which can then be used independently, or as starting points for more advanced analysis. Edge detection and surface generation images are shown in Figure 3. We are now proceeding to create finite element models based on the digitized models, as well as performing geometric analysis on various geometric features of the corn stalks that have been digitized. Finally, this information will be used to create virtual populations of corn stalk models for sensitivity analysis. Figure 3: Representative corn stalk cross-sections: (a) axial CT image (179KB); (b) image overlayed with edges detected by level-set method (edges require 16KB); (c) smoothed & simplified edges contours (requiring less than 1KB total); (d) digitized surface model (15KB for shown geometry). LITERATURE CITED Esechie HA, Maranville JW, Ross WM. 1977. Resistance of stalk morphology and chemical composition to lodging resistance in sorghum. Crop Science 17: 609-612. Gardunia Brian (Dr.), Monsanto Corporation., Private communication. Hagenbauch B. 2007. Corn has deep economic roots as high prices create ripple effect, in USA Today. Hondroyianni E et al. 2000. Corn stalk traits related to lodging resistance in two soils of differing salinity, ed, Vol. 45, Maydica, Bergamo, ITALIE. Li C, Huang R, Ding Z, Gatenby C, Metaxas DN, Gore JC. 2001. A Level Set Method for Image Segmentation in the Presence of Intensity Inhomogeneities with Application to MRI, IEEE Trans. Image Processing 20 (7): 2007- 2016. Loesch PJ, Zuber MS, Grogan CO. 1963. Inheritance of crushing strength and rind thickness in several inbred lines of corn. Crop. Sci. 3: 173-174. Nielsen B, Colville D. 1988. Stalk Lodging in Corn: Guidelines for Preventive Management, Purdue University Cooperative Extension Service, 1988. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 78 A Model-based Approach to Extract Leaf Features from 3D Scans Franz Uhrmann1, Christian Hügel1 , Sabine Paris1, Oliver Scholz1, Michael Zollhöfer2 and Günther Greiner2 1Fraunhofer Institute for Integrated Circuits IIS, Am Wolfsmantel 33, 91058 Erlangen, Germany 2Computer Graphics Group, University Erlangen-Nuremberg, Germany *correspondence: franz.uhrmann@iis.frauhnhofer.de Highlights: We present a flexible and robust method for the extraction of leaf features from 3D point clouds. An adaptable leaf model is automatically fitted to the measured data in order to obtain a precise but compact parameterization of the leaf shape. As an application example the detection of stress using the fitted leaf parameters is demonstrated. Keywords: Phenotyping, leaf model, vitality monitoring INTRODUCTION Modern computer vision technologies allow fast, detailed and yet affordable 3D acquisition of objects. Contactless acquisition methods like stereovision or laser scanning are increasingly used for plant phenotyping systems, as the surface of single plants can be measured at high resolution within seconds (see Seidel 2011, Biskup 2007 or Andersen 2005). The resulting datasets are usually very large containing millions of dense but independent point samples. As they cannot directly be used as interpretable features of the phenotype, a set of comprehensible geometric features e.g. leaf area or orientation has to be extracted from the point cloud. However, the relevant parameters depend on multiple aspects like the research subject or the investigated plant species. Thus the algorithms for feature extraction are highly adapted and customized to the specific problem. In this paper a flexible method for the extraction of leaf features is presented: We introduce a geometric model, which allows the description of a leaf shape with a small set of parameters corresponding to physical properties. The model can easily be adapted to various plant species. Furthermore, we present a method to automatically match the model with a point cloud of a real leaf. As the model parameters provide a compact but detailed description of the leaf geometry, they can directly be used as features for further analysis of the plant phenotype. PARAMETRIC LEAF MODEL The basis of the geometric leaf model is a 2D image of a single leaf of the respective plant species, which is created using a custom flatbed scanner. After separating leaf pixels from the background, a mesh representation of the leaf shape is generated by triangulation of the leaf pixels. To emulate natural leaf deformations in 3D space a series of geometric transformations is defined, which are applied to the initially flat leaf template: Besides a rigid transformation currently 9 leaf-specific transformations are implemented like rolling or bending along the main axis. All transformations are parameterized by a set of currently 26 parameters. Fig. 1. Examples for different leaf model transformations (from left to right): Flat leaf template, bending along leaf axis, rolling along leaf axis and a combination of multiple transformations. 79 MODEL FITTING In order to determine the geometric parameters of the measured leaf, the parametric model representation is fitted to the data. For a set of measured points 𝒑 = {𝑝1, 𝑝2, … ,𝑝𝑛} the model parameters 𝜶 are determined, such that the distance between the points of the transformed leaf model 𝒎(𝜶) = {𝑚(𝜶)1, 𝑚(𝜶)2, … ,𝑚(𝜶)𝑛} and the measured points 𝒑 is minimized. This can be formulated as an optimization problem minimizing 𝑑(𝛼) = ��𝑝𝑖 − 𝑚(𝜶)𝑗�𝑛 𝑖 with 𝑚(𝜶)𝑗 being the nearest neighbor to measurement point 𝑝𝑖 and |… | being the Euclidian distance between two points. As the model transformations contain multiple trigonometric functions and the neighbor relationships change during optimization, 𝑑(𝜶) is nonlinear. Thus the Levenberg-Marquardt optimization algorithm (see e.g. Madsen 2004) was chosen as a numerical solver and applied iteratively. EXPERIMENTS We verified the model-based feature extraction approach with data of a phenotyping system for tobacco plants. The scanning unit covers a maximum size of 1 m³ and uses multiple sheet-of-light units to acquire the surface of the plant with high coverage at a lateral resolution of approx. 0.5 mm (see Fig. 2). Thereafter the resulting point could is segmented into single leaves. For certain types of plants separation of the measured point cloud into single leaves works nicely using a standard point cloud segmentation algorithm (Rabbani 2006, see Fig 3). Finally a leaf model is fitted to each segmented leaf, which can be seen in Fig. 4 for the example of a N. tabacum plant. The monitoring of a plant during application of stress was chosen as an example to show the potential of our approach. In order to cause a quick stress reaction, a single N. tabacum plant was cut at the stem and fixed in a container with saline solution. An initial measurement of the plant was performed immediately after stress induction, a second measurement 35 minutes later. Additionally pictures were taken before each measurement, which are shown in Fig. 5 and Fig. 6. Fig. 2. Phenotyping hardware setup. Fig. 3. Point cloud of measured plant with segmented leaves shown in different colors. Fig. 4. Leaf model fitted to each segmented leaf. In the right half the measurement points are visible as a red dot overlay. 80 Fig. 5. N. tabacum immediately after stress induction Fig. 6. N. tabacum, 35 minutes under stress Fig. 7. Leaf models of both measurements. Green: immediately after stress induction. Red: after 35 minutes under stress RESULTS Comparing the photographs it is difficult to quantify the differences caused by the stress induction. When the fitted model representations are visualized in a common view as can be seen in Fig. 7, the downward bending of the leaves are already clearly visible. The decline is represented by two parameters in our leaf model: The first parameter indicates bending of the lamina defined as the slope of the straight line between lamina base and leaf apex. The second parameter is the absolute height from the top edge of the pot to the base of the leaf lamina. The difference in this parameter of both measurements represents the decline of the lamina caused by the bending of the petiole. Values of this parameter for each leaf are shown in Table 1, with the bases of all leaf laminas being lower in the second measurement with the exception of leaf #6. This leaf is the youngest and has an almost upright petiole, which tilts inwards under stress resulting in a slightly greater height of the leaf base. CONCLUSION AND OUTLOOK We presented a leaf model that is adaptable to different plant species simply by exchanging the leaf template. Along with the fitting algorithm a universal approach was presented that has proven to be robust delivering a compact set of parameters representing a plant’s phenotype in great detail. The ability to derive information about a plant’s state of health simply by reading the appropriate parameters opens up numerous applications, starting with the detection of stress symptoms as shown. By exploring the detailed parametric descriptions of large plant populations during growth, a standard growth behavior and furthermore deviations from this standard growth can be detected. Therefore, this approach is generally suitable for vitality assessment of plants. LITERATURE CITED Andersen HJ, Reng L, Kirk K. 2005. Geometric plant properties by relaxed stereo vision using simulated annealing. Computers and Electronics in Agriculture. 49:219-232 Biskup B, Scharr H, Schurr U, Rascher U. 2007. A stereo imaging system for measuring structural parameters of plant canopies. Plant, Cell and Environment 30:1299-1308. Madsen K, Nielsen HB, Tingleff O. 2004. Methods for Non-Linear Least Squares Problems. Informatics and Mathematical Modelling, Technical University of Denmark, 60p. Rabbani T, van den Heuvel FA, Vosselmann G. 2006 Segmentation of point clouds using smoothness constraint. Proceedings of ISPRS, 36: 248-253 Seidel D, Beyer F, Dietrich H, Fleck, Leuschner C. 2011. 3D-laser scanning: A non-destructive method for studying above- ground biomass and growth of juvenile trees. Agricultural and Forest Meteorology 151:1305−1311. Leaf Index Absolute height of lamina base [mm] Height difference t = 0 min t = 35 min [mm] 1 28 10 17 2 52 45 7 3 77 70 7 4 145 135 10 5 151 144 6 6 153 156 -3 7 156 142 15 Table 1: Comparison of parameter absolute height of lamina base. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 81 Root growth and distribution of gooseberry (Physalis peruviana) under field conditions in the Andean soil Roveda-Hoyos Gabriel1 and Moreno-Fonseca L.P.1 1Department of Agronomy, PO Box 14490, National University of Colombia, Bogotá *correspondence: groveda@gmail.com Highlights: A field technology with the computer model called “RACINE” was used to estimate root-length density (RLD) and the root exploration from root count on soil profiles. The results indicated a drastic reduction on root development due to restrictions as low phosphorous and decreasing organic matter. However, Glomus mosse can promote the root system, on RLD and root front. Keywords: root model, Physalis peruviana, Glomus mosse. A field technology was used to estimated root-length density (RLD) and the root exploration from root count (grid method) on soil profiles. This method includes a computer model, developed by Chopart and Siband (1999), and called “RACINE”, that was calibrated and validated in volcanic soils of South America (Roveda-Hoyos et al., 2001). This research was focused on determining the effect of symbiotic association between arbuscular mycorrhizal fungi (AMF) and gooseberry crops on the root-length density and the root exploration under field conditions (Van der Heijden, 2003). The experiments were done in two localities of Boyacá and Cundinamarca departments of Colombia at 2900 and 2050 meter over sea level, respectively. Both soils were classified as Typic Dystrandepts, with low phosphorous available (< 10 mg Kg-1), low macronutrients saturation (N, K, Ca, Mg y S), and acid pH < 5. Both calibration and validation methods carried out using two experimental designs of random complete blocks were used with 3 treatments and 4 repetitions as follows; with two control treatments without inoculation of AMF, without fertilizing (T0), and 100% of fertilizing (T100) with application of triple superphosphate (TSF), a treatment with 50% fertilizing of TSF and inoculated with AMF, Glomus mosse (T50+G), all treatments were fertilized with N (149.5 Kg Ha-1), K (196.9 Kg Ha-1), Ca (46.9 Kg Ha-1), Mg (14.1 Kg Ha-1), S (21.1 Kg Ha-1), and micronutrients (B, Cu). The experimental results demonstrated that all the treatments had a shallow root system (> 90%) of the total root length, after the top soil deep (15 cm), the RLD showed a drastic reduction of P. peruviana roots, the soil profiles were evaluated at vegetative and flowering stages (2 and 6 month after planting). This shallow root system of gooseberry plants suggested a chemical restrictions, as low availability phosphorous in the soil profile (<5 mg Kg-1), and decreasing organic matter in a deep soil profile, those proprieties are typical in volcanic ash soils. The principal differences in RLD among treatments in the top soil were due to the effect produced by the application of phosphorous fertilizer (TSF) and the inoculation with G. mosse, as follows: The highest values of RLD (14.9 cm cm-3) were found in the inoculated treatment (T50+G) to compare to no inoculated treatments, T100 (12.1 cm cm-3), and T0 (8.0 cm cm-3). There were also differences among these treatments with the maximum rooting deep (root front). The highest root front (35 cm) was observed in inoculated treatment with G. mosse (T50+G) to compare with the no inoculated treatments, T100 (30 cm), and T0 (25 cm). The experimental results indicated a drastic reduction on root development on gooseberry plants as limiting factors, such as low available phosphorous (Vance, 2003) and decreasing organic matter in deep soil profile. Nevertheless, the inoculation of AMF (G. mosse) can promote the root system of gooseberry, on both RLD and root front. LITERATURE CITED Chopart JL, Siband P. 1999. Development and validation of a model to describe root length density of maize form root counts on soil profiles. Plant and Soil 214: 141-157. Roveda-Hoyos G, Chopart JL, Baquero JE, et al. 2001. Modelling growth and distribution of maize (Zea mays L.) roots under field conditions in the eastern plains of Colombia. XIV International Plant Nutrition Colloquium “Food security and sustainability of agro-ecosystems Kluwer Academic Publishers. Hannover, Germany. 576-578. Vance CP, Uhde-Stone C, Allan DL. 2003. Phosphorus acquisition and use: critical adaptations by plants securing a nonrenewable resource. New Phytol. 157: 423-447. Van der Heijden MGA, Sander IR. 2003. Mycorrhizal Ecology. Ed. 2nd Springer-Verlag Berlin Heidelberg, New York. Pg. 234-261. Smith SE, Read DJ. 2008. Mycorrhizal Symbiosis. New York, Academic Press, Third Edition. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 82 Defining reliability coefficients in an automated radial file identification and characterization method in microscopic images of gymnosperms Guilhem Brunel1,2, Philippe Borianne2, Gérard Subsol3, Marc Jaeger2 and Yves Caraglio2 1CIRAD - UMR AMAP, France. 2Université Montpellier 2, France. 3CNRS – LIRMM, France. guilhem.brunel@cirad.fr Highlights: The analysis of wood anatomical sections is of great interest for understanding the growth and development of plants. We propose a novel method for automatically identifying and characterizing radial files in wood microscopic images of gymnosperms. A key point is to be able to assign a priori reliability coefficient to the results, particularly for statistical processing in large-scale analyses. We describe in this paper the principle used to establish reliability coefficients to evaluate the radial file identification process and the geometrical measurements of cells and their components. Keywords: image processing, wood microscopic images, radial file identification, a priori reliability. INTRODUCTION Wood structure reflects the physiological and molecular regulation of cambium activity (Cato et al. 2006) and also registers environmental conditions (Barlow et al. 2005). Understanding cambium growth mechanisms calls for a study of cell pattern regularity, and of cell disruption or modification in space and time (Liang et al. 1997). Two types of organizations are considered: the growth ring representing cell production at a given time, and the radial file representing the activity of an initial cell over time (Rozenberg et al. 2004); radial files help in understanding the development, differentiation and temporal changes of cells. Morphological fluctuations of successive cells along a radial file and the influence of external factors have been investigated for a long time (Ford et al. 1978), but those investigations were greatly restricted by a limited number of radial file comparisons and a restrictive number of successive cell descriptions. Those studies, concerning secondary growth and its relationships with primary growth, were based on fragmentary studies, due to high acquisition and processing costs. Large-scale studies for understanding wood growth and disturbance are available nowadays thanks to automated radial file identification and cell characterization (Brunel et al. 2012, Kennel et al. 2011). In fact, wood continuously records changes in the development of the tree. Such new methodologies and approaches offer real new opportunities for more in-depth investigations of tree biology and climate change (Fonti et al. 2010). The size and shape fluctuations observed along radial files are usually considered to be the result of external constraints (Frankenstein et al. 2005). This is a restrictive and simplified viewpoint: these fluctuations are probably due to a combination of external and internal factors. We aim to promote an objective quantification of these measurements, on the basis of statistics based on numerous image datasets. This paper focuses on the reliability of such data from statistical studies, i.e. produced by automated radial file identification (Brunel et al. 2012). For large-scale data analyses, it is necessary to ensure a posteriori that the measurements are valid in order to find invariants or validate hypotheses. This is a classic line taken in statistics (Bruton et al. 2000) and experimental approaches. MATERIALS We processed histological sections of several gymnosperm species: Pinus caramanica, Pinus nigra and Abies alba. Wood cross-sections with a thickness of 20 μm were produced with a vibratome. The sections were stained to increase the contrast between the lumen and cell walls. They were then digitized with an Olympus DP71 LCD camera on an Olympus BX51 microscope. The square color images produced had a resolution of 4 million pixels. OVERVIEW OF THE METHOD Radial files are alignments of substantially similar cells in terms of color dynamics, shapes and sizes. Intuitively, the notion of cell alignment implies the existence of cellular organization based on the neighborhood relationships between cells. Those properties are used to identify radial files. 83 Our approach, described in (Brunel et al. 2012) was divided into three steps: cell identification which specified single cells, cell organization which detected radial files, and cell classification which gave the biological and qualitative typing of cells and radial files. The incremental construction of radial files was based on two assumptions: (i) such a file is independent from image orientation; (ii) two consecutive cells of a file are very similar. From a methodological point of view, cell individualization was derived from a watershed algorithm (Vincent et al. 1991), and the cell pattern was described by an adjacency graph created from the watershed crest lines. Radial files were then built by finding a reversible path in the graph under spatial constraints (maintaining a specific direction) and similarity constraints (two consecutive cells should show close geometric characteristics). Our method produced several layers of results, respectively corresponding to different observation levels: (i) radial files were classified according to their length, their fractionation and their cell self-similarity, (ii) cells were characterized by geometric parameters (such as size, diameter, shape, etc.) and topological parameters (number of neighbors), (iii) cell component elements (wall, lumen) were characterized by geometric parameters (size, thickness, diameter, etc.). DEFINITION OF A PRIORI RELIABILITY COEFFICIENTS Quality assessment of these results depends on many factors. It concerns the data set itself (image noise, biological configuration complexity, etc.), the process (algorithm approximations, computation costs, stability, etc.), and the geometrical scale (related to the observation level). Each result should be qualified using different indicators, notably to keep the significant outcome while processing high volume data. It is thus relevant to assign an estimated reliability coefficient to each result. We illustrate cases on file and cell scales. Radial file construction reliability. We propose defining this radial file reliability coefficient Rf from three criteria: length, fractionation and similarity. The first criterion derives from the file length, Lf, compared to the threshold value T. T is set by 2means and defines the minimum significant length. Fractionation is evaluated from the file construction algorithmic cost. It involves the total number of cells Lfm stacked to build the file, the length Lf of the file, and the number of sections Nf. The similarity criterion is built from the product of the n-1 consecutive cell surface variations. The final reliability coefficient Rf of the file f is then defined by a product of normalized terms ranging between 0 and 1. When this coefficient tends to 1, the reliability of the radial file increases. 𝑅𝑓 = �1 −𝑚𝑎𝑥 �𝑇 − 𝐿𝑓𝑇 , 0�� �1 − 𝐿𝑓𝑚 − 𝐿𝑓𝑁𝑓 ∗ 𝐿𝑓𝑚��(1 − �𝑆𝑓𝑗 − 𝑆𝑓𝑗+1�𝑆𝑓𝑗 + 𝑆𝑓𝑗+1 )𝑛−1 𝑗=0 Lumen area estimation reliability. The reliability coefficient of the lumen surface is defined on a similar principle, by a product of two normalized terms, based on the cell size and an image local blur estimation. In fact, the watershed algorithm is known as a robust method for extracting cell boundaries, since it is based on intensity discontinuities which are less sensitive to blurring, whereas the lumen area shows high sensitivity to local blur. The cell area definition involves a two-class clustering split, corresponding to the lower and the higher intensity classes. The local blur estimator is derived from (Ladjal 2006), based on the relationship between local dynamics and intensity differences. EXPERIMENTS, CONLUSION AND WORK IN PROGRESS Experiments were performed on ten colored sections of different species of gymnosperms, representative of biological variability. The color quantifies the reliability results, both on a global (Fig. 1) and local (Fig. 2) scale. On a global scale, we can see in Fig. 1 that the reliability estimator properly qualifies the cell files: green colors are assigned to straight and regular cell lines whereas red colors correspond to incomplete cells on the side of the image or incrusted cells. Such a color map alerts the expert to potential unsure classifications and emphasizes the ambiguous biological status of a file or cells. On a local scale, for lumen area computation, the estimator also retrieves obvious cases. The reliability factor also ensures areas showing lower intensity variations (areas in green in Fig. 2, right). Several points were studied. (i) in angiosperms, the vessel morphology is different and calls for a different evaluation of cell similarity which defines the third term of the file reliability coefficient, by taking into account the larger diameter instead of its surface. (ii) other blur estimators were studied, such as estimators based on multi-scale filtering in order to assess the independence of the reliability coefficient with 84 respect to the blur estimation method. (iii) how the local reliability coefficient could be used to correct the measured values according to the local blur estimator relationship (Fig 2. Left). To conclude, we introduced some reliability coefficients for image processing related to cell organization identification and illustrated the cases of radial file detection and of lumen area computation. The reliability coefficients were essentielly used to filter the input data of statistical studies conducted by botanists or to draw attention to special biological configurations. Fig. 1. Left: cross-section of Abies alba. Right: automated identification of radial files. Color value qualifies the reliability coefficient: weakly reliable files appear in red tones and highly reliable files are in green tones. Fig. 2. Left: relationship between a Gaussian blur applied to a cell image and the local blur estimator. The estimator emphasizes the blur tendency; red crosses stand for five microscopic optical blurs, matched from their area variance. Right: the five corresponding lumen areas from the optical blurs: the color qualifies the reliability coefficient, from green for the real lumen area to orange for the reduced lumen area. The authors acknowledge NUMEV Labex and SIBAGHE Graduate School of the University of Montpellier 2 for their support. LITERATURE CITED Barlow PW, Powers SJ. 2005. Predicting the environmental thresholds for cambial and secondary vascular tissue development in stems of hybrid aspen. Annals of Forest Science 65: 565-573. Brunel G, Borianne P, Subsol G, Jaeger M, Caraglio Y. 2012. Automatic characterization of the cell organization in light microscopic images of wood: application to the identification of the cell files, Plant Growth Modeling, Simulation, Visualization and Applications, IEEE press, ISBN 978-1-4673-0070-4, 58-65. Bruton A, Conway JH, Holgate ST. 2000. Reliability: What is it, and how is it measured?, Physiotherap 86:94-100 Cato S, McMillan L, Donaldson L, Richardson T, Echt C, Gardner R. 2006. Wood formation from the base to the crown in Pinus radiata: gradients of tracheid wall thickness, wood density, radial growth rate and gene expression. Plant Molecular Biology 60:565–581. Fonti P, von Arx G, Garcia-Gonzalez I, Eilmann B, Gärtner H, Eckstein D. 2010. Studying global change through investigation of the plastic responses of xylem anatomy in tree rings. New Phytologist 185: 42–53. Ford ED, Robards A, Piney MD. 1978. Influence of environmental factors on cell production and differentiation in the early wood of Picea sitchensis. Annals of Botany 42 (3): 683-692. Frankenstein C, Eckstein D, Schmitt U. 2005. The onset of cambium activity – A matter of agreement? Dendrochronologia 23: 57-62. Kennel P, Subsol G, Guéroult M, Borianne P. 2010. Automatic identification of cell files in light microscopic images of conifer wood. 2nd International Conference on Image Processing Theory Tools and Applications 98–103. Ladjal S. 2006. Blur estimation in Natural Images, 15e congrès francophone AFRIF-AFIA Reconnaissance des Formes et Intelligence Artificielle 112-124. Liang C, Filion L, Cournoyer L. 1997. Wood structure of biotically and climatically induced light rings in eastern larch (Larix laricina). Canadian Journal of Forest Research 27: 1538.1547. Rozenberg P, Schüte G, Ivkovitch M, Bastien C, Bastien JC. 2004. Clonal variation of indirect cambium reaction to within-growing season temperature changes in Douglas-fir. Forestry 77:257-268. Vincent L, Soille P. 1991. Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations, IEE Transactions on Pattern Analysis and Machine Intelligence 13-6:583–598. 3 4 5 6 7 8 9 10 0,3 0,6 1 1,4 1,7 2,1 2,5 2,7 va lu e of th e bl ur e st im at or value of the Gaussian blur Flou Numérique Flou OptiqueN merical blur Optical bl r Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 85 An automated image-processing pipeline for high-throughput analysis of root architecture in OpenAlea J. Diener1*, P. Nacry2, C. Périn3, A. Dievart3, X. Draye4, F. Boudon1, A. Gaujon2, C. Godin1 1Virtual Plants, INRIA, CIRAD, INRA, 34095 Montpellier France, 2 Biochimie et Physiologie Moléculaire des Plantes, INRA, CNRS, UM2, 34060 Montpellier, France, 3 UMR DAP, CIRAD, 34398 Montpellier, France, 4 Unité d’Ecophysiologie et d’Amélioration végétale, Université catholique de Louvain, B-1348 Louvain la Neuve, Belgium. *correspondence: julien.diener@inria.fr Highlights: FSPM analysis of root systems requires structural data obtained on large data set. This paper describes a processing pipeline developed to extract automatically the architecture of root system from images databases. Keywords: Root architecture, Image processing, Analysis pipeline, High-throughput, OpenAlea INTRODUCTION Automated acquisition systems of Root System Architecture (RSA) are now readily available for developmental research and provide high-throughput image data of roots. Existing acquisition systems provide many types of data, from images of dispersed root pieces to full 3d scans of underground root systems. Here we consider RSA grown in Petri plates. This is a traditional experimental protocol for which image data can be acquired easily and in large amount. Their analysis is thus a major challenge for researches on root development. Existing tools range from the automatic estimation of global traits distribution to details extraction of the root architectures through tedious manual work. Software such as Rootreader2d (Clark et al., 2012), EZ- Rhizo (Armengaud et al., 2009), Rootfly (Zeng et al., 2008) and RootTrace (Naeem et al., 2011) extract in a single image a limited part of the architecture data such as the main axes length and the number of lateral roots. Similarly, programs such as WinRhizo (Arsenault et al., 1995) or GiaRoot (Galkovskyi et al., 2012) extract representative value of the whole RSA such as total root length, area, or branching number. These are suitable for processing high-throughput data but do not provide architectural data, as they do not order the detected root segments in an arborescent structure. To extract the full root system architecture, the available software are either entirely manual such as DART (Le Bot et al., 2010), or semi-automated such as SmartRoot (Lobet et al., 2011) or a high-end version of WinRhizo (WinRhizo Pro, 2012b). Those are suitable for detail inspection of architectural trait of a few root systems. But because of the time required by user interaction they cannot be used for high-throughput analysis. In this study, we present a solution for extracting the full root architecture automatically and on a large- scale data set. Because our framework is included in the OpenAlea platform, in addition to traditional data analysis such as the ones provided by existing software, the extracted data can also be used seamlessly as input of all the architectural analysis packages already contained in OpenAlea. MATERIAL AND METHOD For the purpose of development and validation, two data sets have been used. The first set studies the growth of nine genotypes of Arabidopsis thaliana in three different nitrate concentrations (see fig. 2). For each of these experimental modalities, four Petri boxes containing each five root systems are daily imaged during six days. The second data set contains images of rice (Oryza sativa of the nipponbarre genotype) of eight Petri boxes, each containing five root systems, which were scanned once per day avec a 6 days period (see fig. 3). In total both data sets represent 688 images and 3440 root systems in total. Comparisons with expert measurements have been done for around 300 plants. Image acquisition is done either using a high-resolution scanner (~100Mp) with back-lighting for the rice data, or with a camera setup associated with a x-ray film viewer that provide back-lighting (see fig. 1) Fig. 1. Schema of the acquisition setup 86 Fig. 2. One image of the Arabidopsis data set Fig. 3. One image of the Rice data set To allow processing and analysis of large experimental data, the proposed framework organises images data sets in a two level structure. At the bottom, root sequences contain a time sequence of images where each image contains several root systems for a specific experimental modality (e.g. one genotype in one environment condition). On top, root sequences are organized in projects that first automate common processing of image sequences, and second allow comparative analysis of different experimental modalities. All images of the project are processed through a three steps pipeline (see fig 4): 1. Image segmentation Initial root images have to be segmented, i.e. each pixel should be classified as either background or root objects. This is done in two passes. First the smooth but non- uniform background lighting is estimated based on minimum pixel intensity with large-scale distribution. It is then removed from the original images. Second, the pixels are classified by fitting a gaussian mixture model of the remaining background noise and of the root pixels intensity. In addition to this binary classification, seeds and leaves areas are detected using specific characteristics of the observed plants. In the case of Arabidopsis, leaves are difficult to describe by their shape and they are segmented as pixels with higher intensity. Arabidopsis roots being more transparent than leaves, these last one appear whiter (see fig. 2). For rice, it is the seeds that are detected based on their radius, which is much larger than for the roots (see fig. 3). 2. Extraction of a graph representing of the observed root systems In this step, the segmented image pixels are clustered in root segments, i.e. root pieces of linear shape, which contains no branching or crossing. This is done by first applying a thinning algorithm (skeletonization) to the binary images. Then each linear curve of the obtained skeleton is further divided in a set of line segment by fitting a 1st order spline on the curve pixels. A graph is then created containing the set of extracted segments as vertices, and the set of all pairs of segments that are contiguous as edges. At this stage, the constructed graph is not necessarily a tree structure as it usually contains loops. 3. Estimation of a root architecture The root architecture is obtained by converting the root graph to an axial tree structure (Godin et al., 1998). This is done in two passes. First the graph is converted to a tree rooted at the detected seeds or leaves. The tree is computed using the shortest path algorithm that select the parent of each segment such that the sum of the edge cost along the path from the segment to the seed is minimal. The edge cost (i.e. the distance between two segments of the graph) is defined as the turning angle. The algorithm thus generates a tree structure with the straighter possible paths. This conversion breaks graph loops, meaning that it solves the axe crossing ambiguities (as shown by orange circles in the right image of fig. 4). The second pass then identifies branching relationship by selecting for each parent segment its direct child, i.e. that belongs to the same root axe. Again, the selection is done in order to minimize the axes curvature. Fig. 4. Image processing pipeline 87 RESULTS After the image-processing step, the project contains the sequences of the extracted arborescent structure (see fig 5). In order to quantify the accuracy of our reconstruction, reference data were obtained by manual annotation of the analysed root systems. Experts manually specified the root architectures on a series of images. We then compared these reference data with the structures automatically reconstructed with our pipeline. A comparison has been done on a first data set for different RSA scales. Selected results are shown in figure 6. We also have used the structural validation method of (Boudon et al., 2013). Two indices are provided by this method. For the first one, the reference and tested structured are mapped one onto each other to find similarities and differences. This gives the percentage of correctly identified elements. The second characterises the similarity of organisation of these elements in the two structures i.e. the percentage of correct connections between elements. This validation procedure has given promising results on an initial data set (between 80 and 90% correspondence). Results showing more complete analysis and over the whole data sets will be presented and discussed at the conference. a) Smallest convex hull area containing each root system b) Total root length c) Number of secondary root axes per plant Fig. 6: selected comparison with ground truth data. For all subfigures, the y-axis is the ground truth and x-axis the measures obtained with our method. The red line indicates exact match. The compared data are from 40 plants of Arabidopsis thaliana over 2 time steps. LITERATURE CITED Armengaud P, Zambaux K, Hills A, Sulpice R, Pattison RJ, Blatt MR, Amtmann A. 2009. EZ-Rhizo: integrated software for the fast and accurate measurement of root system architecture. The Plant Journal 57:945–956 Arsenault JL, Pouleur S, Messier C, Guay R. 1995. WinRHIZO™, a root-measuring system with a unique overlap correction method. HortScience 30: 906 Boudon F, Preuksakarn C, Ferraro P, Diener J, Nikinma E, Godin C. 2013. Quantitative assessement of automatic reconstructions of branching systems. Submitted Clark R T, Famoso A N, Zhao K, et al. 2012. High-throughput 2D root system phenotyping platform facilitates genetic analysis of root growth and development. Plant Cell & Environment 36:454-466 Galkovskyi T, Mileyko Y, Bucksch A, et al. 2012. GiA Roots: software for the high throughput analysis of plant root system architecture. BMC Plant Biology 12:116 Godin C, Caraglio Y. 1998. A multiscale model of plant topological structures. Journal of Theoretical Biology 191 Le Bot J, Serra V, Fabre J, Draye X, Adamowicz S, Pagès L. 2010. DART: a software to analyse root system architecture and development from captured images. Plant and Soil 326:261-273 Lobet G, Pagès L, Draye X. 2011. A Novel Image Analysis Toolbox Enabling Quantitative Analysis of System Architecture. Plant Physiology 157:29-39 Naeem A, French AP, Wells DM, Pridmore TP. 2011. High-throughput feature counting and measurement of roots. Bioinformatics 27:1337-1338 Preuksakarn C. 2012. Reconstructing plant architecture from 3D laser scanner data. Ph.D. thesis, University of Montpellier 2, France, 126 p. WinRhizo, Pro, 2012b. http://www.regent.qc.ca/assets/winrhizo_software.html Regent Instruments Inc., Canada. Zeng, G., Birchfield, S.T., Wells, C.E. 2008. Rapid automated detection of roots in minirhizotron images. Machine Vision and Applications 21:309–317. Fig. 5. Extracted RSA from the image in figure 2. Each root axe is drawn with a random colour. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 88 Terrestrial LiDAR-based tree/stand model that can simulate light interception and photosynthesis of branches, individuals, and a stand Kiyoshi Umeki* and Akira Kato Graduate School of Horticulture, Chiba University, 648 Matsudo, Matsudo city, Chiba, Japan 271-8510 *correspondence: umeki@faculty.chiba-u.jp Highlights: We developed a tree/stand model that simulates light interception and photosynthesis of first-order branches individuals, and a stand. The architecture of modelled trees was generated using tree skeletons (a main trunk and basal part of first-order branches) extracted from terrestrial LiDAR data and some architectural rules to add foliage to branches. Keywords: first-order branch, light interception, photosynthesis, terrestrial LiDAR, tree architecture Although terrestrial LiDAR has been used to extract architectural information of trees (e.g. Kato et al. 2011), the obtained architectural information has been rarely used in functional-structural plant models. In this study, we developed a tree/stand model by combining the tree skeletons extracted from terrestrial LiDAR data and some architectural rules describing extension of foliage of branches (Delagrange and Rochon 2011) in order to simulate light interception and photosynthesis of branches, individuals, and a stand. We obtained 3D point cloud data for eight Betula platyphylla trees (14.6 – 18.3 m in height) using a terrestrial LiDAR, and extracted architectural information of main trunk (3D position of stem base and tip of main trunk) and first-order branches (position, diameter, and direction of branch). We also measured length, width, and thickness of foliage of 129 first-order branches and obtained architectural rules to predict the expansion of branch foliage from the basal branch diameter that was extracted from LiDAR measurements. We added the predicted foliage to extracted tree skeletons to obtain tree mock-ups (Fig. 1), and voxelized them (Fig. 2). The hourly amount of light intercepted by voxels was determined by a ray tracing method, and converted to hourly photosynthetic gain. The Hourly photosynthetic gains of voxels were summed up to obtain values for branches, individuals, and a stand. The developed model calculated diurnal changes in photosynthetic gains of branches realistically including the effect of mutual shading among branches belonging to the same and neighbouring individuals (Fig. 3). LITERATURE CITED Delagrange S, Rochon P. 2011. Reconstruction and analysis of a deciduous sapling using digital photographs or terrestrial-LiDAR technology. Annals of Botany108: 991–1000. Kato A, Moskal LM, Kobayashi T. 2011. Effect of scan coverage on stem diameter measurement using terrestrial lidar. Proceedings of Silvilaser, Hobart, Australia. Fig. 1 (left). Modelled trees. Fig. 2 (center). Voxelized foliage. Fig. 3 (right). Predicted hourly photosynthetic gain of branches. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 89 Fast automatic method for constructing topologically and geometrically precise tree models from TLS Data Pasi Raumonen1*, Eric Casella2, Mathias Disney3, Markku Åkerblom1 and Mikko Kaasalainen1 1Department of Mathematics, Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland 2Sustainable Forestry and Climate Change, Forest Research Agency, Surrey GU10 4LH – UK 3Department of Geography, University College London, London WC1E 6BT, United Kingdom *correspondence: pasi.raumonen@tut.fi Highlights: We present a computational method that produces automatically precision models of trees from terrestrial laser scanning (TLS) data. The method is fast, typically few minutes per tree, and the resulting model contains both the topological and geometrical information of the tree. The method is validated using artificial and real TLS data. The results show that TLS together with computational reconstruction method provides fast and nondestructive means to collect structural information of trees. Keywords: Tree models, TLS, topological branching structure, branch size distribution INTRODUCTION Scanning the surface of a tree with terrestrial laser scanning (TLS) produces easily and quickly a point cloud with millions of measurements, which form a dense and comprehensive sample of the tree surface. The sample contains information of the topological and geometrical structure of the measured tree. Retrieving this information requires computational methods to process the data (van Leeuwen et al.). We have presented a fast and automatic method producing a tree model containing practically any external structural information of woody parts of the tree (Raumonen et al., Åkerblom et al.). In the method the point cloud is segmented into trunk and branches and then the segments are approximated flexibly with multiple cylinders or their generalizations such as cones. From the resulting tree model one can approximate e.g. the volumes, lengths, and taper of trunk and branches, branch size distribution, branching angles and frequency, branching structure, etc. The method works even when there are some small gaps in the measurement cover and the trunk and branches are not measured all around. THE METHOD In the method the point cloud is first partitioned into small subsets corresponding to connected patches on the tree surface. These subsets form easy-to-handle sample of the tree surface and their size needs to be small enough to capture all the details. Geometrical and topological properties of the sets, such as the neighbor- relation and underlying branch direction, are easy to determine. With these known local details the unknown global tree structure can be reconstructed. First, possible points not part of the tree, such as the measurements from the ground, are automatically removed and the base of the trunk is determined. Because some branches will often shadow other parts of the tree, there are often lots of gaps in the measurement cover and thus the subsets are in multiple connected components. To get the subsets into one component, connections between close by components are formed by updating the neighbor-relation. Then using the neighbor-relation, one can locally expand along the tree surface and recognize bifurcations. This way the subsets are automatically partitioned into segments corresponding to pieces of the trunk and branches: each segment is connected and has no bifurcations, ideally corresponding to a real branch (see Figs. 1 and 2). The segmentation starts from the base of the trunk and proceeds hierarchically separating each branch from its sub-branches. Next the surface of every segment is reconstructed with cylinders using least squares fitting. Also generalized cylinders such as cones and deformed cylinders can be used for the surface reconstruction. Finally, possible gaps between cylinders can be filled with new cylinders and the branching structure can be updated. VALIDATION For validation and controlled testing of the reconstruction method we will use an artificial tree model with simulated scanning to produce point clouds. We also use a real eucalyptus tree (see Fig. 2) and laser scanning in a laboratory. The 3D structural tree model used here represents a 30 yr old Scots pine tree (see 90 Fig. 1). The model is generated using an empirical growth model parameterized by species-dependent branching statistics in conjunction with specified external environmental conditions (Leersnijder). TLS point clouds were simulated using the librat Monte Carlo ray tracing code (Disney et al.). For the artificial tree model we know the cylinders defining it, thus we know all the same attributes as in our reconstructed models. In the eucalyptus the mass (corresponds to volume) of the branches and the trunk is measured. We will test how well the reconstructions correspond to original tree attributes (geometrical and topological) and how the reconstructions depend on the number of scanning positions and density. For the eucalyptus we have used 1 to 4 scanning positions and three different scanning resolutions with angular sampling resolutions of 0.036 (low), 0.018 (mid) and 0.009 (high) degrees. RESULTS AND DISCUSSION Figs. 1 and 2, showing the segmented point clouds and the reconstructed models, show that most of the tree structures are reconstructed faithfully. Particularly for the pine the reconstruction and original model have 100 and 99 first order branches, respectively. The reconstructions of the trunk and large branches are nearly perfect. For the smallest pine branches the measurement cover is too sparse to get meaningful reconstructions (cf. branch lengths and number of branches in Table 1). For the eucalyptus the results (see Table 1) show that the more scanning positions the better the cover is and more branches are revealed. Similarly for the scanning density: higher density reveals more branches. The volume and length of the trunk are quite well reconstructed in all cases. For branches the reconstructed volume is much larger compared to the measured one, but the situation is more complex. Most of the branches in this case are smaller or comparable with the size of the laser spot, which is about few millimeters in size. Also there is few millimeters error when different scans are registered into one coordinate system. Thus in this case the reconstruction of the radius and thus the volume is not accurate for branches. However, the branching structure and the lengths of the branches can be still reconstructed with much less error. Fig. 1. Segmented point cloud (left) and the reconstructed cylinder model (right) of the artificial Scots pine. The point cloud contains measurements from tree scanning positions. Model reconstruction time: 8 min. 91 Table 1. Some tree attributes for the pine and eucalyptus. For the eucalyptus there is measured values and reconstructed values with 1, 2, 3, and 4 scanning positions with “high” resolution and also for 2 scanning positions there are reconstructed values for “low” and “mid” resolutions. tot. vol. (dm3) trunk vol. (dm3) branch vol. (dm3) trunk length (m) branch length (m) Number of branches Pine original 651 348 303 17.2 2623 13607 Pine reconstructed 758 349 409 17.2 2109 7799 Euca measured 3.7 3.2 0.5 4.5 Euca 1 pos. high res. 6.6 3.6 3.0 4.5 62 137 Euca 2 pos. high res. 7.1 3.0 4.1 4.5 77 209 Euca 3 pos. high res. 6.7 2.8 3.9 4.5 82 255 Euca 4 pos. high res. 9.5 2.8 6.7 4.5 87 317 Euca 2 pos. mid res 7.4 2.8 4.6 4.5 48 94 Euca 2 pos. low res. 8.6 2.6 6.0 4.4 26 41 ACKNOWLEDGEMENT We thank Sanna Kaasalainen and Harri Kaartinen for providing measured TLS data from trees for development and validation of the method. LITERATURE CITED Disney M, Lewis P, Saich P. 2006. 3D modelling of forest canopy structure for remote sensing simulations in the optical and microwave domains. Remote Sensing of Environment. 100: 114-132. Leersnijder R.P. 1992. PINOGRAM: A pine growth area model. WAU dissertation 1499, Wageningen Agricultural University, The Netherlands. van Leeuwen M, Nieuwenhuis M. 2010. Retrieval of forest structural parameters using lidar remote sensing. European Journal of Forest Research. 129: 749-770. Raumonen P, Kaasalainen M, Åkerblom M, Kaasalainen S, Kaartinen H, Vastaranta M, Holopainen M, Disney M, Lewis P. 2013. Fast Automatic Precision Tree Models from Terrestrial Laser Scanner Data. Remote Sensing. Åkerblom M, Raumonen P, Kaasalainen M, Kaasalainen S, Kaartinen H. 2012. Comprehensive quantitative tree models from TLS data. Geoscience and Remote Sensing Symposium (IGARSS) 2012, 6507-6510. Fig. 2. Segmented point cloud (left) and the reconstructed cylinder model (right) of the eucalyptus fixed in a stand. The point cloud contains measurements from three high-resolution scans. Model reconstruction time: 30 sec. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 92 A geometrical model generator for quasi-axisymmetric fruit Seppe Rogge*, Shiferaw Beyene, Els Herremans, Thijs Defraeye, Pieter Verboven, Bart Nicolai Flanders Centre of Postharvest Technology / BIOSYST-MeBioS, University of Leuven, Willem de Croylaan 42, B-3001, Leuven, Belgium *correspondence: seppe.rogge@biw.kuleuven.be Highlights: A geometrical model generator for fruit is presented. The generator uses X-ray tomography images of quasi-axisymmetric fruit as input, describes the shape of the fruit with elliptical Fourier descriptors, and uses statistical analysis to randomly generate new representative fruit shapes from this dataset, which can be directly used as CAD models for CFD or FEM analysis. Keywords: elliptic Fourier descriptors, shape description, shape generation, biological variability INTRODUCTION Structure, shape and size are significant features of plant organs for gas and water exchange in relation to physiological processes such as growth (Abera et al., 2012), respiration (Ho et al., 2011) and photosynthesis (Ho et al., 2012), as well as to postharvest quality of plant products such as fruit (Jancsók et al., 2001; Nguyen et al., 2006; Veraverbeke et al., 2006; Delele et al., 2008, 2009; Ambaw et al., 2012). However, realistic descriptors and models of the geometry of biological products are not always available, and complex shapes are often replaced by basic geometries, like ellipsoids (Rashidi & Gholami, 2008) or spheres (Delele et al., 2008, 2009; Ambaw et al., 2012). 2D shape description and representation of complex shapes has recently been achieved (Costa et al., 2011; Moreda et al., 2012). A popular way to describe the contour of a 2D image are Fourier descriptors (FD). FD have some advantages compared with other methods: the descriptors are simple to compute, they have a physical meaning, and they capture both global and local features (Zhang & Lu, 2004). Mebatsion et al. (2011) described the contour of sections of plant organs with these descriptors, and interpolated different contours to construct 3D models of the plant organs. The more complex the shape, the higher the number of contours used for one image. A drawback of this method is its destructive nature. New techniques, such as MRI (magnetic resonance imaging) and X-ray tomography reveal the inner and outer structure of biological material in a non-destructive way (Lammertyn et al., 2003; Herremans et al., 2013). Furthermore, shape description analysis on a set of products opens perspectives to automatic generation of random shapes, based on statistical analysis of the dataset, but has not been explored yet. The resulting database of biological products could introduce biological shape variability, as present in reality, into numerical simulations. Here, we present a geometrical model generator for apple fruit based on X-ray tomography of whole apples; once a limited number of fruit shapes is analysed by means of FD, an unlimited amount of new shapes, representing the variability of a certain species or even cultivar, can be generated. The procedure was entirely coded in Matlab (The MathWorks Inc., Natick, MA), and the amount of necessary manual intervention was reduced to a minimum. METHODOLOGY The geometrical model generator consists of two parts: in the first part, shapes are analysed by means of FD, and in the second part, new models are generated based on the FD statistics. The input dataset consists of X-ray computed tomography (CT) scans of 73 Braeburn apples. For each apple, a cross section image was constructed. This section was chosen manually in such a way that it always contains the centre of the apple, and that the stem appears as little as possible in the image. Large stems cannot appear in the image, because they are curved and disrupt the (quasi-)symmetry of the apple that results in 3D shape artefacts, when generating a new fruit shape. The contour of the section was extracted by Matlab’s built-in edge detection and boundary tracing routines. Fourier descriptors were calculated from the contours. In this study, elliptic Fourier descriptors (EFD) introduced by Kuhl and Giardina (1982), were applied. The important advantage of this type of FD is that they can deal with outlines that curve back on themselves. The number of computed EFD is a multiple of four: a sine and a cosine term both in the r and z-direction (cylindrical coordinates). From sensitivity 93 analysis, 25x4 descriptors were found to be sufficient; higher order descriptors represented unnecessary details in the contour. In the resulting 3D model, fluctuations in the r and z-direction should not be too prominent compared with those in the θ-direction. From the 73 sets of FD, a new set of FD with the average value of each descriptor, and the covariance matrix of all descriptors, was calculated. With the covariance decomposition method described in Alabert (1987), new 2D geometrical contours were generated, using the descriptor averages and the covariance matrix. The first step towards making a 3D model of the new set of descriptors was calculating the EFD of its mirror image along the axis of (quasi)symmetry. Subsequently, a number of new FD sets was generated by interpolating between these two sets of descriptors. Each set is then converted to a contour (see Figure 1). Next, the contours are rotated around the axis of symmetry at an angle between 0 and π. An example with only 20 (for clarity) half- contours can be seen in Figure 2a. This way, a smooth 3D shape is created by interpolation. The final step was creating a NURBS surface, that fits to the set of datapoints, and exporting this surface as an IGES file, a file format which can be directly used as a CAD input in numerical software for modelling transport and physiological processes. Fig. 1. A newly generated contour (thick blue line), the mirror image of this contour (thick red line), and contours created by interpolating between the two sets of EFD of these contours (small lines). Only 10 contours are shown for clarity. RESULTS AND DISCUSSION A resulting apple shape can be seen in Figure 2b. The quality of the generated shapes was tested by comparing the volumes of the original 73 Braeburn apples with the volumes of the generated shapes. For this purpose, 1000 new shapes were generated. They had an average volume of 208 cm³, with a standard deviation of 36 cm³, while the original apples had an average volume of 208 cm³, with a standard deviation of 31 cm³. The perfect agreement of the average volume of the generated shapes with that of the real fruit indicates that the shape generator is a stable algorithm. The slightly higher spread in volumes, on the other hand, can be explained by the fact that only one section is used to generate a new shape. In real apples, cross-sections with a small or large surface will be somewhat averaged out by the other cross-sections. It should be noted that some of the generated shapes do not represent realistic apple shapes with smooth axisymmetric features. These shapes originate particularly when asymmetric contours are revolved. Nevertheless, the majority of the shapes (roughly 80%) are good-quality (both shape and size) apple-like shapes; bad shapes can easily be excluded by the user. In conclusion, a geometrical model generator for quasi-axisymmetric shapes is presented. The method is found to be fast and requires little human intervention. The resulting output are generally realistic apple shapes, which are exported in the form of CAD models, that can easily be used for numerical simulations. 94 Fig. 2. New 3D generated shape of an apple. a) Contours revolved around the rotation axis. The thick blue line at the right and the thick red line at the left describe the original contour. Only 20 half-contours are shown for clarity. b) NURBS surface fitted to the revolved contours. LITERATURE CITED Abera MK, Fanta SW, Verboven P, Ho QT, Carmeliet J, Nicolai BM. 2012. Virtual Fruit Tissue Generation Based on Cell Growth Modelling. Food and Bioprocess Technology in press DOI: 10.1007/s11947-011-0775-4. Alabert F. 1987. The practice of fast conditional simulations through the LU decomposition of the covariance matrix. Mathematical Geology 19:369-386. Ambaw A, Verboven P, Delele MA, et al. 2012. CFD Modelling of the 3D Spatial and Temporal Distribution of 1- methylcyclopropene in a Fruit Storage Container. Food and Bioprocess Technology in press DOI: 10.1007/s11947- 012-0913-7. Costa C, Antonucci F, Pallottino F, Aguzzi J, Sun DW, Menesatti P. 2011. Shape analysis of agricultural products: A review of recent research advances and potential application to computer vision. Food and Bioprocess Technology 4:673-692. Delele MA, Tijskens E, Atalay YT, et al. 2008. Combined discrete element and CFD modelling of airflow through random stacking of horticultural products in vented boxes. Journal of food engineering 89:33-41. Delele MA, Schenk A, Tijskens E, Ramon H, Nicolai BM, Verboven P. 2009. Optimization of the humidification of cold stores by pressurized water atomizers based on a multiscale CFD model. Journal of food engineering 91:228- 239. Herremans E, Verboven P, Bongaers E, et al. 2013. Characterisation of ‘Braeburn’ browning disorder by means of X-ray micro-CT. Postharvest Biology and Technology 75:114-124. Ho QT, Verboven P, Verlinden BE, et al. 2011. A three-dimensional multiscale model for gas exchange in fruit. Plant physiology 155:1158-1168. Ho QT, Verboven P, Yin X, Struik PC, Nicolai BM. 2012. A microscale model for combined CO2 diffusion and photosynthesis in leaves. PloS one 7:e48376. doi:10.1371/journal.pone.0048376 Jancsók PT, Clijmans L, Nicolai BM, De Baerdemaeker J. 2001. Investigation of the effect of shape on the acoustic response of ‘conference’pears by finite element modelling. Postharvest biology and technology 23:1-12. Kuhl FP, Giardina CR. 1982. Elliptic Fourier features of a closed contour. Computer graphics and image processing 18:236-258. Lammertyn J, Dresselaers T, Van Hecke P, Jancsók P, Wevers M, Nicolai BM. 2003. Analysis of the time course of core breakdown in ‘Conference’ pears by means of MRI and X-ray CT. Postharvest biology and technology 29:19-28. Mebatsion H K, Boudon F, Godin C, et al. 2011. A novel profile based model for virtual representation of quasi- symmetric plant organs. Computers and Electronics in Agriculture 75:113-124. Moreda GP, Muñoz MA, Ruiz-Altisent M, Perdigones A. 2012. Shape determination of horticultural produce using two-dimensional computer vision–A review. Journal of Food Engineering 108:245-261. Nguyen TA, Dresselaers T, Verboven P, et al. 2006. Finite element modelling and MRI validation of 3D transient water profiles in pears during postharvest storage. Journal of the Science of Food and Agriculture 86:745-756. Rashidi M, Gholami M. 2008. Determination of kiwifruit volume using ellipsoid approximation and image-processing methods. International Journal of Agriculture & Biology 10:375–380 Veraverbeke EA, Verboven P, Lammertyn J, Cronje P, De Baerdemaeker J, Nicolai BM. 2006. Thermographic surface quality evaluation of apple. Journal of food engineering 77:162-168. Zhang D, Lu G. 2004. Review of shape representation and description techniques. Pattern recognition 37:1-19. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 95 Automatic 3D plant reconstruction from photographies, segmentation and classification of leaves and internodes using clustering Thiago Santos1 and Julio Ueda1 1Embrapa Agricultural Informatics, PO Box 6041, 13083-886 Campinas, Brazil *correspondence: thiago.santos@embrapa.br Highlights: A stereo approach for 3D plant modelling is presented. Using only a set of photographies, the method produces a dense 3D point cloud that samples the plant surface. Clustering automatically segments the plant structure into meaningful parts, which are classified as leaves or internodes. Measurements can be computed for each element, as area or surface normals. Keywords: 3d plant models, image-based reconstruction, multiple view stereo, structure segmentation INTRODUCTION Non-invasive imaging and image analysis are novel technologies that have been employed to narrow the “phenotyping bottleneck”. Three-dimensional plant models are traditionally acquired by invasive, slow and tedious manual measurements, aided by electromagnetic 3D tracking devices. Laser scanning figures as an alternative (Preuksakarn et al., 2010; Delagrance and Rochon, 2011), but it presents some drawbacks as sensitivity to occlusion, lack of color and texture information and the high price of the laser scanning devices. A generated 3D point cloud must be properly segmented and classified for automatic measurement and characterization of the plant structure. Stereo-based techniques are emerging as a cheap and non-invasive alternative for 3D modelling of plants (Quan et al., 2006; Biskup et al., 2007; Santos and Oliveira, 2012). The present work extends our previous work (Santos and Oliveira, 2012) by (a) segmenting the plant models in significant structures using clustering in 3D space, (b) classifying the recovered segments into meaningful classes (leaves and internodes) and (c) performing area measurements in the model and comparing them against ground-truth data, validating the framework as an effective metrology tool. MATERIAL A set of 387 pictures of a mint specimen (Mentha) was acquired by a Canon Powershot G11 camera placed in different positions (see Fig. 1A and Fig. 1B). The potted specimen was photographed indoors, avoiding movements caused by wind. After the image acquisition step, the leaves were removed and placed in a table scanner to acquire the area measurements used as ground-truth. METHOD The proposed technique is composed by the following steps: Multiple view stereo plant reconstruction – The method input is a set of several high-resolution photographies for each specimen. Camera position is automatically recovered by structure from motion. First, the SIFT algorithm (Lowe, 2004) is employed to detect and describe image features in each photography. The feature descriptors are used to find matches between features in different images. Projective reconstruction and robust estimation techniques (Hartley and Zisserman, 2003) are employed to define the relative position between images, i.e., the position of the camera at each image acquisition (Fig. 1B). Once each camera pose is defined, a sparse 3D point cloud for the plant surface is produced based on feature matching. Finally, a region growing multiple view stereo technique is employed to produce a dense 3D point cloud (Fig. 1C). Santos and Oliveira (2012) present a more detailed description of this 3D reconstruction step. Segmentation by clustering of surface normals – The dense point cloud is segmented using a smoothness constraint, as proposed by Rabbani et al. (2006). First, the surface normals are estimated at each point pi. This estimation is performed by finding a plane tangent to the surface by least-squares plane fitting, using the points in the neighbourhood of pi. Then a region growing algorithm is applied: for a point pi in a segment R, each neigh point pj is added to R if the angle between the normal vectors of pi and pj is inferior to a 96 threshold θ. This process is repeated until every point is assigned to a region. The detailed algorithm can be found in Rabbani et al. (2006). (a) (b) (c) (d) Fig. 1. Results for the mint dataset. (a) Input images acquired from different angles. (b) Result from the structure from motion step: camera poses (red cones) and a sparse point cloud for the plant (green). (c) Result from the multiple view stereo step, a dense point cloud sampling of the plant surface. (d) Smooth surfaces for the largest leaves, computed using the NURBS fitting procedure, after leaf segmentation and classification. Classification using width/length ratio – Each segment is composed by a set of 3D points. Features can be computed from this set for segment characterization and further classification. For the specimen used in this work, the recovered segments correspond to leaves, internodes or spurious structures, as fragments from soil. These classes can be easily discriminated using their size and dimensions. Taking each point in the segment as a three-dimensional vector pi = (xi, yi, zi), principal component analysis (PCA) was applied. In the transformed space, the ordered variances were used to describe the segments’ dimensions in their main axes. A simple linear classifier was able to classify the leaves, if properly segmented. Leaf surface fitting using NURBS – Leaves surfaces were approximated by NURBS fitting (Piegl, 1991), getting a smooth and regularized 3D mesh representing the surface (Fig. 1D). RESULTS Fig. 1B shows the recovered camera poses and sparse 3D model produced by structure from motion. The chessboard observed in Fig. 1A is generally used in computer vision for camera calibration, but in the present experiment it is employed just to define the scale factor for the final model – the leaves' textures and edges provide all the image features needed for the camera pose estimation. Fig. 1C shows the 3D dense point cloud produced by the multiple view stereo step. After cloud segmentation and classification, the largest leaves were successfully identified. Small leaves were sub-sampled in the point cloud, resulting in over-segmentation and misclassification. A smoothed surface was produced for each one of the correct leaves by NURBS fitting. Table 1 shows the estimated area vs. the ground-truth data. 97 Table 1. The 3D model as a measurement tool. Individual leaf area computed on the the smooth NURBS surfaces vs. ground-truth produced using a common scanner. Leaf/Area (mm²) Ground-truth Computed on the 3D model Difference 1 1434.48 1510.60 5.31% 2 1464.68 1500.91 2.47% 3 1144.59 1167.69 2.02% 4 1157.50 1177.38 1.72% 5 1007.02 1005.48 -0.15% 6 791.39 735.33 -7.08% 7 899.51 956.64 6.35% 8 954.69 1079.98 13.12% 9 660.58 660.68 0.02% CONCLUSION In the proposed methodology, a free moving camera is able to capture the plant structure from different views, differently of Biskup et al. (2007) fixed-camera approach. The structure is recovered only from image data, without human intervention as the branches sketches employed by Quan et al. (2006). The large number of input images should not be a problem because video acquisition is able to provide thousands of video frames that could be automatically selected. Further steps under development are (i) more extensive tests on different species, (ii) an interactive tool to help human operators to perform computer-aided video acquisition with feedback and (iii) an egomotion system based on structure from motion for robot path planning in automatized platforms. FUNDING This work was supported by Brazilian Agricultural Research Corporation (Embrapa) under grant [03.11.07. 007.00.00]. LITERATURE CITED Biskup B, Scharr H, Schurr U, Rascher U. 2007. A stereo imaging system for measuring structural parameters of plant canopies. Plant, Cell & Environment, 30:1299–1308. Delagrange S, Rochon P. 2011. Reconstruction and analysis of a deciduous sapling using digital photographs or terrestrial-LiDAR technology. Annals of botany, 108:991–1000. Hartley R, Zisserman A. 2003. Multiple View Geometry in Computer Vision, 2th edn. Cambridge: Cambridge University Press. Lowe DG. 2004. Distinctive Image Features from Scale-Invariant Keypoints. International Journal of Computer Vision, 60:91-110. Piegl L. 1991. On NURBS: a survey. IEEE Computer Graphics and Applications, 11(1):55-71. Preuksakarn C, Boudon F, Ferraro P, Durand J-B, Nikinmaa E, Godin, C. 2010. Reconstructing plant architecture from 3D laser scanner data . In Proc. of the 6th Intl. Workshop on Functional-Structural Plant Models, 14-16. Quan L, Tan P, Zeng G, Yuan L, Wang J, Kang SB. 2006. Image-based plant modelling. ACM Transactions on Graphics, 25: 599–604. Rabbani T, van den Heuvel F, Vosselmann G. 2006. Segmentation of point clouds using smoothness constraint, In International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 36(5):248–253. Santos TT, Oliveira AA. 2012. Image-based 3D digitizing for plant architecture analysis and phenotyping. In Workshop on Industry Applications (WGARI) in SIBGRAPI 2012 (XXV Conference on Graphics, Patterns and Images), 21-28. http://www.decom.ufop.br/sibgrapi2012/index.php/call/wgari. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 98 Monitoring the diel growth of individual Arabidopsis leaves using a laser scanning approach Tino Dornbusch*, Olivier Michaud and Christian Fankhauser 1Center for Integrative Genomics, Faculty of Biology and Medicine, University of Lausanne, 1015 Lausanne, Switzerland *correspondence: tino.dornbusch@unil.ch Highlights: A novel phenotyping approach is presented to monitor diel variation in elongation and elevation angle of individual leaves with high precision and throughput. Leaf elongation and changes in leaf elevation angle follow characteristic diel rhythms and show an overall decrease with increasing leaf age. Keywords: Arabidopsis, phenotyping, leaf growth, laser scanning INTRODUCTION During their life cycle, flowering plants are frequently facing fluctuating environmental conditions, which are often sub-optimal for growth. To cope with that, plants possess a range of adaptive growth responses and protection mechanisms. The model plant Arabidopsis thaliana provides a good platform to link phenotypic plasticity to the function of specific genes, proteins or protein complexes. Indeed genetic resources are well explored and available tools are extremely well developed. On the other hand, phenotyping of leaf growth have largely depended on semi-automated two-dimensional (2D) image processing (Millenaar et al. 2005; Wiese et al. 2007; De Vylder et al. 2012). These methods are of limited throughput and usually restricted to analyze few time-points, since imaging (in particular at night) interferes with growth processes. We have applied a laser scanning technique using the Scanalyzer HTS (Lemnatec GmbH, Würselen, Germany) to monitor the diel growth pattern of individual leaves. Laser scanner images of growing Arabidopsis plants were recorded at intervals of 10 to 60 minutes. Images, containing the 3D information of individual plants were processed. As principal output, length and elevation angle of individual leaves were computed. MATERIAL AND METHODS Plants were grown in pots filled with a mixture of peat-rich soil and vermiculite. Before their transfer to the Scanning device ScanAlyzer HTS (Lemnatec GmbH, Würselen, Germany) they were kept 10 days in a Percival CU-36 L4 incubator (Percival Scientific Inc., Perry, IA, USA). The photoperiod was 16 h. Relative humidity inside the Percival incubator was between 80-85% and temperature was maintained at 21°C. More detailed information on growth conditions and laser scanning protocol are given by Dornbusch et al. (2012). Plants were imaged over a period of 9 days. Images were taken each 60 min. The image-processing pipeline to extract geometric features of individual leaves is illustrated in Figure 1. As a result, length l and elevation angle φ are displayed as function of time t. RESULTS AND DISCUSSION As an example, we present here the growth pattern of the first four leaves (two cotyledons not counted) by looking at the diel pattern of leaf elongation (ltip, Fig. 2a) and leaf elevation angle (φtip, Fig. 2b) for the first four leaves (leaf 4 being the youngest). Leaf 1,2 developed at the same time and grew at similar rates. At day 4, the younger leaves 3 and 4 were shorter than leaf and 2, but they were expanding at a higher rate during this specific period and became longer starting from day 6. Leaf elongation was reduced during night periods and increased shortly after dawn (Fig. 2a) and generally decreased with increasing leaf age. 99 Fig. 1. Flow chart representing the different steps of the developed image processing algorithm: (a) 2.5D height-scaled images of plants, which are transformed into 3D point clouds, recorded at different scanning or iteration steps i. 3D point clouds of individual plants are obtained by segmentation, (b) 3D point cloud of the plant circled in Fig. 2a (example here for illustrating the following algorithm), (c) superimposition of point clouds of the plant in (b) at different iteration steps i, (d) As first step of the iterative loop: PT’ is determined by the user if i =1 or PT’=PT (i -1) if i > 1, (e) result of the filtering with the selection of points (in green) that are in a defined area around PT’, (f) computation of PT(i) from filtered points, (g) Point cloud in (f) rotated and normalized such that PT(i) = [1,0,0]. The considered leaf is hence in the x-y plane. In yellow, points nearby the tip of the leaf, (h) same projection than in (g). In yellow, points resulting from an additional filtering, which should cover most of the leaf surface (leaf 2 here), (i) Computing the maximum of the first derivative of the ‘width’ of the leaf, (j) Obtaining PP(i), which is the centroid of the set of points close to the computed max. derivative (highlighted by the black box); Having computed PT(i) and PP(i), the point cloud of the next time step i+1 is processed, initiating the same loop (d) to (i) using PT (i -1) as input for (d). Note that apart from the first iteration step i=1, the algorithm is fully automated. 100 Fig. 2. (a) Mean leaf length ltip and (b) leaf elevation angle Φtip for leaves 1 to 4 plotted against time (t). Grey bands represent night periods. One curve represents the mean value computed from 5 individual leaves, which were tracked over the whole period. The dashed lines in (b) represent the trend lines to illustrate the decreasing leaf angle. In general, leaves followed a sinusoidal diel pattern of leaf elevation angle (φtip), being most horizontal in the early morning and most vertical in the evening (Fig. 2b). An abrupt upward movement of leaves (increase in φtip) was measured at day-night transitions for all four leaves throughout the whole period. There was a clear trend of decreasing φtip with increasing leaf age (dashed lines in Fig 2b). At the same time the maximal difference in elevation angle (amplitude during 24 h) was also reduced with leaf age (Fig. 2b) in the same fashion as leaf elongation (Fig. 2a). This leads to the interesting question to what extent leaf elongation and concomitant changes in leaf angle of Arabidopsis leaves are linked and rely on the same growth mechanisms. For instance, Schuster and Engelmann (1997) have shown that circumnutations in hypocotyls (similar to changes in elevation angle in leaves) were more prominent for young hypocotyls growing at faster rates. To the best of our knowledge, no comparable study has been done for Arabidopsis leaves. To conclude, we have presented a non-invasive methodology that allows phenotyping of individual Arabidopsis leaves at high temporal and spatial resolution. The throughput is compatible with genetic screens and, in combination, both would allow to unravel molecular mechanisms behind the dynamic aspects of leaf growth. LITERATURE CITED De Vylder J, Vandenbussche F, Hu Y, Philips W, VanDerStraeten D. 2012. Rosette Tracker: an open source image analysis tool for automatic quantification of genotype effects. Plant Physiology 160:1149-1159. Dornbusch T, Lorrain S, Kuznetsov D, Fortier A, Liechti R, Xenarios I, Fankhauser C. 2012. Measuring the diurnal pattern of leaf hyponasty and growth in Arabidopsis–a novel phenotyping approach using laser scanning. Functional Plant Biology 39:860-869. Millenaar F, Cox M, van Berkel Y. 2005. Ethylene-induced differential growth of petioles in Arabidopsis. Analyzing natural variation, response kinetics, and regulation. Plant Physiology 137:998-1008. Schuster J, Engelmann W. 1997. Circumnutations of Arabidopsis thaliana seedlings. Biological Rhythm Research 28: 422-440. Wiese A, Christ MM, Virnich O, Schurr U, Walter A. 2007. Spatio-temporal leaf growth patterns of Arabidopsis thaliana and evidence for sugar control of the diel leaf growth cycle. New Phytologist 174:752-761. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 101 A Blender addon for the 3-d digitizer FASTRAK for plant structure acquisition Katarzyna Wasilczuk,1 Michael Henke,1 Katarína Smoleňová,1 Yongzhi Ong1 and Winfried Kurth1* 1Department Ecoinformatics, Biometrics and Forest Growth, Georg-August University of Göttingen, Büsgenweg 4, 37077 Göttingen, Germany *correspondence: wk@informatik.uni-goettingen.de Highlights: An addon for the open-source 3-d graphical modelling software Blender was implemented. It enables communication with the electromagnetic 3-d digitizer FASTRAK via a serial interface. Discrete and continuous point acquisition mode, immediate visualization in Blender's 3-d view, acoustic feedback, creation of standard geometry (e.g., cylindrical internodes) and of free-form volumetric shapes (for fruits, tree trunks etc.), calibration and rectification in case of field disturbances, and MTG export are supported. Tests confirmed that the addon has some advantages against previous software for the FASTRAK digitizer. Keywords: electromagnetic digitizer, 3-d data, position tracking, Blender, FASTRAK, Polhemus Blender (Blender Foundation 2012) is a multi-purpose, open-source 3-d modelling tool providing various interactive navigation, editing and animation functions. We implemented an addon which can be activated within the GUI of Blender and which communicates with the Polhemus FASTRAK digitizer. Our addon provides some extensions compared to existing software (e.g., Donès et al. 2006), namely, the option to switch between discrete and continuous position acquisition mode, improved calibration and rectification facilities (using linear transformations) and sound feedback during the tracking process. Export of the resulting 3-d virtual plants in simple tables and in a subset of the MTG data format (Cokelaer & Pradal 2009), which can be processed by GroIMP (Kniemeyer & Kurth 2008) and by OpenAlea (Pradal et al. 2008), are supported. Future improvements will include extensions to the MTG export and enhancement of the triangulation method which we currently use for free-form shapes (leaves, fruits, flowers). – This research was partially funded by DFG under project identifier Ku 847/8-1. All support is gratefully acknowledged. Fig. 1 (from left to right): Screenshot of Blender, photograph of a strawberry plant and virtual reconstruction as result of using the FASTRAK 3-d digitizer with the new Blender addon (from Wasilczuk 2012). LITERATURE CITED Blender Foundation. 2012. Blender Documentation Contents – Blender 2.62.2 – API documentation. http://www.blender.org/documentation/blender_python_api_2_62_2/ (last access: Sept. 10, 2012). Cokelaer T, Pradal C. 2009. MTG User Guide. http://openalea.gforge.inria.fr/doc/vplants/mtg/doc/html/user/ (last access June 11, 2012). Donès N, Adam B, Sinoquet H. 2006. PiafDigit – software to drive a Polhemus Fastrak 3 SPACE 3D digitiser and for the acquisition of plant architecture. Version 1.0. UMR PIAF INRA-UBP: Clermont-Ferrand. Kniemeyer O, Kurth W. 2008. The modelling platform GroIMP and the programming language XL. In: Schürr A, Nagl M, Zündorf A (eds.): AGTIVE ’07. LNCS 5088, Springer, Berlin, 570-572. Pradal C, Dufour-Kowalski S, Boudon F, Fournier C, Godin C. 2008. OpenAlea: A visual programming and com- ponent-based software platform for plant modeling. Functional Plant Biology 35:751-760. Wasilczuk, K. 2012. Implementation, Test und Dokumentation einer nutzerfreundlichen Schnittstellensoftware für den 3D-Scanner FASTRAK. B.Sc. thesis, Department of Computer Science, University of Göttingen. EXCHANGE AND TRANSPORT PROCESSES IN PLANTS Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 105 KEYNOTE: Interplay between material flows and structural properties in dynamics of tree Teemu Hölttä and Eero Nikinmaa Department of Forest Sciences, PO Box 27, 00014 University of Helsinki, Finland *correspondence: teemu.holtta@helsinki.fi Highlights: A whole tree level theoretical framework on the linkage between leaf gas exchange, long distance xylem and phloem transport and tree growth is presented. Keywords: cambial growth, cavitation, hydraulic architecture, phloem transport, stomatal control, xylem transport INTRODUCTION Pressure driven transport in the xylem and phloem of trees means that leaf gas exchange, long distance material transport, growth and structural development are linked processes with feedbacks. However, the time constants of these different processes are very different which makes integrating studies of these phenomena a challenging task. Proper matching of the gas exchange, current structural growth and accumulated structure with the environmental conditions is crucial to the success and survival of trees (Brodridd 2009), particularly in the rapidly changing climate. This determines both the competitive capacity and resistivity to extreme conditions of trees. The efficiency xylem transport is crucial for tree productivity, growth and overall performance (Bond and Kavanagh 1997). Water in the xylem is in a metastable state under negative hydrostatic pressure and thus vulnerable to phase transition by cavitation, which threatens xylem transport capacity (Tyree and Sperry 1989, Choat et al. 2012). Excessive cavitation during drought has been suggested to be main reason for tree mortality during drought (McDowell 2011). The requirements for xylem efficiency (i.e. hydraulic conductance) and safety (ability to withstand negative pressure without cavitation) are in conflict with each other; more conductive tissue tends to be more vulnerable to cavitation (e.g. Martinez-Vilalta et al. 2002). Xylem conductance increases, and vulnerability to cavitation decreases, with increasing xylem conduit size and increasing porosity of the pit membrane found between neighbouring conduits (Sperry and Hacke 2004). Osmotic matching of the negative xylem hydrostatic pressure is involved in a number of central plant processes such as in leaf gas exchange, phloem transport and cambial growth. In phloem transport the positive turgor pressure required to drive the flow is obtained by active loading of osmotic substances, mainly sugars, to the phloem at the sources. Phloem transport and utilization of photosynthates in sinks have to maintain the rate of carbon assimilation in photosynthesis, or carbohydrate accumulation will force stomatal closure and down-regulation of photosynthesis (Paul and Foyer, 2001). The functioning of the phloem tissue in relation to environmental and structural factors is not well understood, although some theoretical predictions (e.g. Hölttä et al. 2009) and laboratory measurements (Mullendore et al. 2012) relating phloem structure to flow rate have been made. Adjustment of the stomatal opening controls leaf gas exchange in response to various environmental and internal signals. This topic has long been under rigorous study, but is still far from being understood (Buckely 2005). One obstacle is that our present understanding is based mainly on leaf level relations (Ball et al. 1987) without much consideration having been paid to whole tree level interactions and constraints. As in the case of leaf gas exchange and phloem transport, the growth of new tissues also requires high carbohydrate availability and high turgor pressure in the different phases of growth including cell division, enlargement, and cell wall synthesis. The positive turgor pressure results from the interplay between the negative water pressure in xylem and sufficient sugar concentration in the living cambium to maintain positive pressure osmotically. In addition, carbon assimilates have a dual role in growth as apart from providing the sufficient enlarging pressure, they provide the raw material for cell wall thickening (e.g. DeSchepper and Steppe 2010, Hölttä et al. 2010, Pantin 2012). Maintenance of the balance between hydrostatic and osmotic pressures set strong boundary conditions for leaf gas exchange, within tree transport, storage, structure and growth and help to reveal how biological regulation needs to work to maintain measurable attributes, such as pressure and sugar concentration, within observed range. Resource wise, the construction and maintenance of the xylem and phloem tissue require a major proportion of the trees carbon 106 and nitrogen. With growth in tree height, the transport distance within the tree increases, and the transport of water (e.g. Koch et al. 2004), and perhaps even that of the assimilate products (e.g. Thompson 2006), become increasingly limiting for tree performance and growth. At the same time, the proportion of resource allocation to both of these tissues must increase. Here we present a whole tree level theoretical framework on the linkage between leaf gas exchange, long distance xylem and phloem transport, and sink relations such as growth. Using this theoretical framework we demonstrate how xylem and phloem transport constrain whole tree level water and carbon exchange and growth in varying environmental conditions. WHOLE TREE LEVEL LINKAGE OF LEAF GAS EXCHANGE, XYLEM AND PHLOEM TRANSPORT AND SINK RELATIONS The interconnections and the underlying mathematical formulation amongst transpiration, photosynthesis, xylem and phloem transport, soil water status, and sink sugar status are depicted in Fig. 1. At leaf level, water is lost and carbon assimilated to and from atmosphere through stomatal openings (*). The driving forces for these fluxes are saturation pressure deficit (CH2O,i-CH2O,a) of water vapor in the atmosphere, and the difference in CO2 concentration between the ambient air and the internal CO2 concentration in the gas phase in the leaf (CCO2,a-CCO2,i). The utilization of CO2 in photosynthesis (**, inside the dotted box) creates and maintains the difference in the CO2 concentration required for assimilation. Accumulation of assimilated sugars and/or decrease in water potential in the leaf may decrease photosynthesis (**) due to stomatal and non-stomatal factors, e.g. due to down-regulation of photosynthetic machinery and decreases in mesophyll conductance (e.g. Chaves et al. 2003). The sugars assimilated by photosynthesis are passed mostly passively along the concentration gradient in trees (Turgeon 2010) from the mesophyll cells (where photosynthesis occurs) to the phloem. The photosynthesis box (**) contains many processes including the solution of CO2 to the liquid phase and its diffusion in it, light and dark reactions of photosynthesis, and phloem loading which are not depicted in the figure. Water loss at the transpiring surfaces in the leaves lowers the leaf xylem water potential which creates a force to draw water to the leaves though the xylem tissue from all the way from the roots and soil in the direction of the xylem water potential gradient (†). The assimilated sugars loaded to the leaf phloem draw osmotically water from the adjacent xylem tissue to maintain water potential equilibrium (††) and increase phloem hydrostatic (turgor) pressure. This positive pressure in the leaf phloem pushes water and dissolved sugars in the direction of the pressure gradient (†††) towards locations where the sugars are used in carbon sinks. Sugar utilization in the sink (***) lowers the osmotic concentration of the sap and keeps the turgor pressure low. In the absence of sugar utilization in the sink, the information of increase in sugar concentration at the sink is transmitted rapidly though the phloem to the source (leaves) due to pressure changes. Water potential equilibrium between the xylem and phloem is maintained at all locations in the tree (††). Cambial growth (‡) occurs as sugars are unloaded from phloem to cambium and this draws water osmotically from the xylem to the cambium to create pressure for cell expansion. All these processes are coupled and constrained by one another. In steady state, the transpiration rate (E) must equal xylem sap flow rate (Jx), CO2 assimilation rate (A) must equal the phloem sap flow rate (Jp), which in turn must equal the rate of sugar utilization at sink. The xylem and phloem are hydraulically coupled so that phloem turgor pressure plus osmotic pressure must equal the xylem water potential in all parts of the tree (††). Xylem conductance (kx) is dependent on xylem water potential due to embolism formation by cavitation (Tyree and Sperry 1989), and phloem conductance (kp) is dependent on phloem sugar concentration due to viscosity, which increase highly non-linearly with sugar concentration (Hölttä et al. 2009). Conductances also depend on temperature due to the temperature dependency of viscosity. Furthermore, there seems to be a connection between phloem transport and recovery of xylem from embolism (Nardini et al. 2011). Transpiration, soil water availability, photosynthesis and sugar utilization at the sinks set the pressure gradients for xylem and phloem transport. In addition, photosynthesis is directly coupled to leaf xylem water potential and osmotic concentration, which, in turn are closely linked to avoid loss of turgor pressure and leaf dehydration. Finally, the rate of cambial growth at each height is dependent on pressure in the cambium, which is tightly linked to local phloem sugar concentration and xylem pressure. The formation of new xylem and phloem tissue in cambial growth affects the xylem water pressure and phloem turgor pressure after growth has been completed. 107 Fig. 1. Xylem and phloem transport, stomatal conductance and photosynthesis, and sink relations are interrelated. E is transpiration rate, Jx xylem sap flow rate, kx xylem conductance, ψleaf leaf xylem water potential, ψsoil root xylem water potential, g stomatal conductance, CH2O,a ambient H2O concentration, CH2O,i leaf internal H2O concentration, A photosynthesis rate, c “average” sugar concentration in phloem, kp phloem conductance, Pleaf turgor pressure in leaf, Proot turgor pressure in root, Jp phloem sap flow rate, CCO2,a ambient CO2 concentration, CCO2,i leaf internal CO2 concentration, R a physical constant, T temperature, G is growth rate, Ф is cell wall (irreversible) extensibility, and P0 is threshold pressure for cell wall extensibility. The structure of the xylem, i.e. mainly conduit size and number and pit pore size and density, will determine vulnerability to cavitation and the specific xylem conductivity which together with xylem cross- sectional determines xylem conductive capacity (kx). Similarly, the structure of the phloem, i.e. sieve tube size and number, and sieve plate or pore size and number, will determine the conductive capacity of phloem which together with phloem cross-sectional area determines phloem conductivity (kp). Phloem osmotic pressure and turgor depend, in addition, on the phloem loading and unloading dynamics as they determine the sugar concentration (c) in phloem. The former is linked to photosynthesis especially tightly in trees where the sugars diffuse from the mesophyll cells to phloem sieve tubes passively along a concentration gradient (e.g. Turgeon 2010), and the latter is linked to sugar utilization for growth, respiration and root exudates. Structural development of tree is an outcome of resource capture, allocation and turnover of structures. The rate of resource capture and allocation between productive (capturing) and non-productive organs determine the long term growth rate. Size increase will change the balance between productive and non-productive tissue. The change depends on the scaling of the xylem and phloem tissue properties but the size also influences the flow rates and the specific capacities of the active tissue. Dynamics of tissue specific activities, allocation between productive and non-productive tissue and organ turnover rate influence the rate of development and attainable final size of trees. LITERATURE CITED Ball JT, Woodrow IE, Berry JA. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. Progress in Photosynthesis Research, Vol. IV (ed. I. Biggins), pp. 221–224. Bond B, Kavanagh K. 1997. Stomatal behavior of four woody species in relation to leaf-specific hydraulic conductance and threshold water potential. Tree Physiology 19: 503-510. 108 Brodribb TJ. 2009. Xylem hydraulic physiology: the functional backbone of terrestrial plant productivity. Plant Science 177: 245-251. Buckley TN. 2005. The control of stomata by water balance. New Phytologist 168: 275–292. Chaves MM, Maroco JP, Pereira JS. 2003. Understanding plant response to drought: from genes to the whole plant. Functional Plant Biology 30: 239–264. Choat B, Jansen S, Brodribb TJ, et al. 2012. Global convergence in the vulnerability of forests to drought. Nature 491:752-756. DeSchepper V, Steppe K. 2010. Development and verification of a water and sugar transport model using measured stem diameter variations. Journal of Experimental Botany 61: 2083-2099. Hölttä T, Mencuccini M, Nikinmaa E. 2009. Linking phloem function to structure: Analysis with a coupled xylem– phloem transport model. Journal of Theoretical Biology 259: 325-337. Hölttä T, Mäkinen H, Nöjd P, Mäkelä A, Nikinmaa E. 2010. A physiological model of softwood cambial growth. Tree Physiology 30: 1235-1252. Hölttä T, Mencuccini M, Nikinmaa E. 2011. A carbon cost–gain model explains the observed patterns of xylem safety and efficiency. Plant, Cell and Environment 34: 1819–1834. Hölttä T, Nikinmaa E. 2013. Modelling the Effect of Xylem and Phloem Transport on Leaf Gas Exchange. accepted to Acta Horticulturae. Koch GW, Sillett SC, Jennings GM, Davis SD. 2004. The limits to tree height. Nature 428: 851–854. McDowell N. 2011. Mechanisms linking drought, hydraulics, carbon metabolism, and vegetation mortality. Plant Physiology 155:1051–1059. Martinez-Vilalta J, Prat E, Oliveras I, Pinol J. 2002. Xylem hydraulic properties of roots and stems of nine Mediterranean woody species. Oecologia 133: 19–29. Mullendore DL, Windt CW, Van As H, Knoblauch M. 2010. Sieve tube geometry in relation to phloem flow. Plant Cell 22: 579–593. Nardini A, Lo Gullo M, Salleo S. 2011. Refilling embolized xylem conduits: is it a matter of phloem unloading? Plant Science 180: 604-611. Nikinmaa E, Hölttä T, Hari P, Kolari P, Mäkelä A, Sevanto S, Vesala T. 2013. Assimilate transport in phloem sets conditions for leaf gas exchange. Plant Cell Environ. 36: 655-669. Pantin F, Simonneau T, Muller B. 2012. Coming of leaf age: control of growth by hydraulics and metabolics during leaf ontogeny. New Phytologist 196: 349–366. Paul MJ, Foyer CH. 2001. Sink regulation of photosynthesis. Journal of Experimental Botany 52:1383–1400. Sperry JS, Hacke UG. 2004. Analysis of circular bordered pit function. I. Angiosperm vessels with homogenous pit membranes. American Journal of Botany 91: 369–385. Thompson MV. 2006. Phloem: the long and the short of it. Trends in Plant Science 11: 26–32. Turgeon R. 2010. The role of phloem loading reconsidered. Plant Physiology 152: 1817-1823. Tyree MT, Sperry JS. 1989. Vulnerability of xylem to cavitation and embolism. Annu. Rev. Plant Physiol. Plant Mol. Biol. 40: 19-38. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 109 Transpiration from stomata via the leaf boundary layer: a microscale modelling approach Thijs Defraeye1*, Pieter Verboven1, Jan Carmeliet3,4, Dominique Derome3 and Bart Nicolai1,2 1 MeBioS, Department of Biosystems, University of Leuven, Willem de Croylaan 42, 3001 Heverlee, Belgium, 2 VCBT, Flanders Centre of Postharvest Technology, Willem de Croylaan 42, 3001 Heverlee, Belgium, 3 Laboratory for Building Science and Technology, Swiss Federal Laboratories for Materials Testing and Research (Empa), Überlandstrasse 129, 8600 Dübendorf, Switzerland, 4 Chair of Building Physics, Swiss Federal Institute of Technology Zurich (ETHZ), Wolfgang-Pauli-Strasse 15, 8093 Zürich, Switzerland *correspondence: thijs.defraeye@biw.kuleuven.be Highlights: Convective mass transport from entire leaf surfaces was investigated with computational fluid dynamics. A novel aspect is that the stomata were modelled discretely. The convective exchange rate was relatively large, even for the limited surface coverage by stomata, and had a complex dependency on surface coverage and air speed. In addition, insight into the boundary-layer transfer at microscale level was obtained. Keywords: convective transfer, transpiration, leaf, computational fluid dynamics, stomata INTRODUCTION Stomata are local elliptical perforations in the leaf’s epidermis which have sizes of a few tens of micron and which occupy one to a few percent of the leaf surface. As the cuticle is quasi impermeable, leaf transpiration occurs predominantly via stomata. Hence, they play an important role in the plant hydrological cycle (Berry et al., 2010) and influence plant water uptake and water stress. Apart from the stomatal aperture and density, the transpiration rate is also dependent on the air flow in the boundary layer on the leaf surface, and the exchange processes therein (Nobel, 2005). This convective exchange between stomata and the environment is a subject of active research (Roth-Nebelsick et al., 2009). As stomata are distributed discretely over the leaf surface, they lead to a very heterogeneous (non- uniform) mass exchange over the leaf surface, at a microscale level (10-5 m). The impact of these small mass sources on the convective exchange is usually not considered by conventional convective transfer studies on leaves: for real leaves, measurements of individual stomatal transpiration rate are not straightforward, and therefore only bulk transpiration of leaves is assessed; for numerical studies or experimental studies using artificial leaves, homogeneous mass boundary conditions are usually imposed at the leaf surface, such as a uniform distribution of water vapour pressure over the entire surface. Only a few researchers have investigated in detail the effect of discretely-distributed moisture sources on mass transfer, but mainly for applications related to droplet evaporation (Cannon et al., 1979; Leclerc et al., 1986). The aforementioned experimental studies often considered macroscale moisture sources (> 10-3 m) and only the total convective transfer rate was determined. An assessment of the local exchange processes in the boundary layer was not performed as this is very challenging at the microscale. Some of these limitations could be alleviated by numerical modelling, which is the perspective of the present study. To the knowledge of the authors, the only numerical study undertaken to quantify transpiration via microscopic sources (Roth- Nebelsick et al., 2009) considered stomata arranged in a single stomatal crypt and investigated their effect on the crypt conductance. In the present study, the convective exchange in the boundary layer is modelled with computational fluid dynamics (CFD, both 2D and 3D) from leaf level (10-1-10-2 m) down to the stomatal scale (10-5 m), thus covering a very large spatial range for a numerical study. This is particularly challenging with respect to numerical grid generation, which is required to accurately solve the governing equations in the boundary layer. A systematic study is undertaken to identify the effect of the stomatal surface coverage and the air speed on the convective exchange. SIMULATIONS A 2D and 3D model of a leaf were constructed to study convective transfer from microscopic scalar sources, such as stomata. Both models represent a flat leaf, which was placed in low turbulent air flow with a free-stream speed Ub. The length of the leaf was 100 mm in 2D and 25 mm in 3D. The computational grids contained 0.226 x 106 cells and 5.88 x 106 cells, for 2D and 3D, respectively. In order to model the microscopic stomata discretely, very small computational cells (~ 50 μm) were required on the leaf surface. 110 Instead of modelling mass transfer from these sources, heat transfer (i.e., a passive scalar) was modelled since this led to a significant decrease of the computational cost: in this case, the flow field had to be solved only once at each air speed, since the air properties (e.g., density) could be taken constant. As such, only the scalar (heat) transfer, and not the flow field, had to be recalculated for the different imposed boundary conditions, i.e., stomatal coverage ratios. The resulting heat transfer data can easily be converted to mass transfer by means of the heat and mass transfer analogy, and is presented in dimensionless form anyway in the present study. The boundary-layer development is also similar since the Lewis number is almost equal to one (≈ 0.8). As such, heat (or mass) will be referred to as a scalar from now on. Only air-side transfer was modelled. A constant scalar value (temperature) was imposed at the stomata and a no-flux condition was used on the rest of the leaf surface. Different coverage ratios (CR) were evaluated, representative for those of real stomata, which vary roughly between 0.2% and 5%. The coverage ratio is defined as the ratio of the area occupied by the stomata (Aeff [m²]), to the total leaf area (A [m²]), i.e., CR = Aeff/A. The CFD simulations were performed with the commercial code ANSYS Fluent 13. Steady Reynolds-averaged Navier-Stokes (RANS) was used in combination with the shear stress transport (SST) k-ω model (Menter, 1994). Low- Reynolds number modelling (LRNM) was applied to resolve the transport in the boundary-layer region. This RANS turbulence model, in combination with LRNM, has already been shown to be very accurate for similar complex flow problems (e.g., Defraeye et al., 2012). (a) 2D leaf model (b) 3D leaf model 0 m s-1 2 m s-1 Flow 2.5mm Fig. 1. (a) Scalar concentration contours (isocontours) in the boundary layer at the leading edge of the 2D leaf for a coverage ratio of 5% for different air speeds. (b) Top: distribution of stomata on 3D leaf surface (only one half shown) for a coverage ratio of 1%; Bottom: air speed on a scalar isosurface (i.e., a surface which represents a constant scalar concentration in the computational domain) in the boundary layer of the 3D leaf and on both vertical and horizontal symmetry planes for a coverage ratio of 1% for Ub = 2 m s-1. RESULTS AND DISCUSSION In Fig. 1a, the scalar concentration contours are shown at the leading edge of the 2D leaf for different air speeds (Reynolds numbers) for a coverage ratio of 5%. The scalar boundary-layer thickness decreases with increasing air speed. At low speeds, the contours look more symmetrical on both sides of the sources, but at higher speeds, the scalar is convected more downstream and a wake zone is observed. In Fig. 1b, the air speed on a scalar isosurface in the boundary layer of the 3D leaf, and on both vertical and horizontal symmetry planes is shown for a coverage ratio of 1%. The boundary layer clearly becomes more saturated downstream of the leading edge, as the size of the volume occupied by the isocontour clearly increases. The surface-averaged convective scalar flows (Qc,w,avg) from the 2D leaf are shown in Fig. 2a as a function 111 of the coverage ratio. The results at different air speeds (Ub), thus d/δVSL ratios, are presented. Here d is the size of the scalar sources (50 μm) and δVSL is the average thickness of the viscous sublayer, i.e., the lower part of the boundary layer where laminar transport occurs and where large velocity and scalar gradients are found. These scalar flows are scaled with the surface-averaged scalar flow for a coverage ratio of 100% (Qc,w,avg,100%). Note that these scalar flows are directly proportional to the leaf’s convective transfer coefficient. Similar results are shown in Fig. 2b for the 3D leaf, but only for a single air speed (Ub = 2 m s-1). From Fig. 2, relatively high scalar flows at the surface are found at low coverage ratios (for all d/δVSL ratios), thus they clearly do not vary linearly with the coverage ratio. This trend is predicted by both 2D and 3D modelling. This effect is more pronounced at low d/δVSL (Fig. 2a), implying low air speeds (or small source sizes). These findings however also indicate that well-established convective transfer coefficients from plates or leaf models, obtained for a coverage ratio of 100%, can result in a significant overprediction of the convective exchange, compared to a more realistic, lower, stomatal coverage ratio, due to the discrete distribution of these microscopic sources. Furthermore, the largest decrease in scalar flows with coverage ratio was found at low coverage ratios (CR < 10%, i.e., the range shown in Fig. 2), which implies that small variations in the leaf’s stomatal density (CR), e.g., due to biological variability, or a temporal variation of stomatal aperture have a large impact on the convective exchange as well. In conclusion, the convective exchange from stomata was shown to be strongly dependent on surface coverage and air speed. The applied microscale modelling aproach provided more insight in convective exchange processes at the stomatal level. Such a numerical modelling framework seems promising in contributing to the understanding of leaf transpiration, but also of microclimatic conditions in the boundary layer and the transport therein. 0 10 20 30 40 50 60 70 80 90 100 0 0.1 Q c, w ,a vg /Q c, w ,a vg ,1 00 % (% ) Aeff/A (-) d/δ = 0.161 (2 m/s) 0 10 20 30 40 50 60 70 80 90 100 0 0.1 Q c, w ,a vg /Q c, w ,a vg ,1 00 % (% ) Aeff/A (-) d/δ = 0.004 (0.02 m/s) d/δ = 0.018 (0.2 m/s) d/δ = 0.095 (2 m/s) d/δ = 0.527 (20 m/s) (a) 2D (b) 3D Fig. 2. Surface-averaged convective scalar flows at the leaf surface as a function of the coverage ratio, for CR up to 10%. The flows are scaled with the surface-averaged scalar flow for a coverage ratio of 100% (Qc,w,avg,100%): (a) 2D model at different air speeds (Ub, i.e., d/δVSL ratios); (b) 3D model at a single air speed. LITERATURE CITED Berry JA, Beerling DJ, Franks PJ. 2010. Stomata: key players in the earth system, past and present. Current Opinion in Plant Biology 13:233-240. Cannon JN, Krantz WB, Kreith F, Naot D. 1979. A study of transpiration from porous flat plates simulating plant leaves. International Journal of Heat and Mass Transfer 22:469-483. Defraeye T, Herremans E, Verboven P, Carmeliet J, Nicolai B. 2012. Convective heat and mass exchange at surfaces of horticultural products: a microscale CFD modelling approach. Agricultural and Forest Meteorology 162- 163:71-84. Leclerc MY, Schuepp PH, Thurtell GW. 1986. Electrochemical simulations of mass transfer from isolated wet spots and droplets on realistic fluttering leaves. Boundary-Layer Meteorology 34:399-410. Menter FR. 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32:1598-1605. Nobel PS. 2005. Physicochemical and Environmental Plant Physiology. 3rd Edition, Elsevier Academic Press, London. Roth-Nebelsick A, Hassiotou F, Veneklaas EJ. 2009. Stomatal crypts have small effects on transpiration: a numerical model analysis. Plant Physiology 151:2018-2027. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 112 LEAFC3-N: Modeling Effects of Drought Stress on Photosynthesis, Stomatal Conductance and Transpiration Jens Bastet*, Johannes Müller and Olaf Christen Institute of Agricultural and Nutritional Sciences, University of Halle-Wittenberg, D-06900 Halle, Germany *correspondence: jens.bastet@landw.uni-halle.de Highlights: LEAFC3-N combines photosynthesis, stomatal conductance, transpiration, leaf energy balance, and leaf nitrogen content. The response to drought is simulated accounting for the effect of leaf water potential on stomatal conductance and of a finite mesophyll conductance on intracellular CO2 concentration. Keywords: Photosynthesis, drought stress, water potential, model. INTRODUCTION A previous version of LEAFC3-N (Braune et al., 2009) accounts for drought stress based on effects of leaf water potential (Ψl) on stomatal conductance (gsv), carboxylation, and electron transport. Mesophyll conductance (gm) was assumed infinite. However, a finite gm may significantly affect photosynthesis under drought (Niinemets et al., 2009). Here we re-analyse these patterns by including a finite gm into LEAFC3-N. MODEL DESCRIPTION LEAFC3-N (Müller et al., 2005) extends the LEAFC3 model (Nikolov et al., 1995) of the coupled processes of photosynthesis, stomatal action, transpiration, and leaf energy balance by relating the characteristics Vm, Jm, Tp, φa, m, θ, and Rd in the equations below to leaf nitrogen content per leaf area, Na. For the Na–dependencies currently used see Braune et al. (2009). Below we list only main model equations related to this study. For further explanation see the references above, and for a complete description of the model and for improvements recently introduced (accounting for different stomata frequencies at each leaf side, dynamic model of plant water transport, advanced solution algorithms, user interface and simulation tools, model extension for a finite gm) consult documentation and code which are available by request. An: net photosynthesis rate; Ag: CO2 exchange rate defined as the minimum of Ag,c, Ag,j, and Ag,p; Ag,c, Ag,j, and Ag,p: see eqs. (5), (6), (7); Cc: intracellular CO2 concentration; fΨ: function defining a sigmoid response to Ψleaf (eq.(13)); Kc and Ko: Michaelis-Menten parameters of Rubisco for carboxylation and oxygenation of RuBP, respectively; J: electron transport rate; Jm: light saturated J; O: concentration of O2; Qa: absorbed photosynthetic photon flux density; Rd: mitochondrial respiration rate at given incident photo- synthetic photon flux density (‘day respiration’); Tp: potential rate of triose phosphate utilisation; Vm: maximum carboxylation rate; α: coefficient defining the smoothness of the transition between Ag,c and Ag,j; αp: fraction of glycolate carbon not returned to chloroplast; β: coefficient defining the smoothness of the transition between Ag,p and Ag,e; Γ*: CO2 compensation point in the absence of Rd; φa: quantum yield of electron transport based on Qa; µ1 and µ2: coefficients quantifying the electron requirement for the formation of NADPH+ and ATP in terms of mol electrons per mol CO2 fixed; θ: curvature coefficient. 2 g g,e g,p g g,e g,p 2 g,e g,c g, j g,e g,c g, j ( ) ( 0, 0 1, 0, 0) (2) , 3)1 ( A A A A A A A A A A A A β α α β− + − + + = ≤ ≤ + = ≤ ≤ cm c c g,c g,j * p g,p c c o 1 c 2 c p , , (5, 3 (1 3 ) ), (6), (7) (1 / ) T CV C J CA A C K O K µ C µ Γ A C α Γ ∗ = − + = = + + + 2 m a a m a a a a m( ) ( ) 4 / 2 , (8)J J Q J Q Q Jϕ ϕ θϕ θ = + − + −  * c p (1+3 ) :C α Γ≤elseif * c p (1+3 ) :C α Γ>if * n g c d(1 / ) , (1)A A Γ C R= − − 2 g g,c g, j g g,c g, j (4)0, 0 1.( )A A A A A Aα α+ = ≤ ≤− + 113 Cc, Ca: concentration of CO2 at the reaction site in the chloroplast, in the ambient air; gt: total conductance for CO2 transport. gbv and gsv: two-sided leaf boundary layer and leaf stomatal conductance, respectively, Mbv: function accounting for the effective portion of gbv arranged in series with gsv depending on the ratio of the numbers of stomata on each leaf side. The stomatal part gsv of gt is calculated by a modified Ball et al. (1987) model: gsv0: minimum gsv; m: coefficient (dimensionless) that defines the combined sensitivity of gs to An, hb, and Cb; hb, Cb: relative humidity (decimal fraction) and CO2 concentration (µmol mol-1) of the air at the leaf surface within the leaf boundary layer, respectively; fΨ defines a sigmoid response to Ψl; Ψc: critical leaf water potential [Pa]; kΨ: curvature parameter [dimensionless]. The mesophyll part gm of gt is calculated according to Yin et al. (2009): gm0: minimum gm; δ: proportionality factor that defines the combined sensitivity of gm to An + Rd and Cc. EXPERIMENTAL DESIGN Spring barley (Hordeum vulgare L., cv. ‘Scarlett’) was grown in a climate chamber in pots containing sandy loam soil at different treatments of water supply (W1, W2). Wc1 was maintained at optimum soil water content, which corresponds to 60 % of soil water capacity (Wc) or a water content of 23.1 vol. %. Wc2 was dried to 35 % of Wc (or 13.5 vol. %) and then kept on this level. The drought stress period of nine days was started when the visible part of leaf number four of the main tiller had reached a length of 10 cm. Further growth conditions were: incident photon flux density Qi = 310 μmol m-2 s-1, Ca ≈ 360 µmol mol-1, and ambient air humidity ha ≈ 60 %. On leaves of rank four, the following characteristics required for analyzing the data with the LEAFC3-N model were measured: area, contents of chlorophyll and total nitrogen (N), water potential (Ψl), light and CO2 response curves of net photosynthesis rate. After gas exchange measurements, the leaf blades were quickly covered by plastic sheaths made of thin foil and then cut off at the proximal emersion point at the measurement chamber. The water potential of these leaf parts was then measured using a scholander pressure bomb. RESULTS AND DISCUSSION In the present simulation study, the basic parameterization of LEAFC3-N was adopted from Braune et al. (2009). However, the parameters Kc, Ko, Vm, and Jm (respectively the slopes sv and sj of the linear relations of Vm and Jm to Na) were revised as required in case of introducing a finite gm. Considering corresponding results of Bernacci et al. (2002) and Yin et al. (2009), we re-analyzed the diurnal time course measurements of An, Tr, and gsv given by Braune et al. (2009). The revised parameters introduced on this basis were Kc = 272 µmol mol-1, Ko = 166 mmol mol-1 (Bernacci et al., 2002), sv = 91.62 µmol CO2 (g N)-1, and sj = 158.6 µmol e- (g N)-1. Further, we derived from that parameterization study with respect to the Na–dependency of m (eq. (12)): k0,m = 20.58 m2 g-1 and k1,m = -0.45, with respect to fΨ (eq. (13)): Ψc = -1.7 MPa and kΨ = 3, and with respect to gm (eq. (14)): δ = 1.1 and gm0 = 0.1 mol m-2 s-1. Based on this parameterization, the diurnal time courses of An, Tr, and gsv, including the midday depression, could be reproduced well by the new model version that was extended by introducing a finite gm (eqs. (10) and (14)). No additional effects of Ψl on Vm and Jm were assumed as in Braune et al. (2009). This result here was confirmed based on data obtained by the special experimental design described above. With the same parameter values as before, except setting Ψc = -1.2 MPa, An, Tr, and gsv simulated for a range of incident photon flux density (Qi) and Ψl agreed quite well with the corresponding measurements (Fig.1, Table 1). - bsv 1 -1 n d b b sv0 s bv sv 200 µmol mol 200 µmo , (11) ( ,l mol ) g m f A R h C g g g if C C else = Ψ= + + ≥ = ) /( cl (13)1 1 ( ) , 0 1, k/f / fΨ ΨΨ ΨΨ = + ≤ ≤  c a n t/ , (9)C C A g= − bv bv sv m t bv bv sv bv bv m sv m , (10) 1 6 1 37 M g g gg M g g . M g g . g g = + + * * m m0 n d c c( ) / ( ), , (14)g g A R C if Cδ Γ Γ= + + − > 0,m 1,m a (1, 2) km k N= 114 Table 1. Linear regression of simulated vs. measured values: r2 = coefficient of determination a1 = slope of regression a0 = absolute term of regression LITERATURE CITED ACKNOWLEDGEMENT This research was supported by the Deutsche Forschungsgemeinschaft (DFG, contract No. DFG 1379/2-1). LITERATURE CITED Braune, H., Müller, J., Diepenbrock, W. 2009. Integrating effects of leaf nitrogen, age, rank, and growth temperature into the photosynthesis-stomatal conductance model LEAFC3-N parameterised for barley (Hordeum vulgare L.). Ecol. Model. 220:1599–1612. Ball, J.T., Woodrow, I.E., Berry, J.A. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Biggins J (ed.), Progress in Photosynthesis Research. Proceedings of the VII. International Congress on Photosynthesis. Martinus Nijhoff Publishers, Dordrecht-Boston-Lancaster, 4:221–224. Bernacchi, C.J., Portis, A.R., Nakano, H., von Caemmerer, S., Long, S.P. 2002. Temperature response of mesophyll conductance. Implications for the determination of Rubisco enzyme kinetics and for limitations to photosynthesis in vivo. Plant Physiology 130:1992–1998. Niinemets, Ü., Díaz-Espejo, A., Flexas, J., Galmés, J., Warren, C.R. 2009. Importance of mesophyll diffusion conductance in estimation of plant photosynthesis in the field. Journal of Experimental Botany 60:2271–2282. Müller, J., Wernecke, P., Diepenbrock, W. 2005. LEAFC3-N: a nitrogen-sensitive extension of the CO2 and H2O gas exchange model LEAFC3 parameterised and tested for winter wheat (Triticum aestivum L.). Ecol. Model. 183:183-210. Nikolov, N.T., Massman, W.J., Schoettle, A.W. 1995. Coupling biochemical and biophysical processes at the leaf level: An equilibrium photosynthesis model for leaves of C-3 plants. Ecol. Model. 80:205-235. Yin X., Struik P.C., Romero P., Harbinson J., Evers J.B. 2009. Using combined measurements of gas exchange and chlorophyll fluorescence to estimate parameters of a biochemical C3 photosynthesis model: a critical appraisal and a new integrated approach applied to leaves in a wheat (Triticum aestivum) canopy. Plant, Cell Environ. 32:448–464. W r2 a1 a0 An 1 0.97 1.04 -0.390 Tr 0.89 1.09 -1.822 gsv 0.79 1.03 -0.151 An 2 0.96 1.09 -0.295 Tr 0.82 1.06 -0.397 gsv 0.78 1.05 -0.023 Fig. 1. Simulation results for a) An, b) Tr, and c) gsv for a range of Ψleaf and Qi; measurements W1 (x), W2 (○) and simulations W1 (+), W2 (□). -1.5 -1 -0.5 0 500 1000 1500 -10 0 10 20 30 40 Q i (µmol m -2s -1) Ψ leaf (MPa ) a) A n (µ m ol m -2 s- 1 ) -1.5 -1 -0.5 0 500 1000 1500 0 5 10 Q i (µmol m -2s -1) Ψ leaf (MPa ) b) Tr (m m ol m -2 s- 1 ) -1.5 -1 -0.5 0 500 1000 1500 0 0.5 1 1.5 Q i (µmol m -2s -1) Ψ leaf (MPa ) c) g s v ( m ol m -2 s- 1 ) Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 115 Modelling transport processes in tissues and organs at a mesoscopic scale Ansgar Bohmann1, Juliane Claus1 and Andrés Chavarría-Krauser1,* 1Interdisciplinary Center for Scientific Computing & Center for Modelling and Simulation in the Biosciences, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany *correspondence: andres.chavarria@bioquant.uni-heidelberg.de Highlights: Three mesoscopic models of transport processes in plants are presented: water fluxes in tissues, zinc uptake in roots, and gas fluxes in leaves. The models aim at increasing our understanding of the interaction between physical and biological processes in plants. Besides giving ideas for derivation of other mesoscopic models, the presented results can be of use in functional-structural plant models. Keywords: transport, uptake, transpiration, metals, zinc, nutrients, water, roots, leaves, genetic regulation INTRODUCTION Transport of water, nutrients and gases in tissues and organs takes place in highly structured domains with multifaceted paths: symplastic, apoplastic and transcellular (Steudle, 2000). While the apoplast is a porous medium in which Darcy's law applies, fluid movement in the symplast follows a viscous flow law (e.g. Stokes). In general, different physical processes have to be considered, in particular when these are coupled. To obtain mesoscopic mathematical models of sufficient physiological background, it is necessary to pose microscopic models, valid at e.g. the cell scale, to couple the microscopic domains by transmission conditions, and to derive mesoscopic/macroscopic models by “upscaling” for simulation and analysis. This approach is used widely in engineering (Hornung, 1997), but much less in biology (e.g. Marciniak-Czochra and Ptashnyk, 2008; Chavarría-Krauser and Ptashnyk, 2010). Regardless of the mathematical technicality, the ideas and steps carried out are intuitive: modelling of microscopic processes, determination of macroscopic models and simulation. Depending on the problem's scale, upscaling might be senseless as in discrete or semi-discrete models of auxin transport and morphogenesis (e.g. Goldsmith et al., 1981; Kramer, 2004; Chavarría-Krauser et al., 2005; Jönsson et al., 2012). Transport, deformation, flow, etc. are physical processes occurring in general independently of organisms yet tamed by cells to accomplish a specific function. For example, zinc uptake and transport in roots follow diffusion-advection-reaction laws modulated by expression of ZIP-transporters (Krämer and Sinclair, 2012; Claus et al., 2012). Regarding transport processes in plants, a duality between physical and biological processes is found. Understanding this duality is important to establishing functional-structural plant models (FSPM) and to plant physiology in general. We present three models to exemplify how mesoscopic integrative plant models can be obtained and elucidate further the interaction between physical and biological processes in plants. We focus on: water fluxes in tissues, regulated zinc uptake in roots, and gas fluxes in leaves. Fig. 1. A, Microscopic model based on conservation of mass and momentum. Transmission conditions account for transport over the membrane. B, Mesoscopic model obtained using periodic homogenization. The model is based on one pressure p, one velocity v and two concentrations: ca and cs. 116 WATER FLUXES IN TISSUES The existence of the apoplast and symplast in plant tissues opens diverse paths to water (Steudle, 2000). The contribution of the symplastic, apoplastic and transcellular paths is still unknown. We derive a model to analyse further these contributions by assuming an ideal tissue of perfect periodicity. The cells are assumed to have cell walls, plasma membranes and cytoplasm; plasmodesmata join their cytoplasms (Fig. 1A). The microscopic model consists of flow and transport equations for water and osmotic solutes. The flow is assumed to follow Darcy in the apoplast and plasmodesmata and Stokes in the symplast (Fig. 1A). We derive transmission conditions connecting the symplast and apoplast by balancing the fluxes at the interface. A regulation of transport is considered via ordinary differential equations describing the amount of free and bound transporters. Although the microscopic model is continuous, it could be reformulated as a discrete cellular model. Using homogenization techniques (Hornung, 1997), we obtain an average “upscaled” mesoscopic model (Fig. 1B). It is a Darcy law with a force term proportional to the local difference in solute concentration. Representations of the average transport coefficients are obtained from solutions of unit cell problems, which are posed for one cell and account for the microscopic structure. The mesoscopic model obtained is simple in structure, straightforward to solve numerically and can be applied in FSPM to describe water fluxes in tissues and organs. REGULATED ZINC UPTAKE IN ROOTS The heavy metal zinc is an essential micronutrient yet potentially toxic for plants. Its uptake in roots needs to include mechanisms for the quick adaptation to a varying environment. Transport of zinc from the root epidermis to the central cylinder depends on three main processes: diffusion in the medium, advection with water, and cross-membrane transport. Modelling these processes allows analysing their relative impact and question biological hypotheses. Strict regulation of zinc uptake is presumably accomplished by modulation of zinc transporters in the membrane in response to changes of the cells' internal zinc concentration. Experimental measurements showed that the number of transporters is adjusted according to external concentrations by a still unknown system of transcription factors and activating and inhibiting agents (Talke et al., 2006; Assunção et al., 2010). We analysed the biological relevance of different simple scenarios comprising a simple activator, a dimerizing activator, and an additional inhibitor in an ordinary differential equations model (Fig. 2A). Our simulations suggest the existence of a dimerising activator and an inhibitor due to advantages in stability and robustness (Claus and Chavarría-Krauser, 2012a). Zinc uptake in roots depends also on passive diffusion and radial flow of water towards the xylem. To analyse the relative significance of these processes and the effect of geometry and microstructure, we posed a spatio-temporal transport model of the root of Arabidopsis thaliana (Fig. 2B; Claus et al., 2012b). The simulations show an inverse relation between accumulation and the level of the efflux transporter HMA4 (Fig. 2C), which is in accordance with measurements of HMA4 over expression (Hanikenne et al., 2008). Fig. 2. Zinc and water uptake in roots. A, Schematic description of feasible zinc regulation models: (i) activator only, (ii) activator with dimerization, (iii) activator-inhibitor. B, Schematic description of radial transport of zinc. C, Simulation result showing zinc distributions under different levels of HMA4 (lower panel). 117 GAS FLUXES IN LEAVES To gain insight in the physics and regulation of gas exchange (water vapour, carbon dioxide, and oxygen) in plant leaves we propose a dynamical first-principle model for a small disc-shaped section of a leaf around a single stoma (see Fig. 3). We focus on the mechanical interaction between epidermis cells and guard cells, coupled to water and solvent transport in the epidermis (symplastic and apoplastic compartments), as well as evaporation into and diffusion within the interstitial air space. Vapour exchange to the ambient air is controlled by the stomatal aperture which in turn is determined by the mechanics and the guard cell solute content. The underlying physical processes along with typical parameter values are described in standard literature (e.g. Nobel, 2005). The structure of the resulting model is a coupled system of ordinary and partial differential equations providing a more detailed description as compared to resistor network models. It also captures dynamic effects, and links microscopic physical properties to observable variables such as stomatal aperture and water loss. The model provides a physically accurate explanation to the inverse behaviour of stomatal aperture after sudden changes in ambient parameters, such as ambient moisture (Mott et al., 1997). This model is intended to serve as one building block for a future more comprehensive model of the leaf. Fig. 3. Section through leaf epidermis centered around a single stoma. LITERATURE CITED Assunção AGL, Schat H, Aarts MGM. 2010. Regulation of the adaptation to zinc deficiency in plants. Plant Signaling & Behavior 5:1553-1555. Chavarría-Krauser A, Jäger W, Schur U. 2005. Primary root growth: a biophysical model of auxin-related control. Func. Plant Physiol. 32: 849-862. Chavarría-Krauser A, Ptashnyk M. 2010. Homogenization of long-range auxin transport in plant tissues. Nonlinear Anal.-Real. 11: 4524-4532. Claus J, Chavarría-Krauser A. 2012a. Modeling Regulation of Zinc Uptake via ZIP Transporters in Yeast and Plant Roots. PloS ONE 7(6):e37193. Claus J, Bohmann A, Chavarría-Krauser A. 2012b. Zinc uptake and radial transport in roots of Arabidopsis thaliana: a modelling approach to understand accumulation. Annals of Botany, doi: 10.1093/aob/mcs263 Marciniak-Czochra A, Ptashnyk M. 2008. Derivation of a macroscopic receptor-based model using homogenisation techniques. SIAM J. Math. Anal. 40: 215-237. Goldsmith MHM, Goldsmith TH, Martin MH. 1981. Mathematical analysis of the chemiosmoticpolar diffusion of auxin through plant tissues. Proc. Natl. Acad. Sci. USA 78: 976-980. Hanikenne M, Talke IN, Haydon MJ, et al. 2008. Evolution of metal hyperaccumulation required cis-regulatory changes and triplication of HMA4. Nature 453:391-395. Hornung U. 1997. Homogenization and porous media. Springer-Verlag. Jönsson H, Gruel J, Krupinski P, Troein C. 2012. On evaluating models in Computational Morphodynamics. Curr. Op. Plant. Biol. 15: 103-110. Kramer EM. 2004. PIN and AUX/LAX proteins: their role in auxin accumulation. TRENDS in Plant Sci. 9: 1360-1385. Krämer U, Sinclair SA. 2012. The zinc homeostasis network of land plants. BBA Molecular Cell Research 1823: 1553-67. Mott KA, Denne F, Powell J. 1997. Interactions among stomata in response to perturbations in humidity. Plant, Cell & Environment, 20: 1098–1107, 1997. Nobel, PS. 2005. Physicochemical and environmental plant physiology. Elsevier, 3rd edition. Steudle E. 2000. Water uptake by plant roots: an integration of views. Plant Soil 226: 45-56. Talke IN, Hanikenne M, Krämer U. 2006. Zinc-dependent global transcriptional control, transcriptional deregulation, and higher gene copy number for genes in metal homeostasis of the hyperaccumulator Arabidopsis halleri. Plant Physiology 142:148-167. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 118 Spatial and temporal variability of leaf gas exchange and temperature responses of apple trees to drought assessed by a 3D turbid medium model Jérôme Ngao1,2, Boris Adam1,2, Marie Charreyron 1,2 and Marc Saudreau1,2 1INRA, UMR 547 PIAF, F-63100 Clermont-Ferrand, France, 2UBP, UMR547 PIAF, F- 63000 Aubière, France *correspondence: jerome.ngao@clermont.inra.fr Highlights: Drought stress alters tree carbon and water balance, and it could affect pest and disease development as affected by changes in microclimate. Spatial and temporal variability of leaf gas exchange and microclimate (through leaf temperature) were assessed by adapting a 3D turbid medium model to drought stress and comparing model outputs to drought experiments. Keywords: canopy microclimate, drought, leaf nitrogen, RATP model, stomatal conductance, transpiration INTRODUCTION Tree 3D-structure induces environmental and physiological gradients, which have to be taken into account for understanding the acclimation of various plant processes such as photosynthetic assimilation (Anet), stomatal conductance (gS) and leaf transpiration (TR) to the main driving factors, particularly intra- canopy microclimate. Modelling such variability is also a prerequisite for upscaling to the whole plant or population. Numerous studies have investigated the acclimation of gS and Anet to local light interception (Hollinger1996; Leuning et al. 1991). Spatial variability of Anet has been shown to be tightly related to that of light interception via leaf nitrogen distribution expressed per surface area (Na, Thornley 2004). Characterization of the spatial distribution of gS within the canopy has been done generally to relate it with hydraulic traits (Sperry et al., 2008), or to Anet (Prieto et al. 2012). Another consequence of the canopy light gradient is the spatial variability of the energy balance, particularly that of the latent heat (determined by gS) and the sensible heat (leaf temperature, Tleaf) terms (Monteith and Unsworth 1990). Thus gS may allow assessing and modelling spatial variability of Tleaf, which is an agronomic challenge in fruit tree species as the development of numerous pests are temperature-dependent. The effects of summer drought on Anet, TR and gS have been widely studied, and various models have been proposed (Damour et al. 2010). However, intra-canopy variability of such responses has received much less attention than temporal dynamics. One major difficulty lies on the tools available for assessing both the processes of interest (light interception, carbon assimilation, etc.) and their spatial distribution in a realistic way (Niinemets, 2012). Moreover, there are still very few models able to simulate Tleaf spatially distributed, and include leaf functions together with Anet and gS. The RATP model (Sinoquet et al., 2001) allows simulating (i) the radiation intercepted by the crown foliage, (ii) leaf temperature (Tleaf) and gS as outputs of the energy balance, and (iii) Anet and TR (Fig. 1). It considers the canopy 3D structure by discretizing the crown foliage into voxels as turbid media, and thus allowing simulation of Anet and TR at both canopy level and voxel levels. This model has been applied for various aims, for example assessing the foliage randomness (Sinoquet et al., 2005), simulating the thermal microclimate and its effect on leaf miner development (Pincebourde et al., 2007), and disentangling structural and functional effects on TR and Anet (Massonnet et al., 2008). But until now, the RATP model relied on optimal water conditions, as the Jarvis gS submodel (Jarvis, 1976) did not simulate the response to water potential, thus the model was not adapted to drought conditions. Our aim was to assess spatial variability, and its temporal evolution, of transpiration, stomatal conductance and temperature responses of young apple trees to drought (Malus pumila Mill., var. Delbard Jubilé®). We adapted the RATP model to drought by adding a response function to soil water content in the Jarvis sub-model. We tested the TR outputs (TRRATP) against xylem sapflow measurements as proxi values of total tree canopy transpiration (TRsap) during drought experiments. MODEL DEVELOPMENT AND PARAMETRIZATION The gS submodel as formulated by Jarvis (1976) was first parameterized for the photosynthetically active radiation (PAR), Tleaf, and vapour pressure deficit (VPD) response functions in optimal irrigation conditions. 119 Then during a two-week-long drought period, gS was measured at different dates during which the PAR, Tleaf and VPD values were concurrently measured. The residuals between gS simulated with the measured microclimatic variables and actual gS, were linearly related to normalized soil water content. This linear relationship was added in the Jarvis subroutine. For the foliage structure, only leafy shoots were digitized, and individual leaves were reconstructed by allometric relationships (Sonohat et al., 2006). Computations of transpiration and leaf temperature were performed at a 30-min time step according to the meteorological dataset. The model has been implemented in RATP and integrated into the OpenAlea plant modelling platform (Pradal et al., 2008) RESULTS AND DISCUSSION The temporal evolution of TRsap prior the drought was mostly well reproduced by the model. TRsap decreased dramatically eight days after the start of the water shortage and remained very low for several days after the end of the drought (Fig. 2). Driven by soil water content input data, simulated TRRATP decreased dramatically six days after the start of the water shortage. The temporal shift between the TRsap measurements and TRRATP simulations may be attributed to the buffering effect of tree hydraulic capacitance (Sperry et al., 2008), which should be included in the response function, but not represented as input or intermediate data. Furthermore, while TRRATP increased rapidly after irrigation restart, TRsap for unharmed trees remained at very low level, and increased regularly up to five days after restarting irrigation, despite a very fast recovery of gS. This could be explained by xylem embolism which may have developed during the drought period and decreased the sap flow rate (Cruiziat et al., 2002). Even if gS recovered quickly to pre- drought levels, xylem vessels have to be refilled by water, but the involved mechanisms are still discussed (Nardini et al., 2011). -1 1 3 5 7 9 09/06/2011 14/06/2011 19/06/2011 24/06/2011 29/06/2011 C an op y tr an sp ira tio n (m m ol s -1 ) Xylem sapflow TR with f(SWC) TR without f(SWC) Fig. 1. Main features of the RATP model. The blue boxes are the input data, the main computation processes are in the yellow boxes and the outputs are in the green boxes. Each calculation step is done for each voxel at a 30-min time-step. Fig. 2. Temporal course of canopy transpiration (i) as measured by xylem sapflow measurements (blue circles), (ii) as simulated by taking into account soil water shortage (orange lines) or not (green broken lines). The water shortage started on June 7, 2011. The simulations were stopped after June 22 as visible damages on the leaf crown were observed. As expected, there was a large variability in TRRATP values (Fig. 3a) when the trees experienced optimal irrigation conditions. At the end of the drought experiment, TRRATP values were very low and varied in a very narrow range (Fig. 3b). Further simulations will allow determining the degree of heterogeneity of TR decrease during drought. On the other hand, the mean Tleaf varied temporally according to the air temperature. Moreover, the Tleaf range under optimal water conditions varied at the diel scale up to 4°C (Fig. 4a), and according to air temperature. But when both simulations and measurements values of TR were very low, typically at the end of the drought period, the diel range of Tleaf decreased, averaging ≈ 2.5°C, even if the mean air temperature increased (Fig. 4b). This is in good agreement with measurements done on almond trees under drought by Gonzalez-Dugo et al. (2012). Among the model parameters, the leaf nitrogen content expressed per area unit (Na) had an important influence in the simulation outputs. In RATP, Na drives the maximal gS (gSmax) which is degraded by the response functions of the Jarvis submodel. Leroux et al (1999) found a linear relationship between the daily cumulated PAR averaged over several days and Na, allowing a fixed distribution of Na within the canopy 120 Prieto et al. (2012) showed that Na varied over the growing seasons in grapevines. This implies that seasonal changes in Na distribution within the canopy have to be taken into account, as well its relationship with gSmax for which Leroux et al. (1999) showed seasonal differences. Fig. 3. Example of spatial distribution of sunlit leaf transpiration (a) on June 5th (optimal soil water content) and (b) on June 21st (end of the drought period). Both pictures display transpiration values at 12:00. Fig. 4. Example of spatial distribution of sunlit leaf temperature (a) on June 5th (optimal soil water content) and (b) on June 21st (end of the drought period). Both pictures display transpiration values at 12:00. LITERATURE CITED Cruiziat P, Cochard H, Ameglio T. 2002. Hydraulic architecture of trees: main concepts and results. Annals of Forest Science 59:723-752. Damour G, Simonneau T, Cochard H, Urban L.2010. An overview of models of stomatal conductance at the leaf level. Plant, Cell & Environment 33:1419–1438. Gonzalez-Dugo V, Zarco-Tejada P, Berni JAJ, Suarez L, Goldhamer D, Fereres E. 2012. Almond tree canopy temperature reveals intra-crown variability that is water stress-dependent. Agricultural and Forest Meteorology 154:156-165. Hollinger DY. 1996. Optimality and nitrogen allocation in a tree canopy. Tree Physiology 16:627-634. Jarvis PG. 1976. The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Philosophical Transactions of the Royal Society B 273:593–610. Le Roux X, Sinoquet H, Vandame M. 1999. Spatial distribution of leaf dry weight per area and leaf nitrogen concentration in relation to local radiation regime within an isolated tree crown. Tree Physiology 19: 181-188. Leuning R, Wang YP, Cromer RN. 1991. Model simulations of spatial distributions and daily totals of photosynthesis in eucalyptus-grandis canopies. Oecologia 88:494-503. Massonnet C, Regnard JL, Lauri PE, Costes E, Sinoquet H. 2008. Contributions of foliage distribution and leaf functions to light interception, transpiration and photosynthetic capacities in two apple cultivars at branch and tree scales. Tree Physiology 28:665–678. Monteith JL, Unsworth MH. 1990. Principles of Environmental Physics. Edward Arnold, London, p.291. Nardini A, Lo Gullo MA, Salleo S. 2011. Refilling embolized xylem conduits: Is it a matter of phloem unloading? Plant Science 180:604-611. Niinemets Ü. 2012. Optimization of foliage photosynthetic capacity in tree canopies: towards identifying missing constraints. Tree physiology 32:505-509. Pincebourde S, Sinoquet H, Combes D, Casas J. 2007. Regional climate modulates the canopy mosaic of favourable and risky microclimates for insects. Journal of Animal Ecology 76:424-438. Pradal C, Dufour-Kowalski S, Boudon F, Fournier C, Godin C. 2008. OpenAlea: a visual programming and component-based software platform for plant modelling. Functional Plant Biology 35:751-760. Prieto JA, Louarn G, Pena JP, Ojeda H, Simonneau T, Lebon E. 2012. A leaf gas exchange model that accounts for intra-canopy variability by considering leaf nitrogen content and local acclimation to radiation in grapevine (Vitis vinifera L.). Plant Cell & Environment 35:1313-1328. Sinoquet H, Le Roux X, Adam B, Ameglio T, Daudet FA. 2001. RATP: a model for simulating the spatial distribution of radiation absorption, transpiration and photosynthesis within canopies: application to an isolated tree crown. Plant Cell & Environment 24:395-406. Sinoquet H, Sonohat G, Phattaralerphong J, Godin C. 2005. Foliage randomness and light interception in 3-D digitized trees: an analysis from multiscale discretization of the canopy. Plant Cell & Environment 28:1158-1170. Sonohat G, Sinoquet H, Kulandaivelu V, Combes D, Lescourret F. 2006. Three-dimensional reconstruction of partially 3D-digitized peach tree canopies. Tree physiology 26:337-351. Sperry JS, Meinzer FC, McCulloh KA. 2008. Safety and efficiency conflicts in hydraulic architecture: scaling from tissues to trees. Plant Cell & Environment 31:632-645. Thornley JHM. 2004. Acclimation of photosynthesis to light and canopy nitrogen distribution: an interpretation. Annals of Botany 93:473-475. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 121 Dynamic properties of foliage photosynthesis E. David Ford* and Shawn Behling School of Environmental and Forest Science, University of Washington, Box 352100, Seattle, WA 98195, United States. *correspondence: edford@u.washington.edu Highlights: Increasing results illustrate the importance of modelling photosynthesis as a dynamic process where the parameters of the standard photosynthesis curve vary in response to fluctuations in environmental conditions and developmental status of the plant. We describe how engineering approaches to the analysis of dynamic systems can be used and provide information for incorporating the dynamics of photosynthesis into large scale FSPMs. Keywords: Photosynthesis, stomatal conductance, time constant, dynamic properties. INTRODUCTION An achievement of Functional-Structural Plant Modelling (FSPM) has been development of techniques for measurement and representation of the spatial distribution of plant organs and their connections. This in turn has led to a standpoint, expressed by Godin and Sinoquet (2005), that “the growth of the plant continuously modifies the network of components and space occupation, which in turn changes the general balance between organ demand and production.” They refer to this as representing dynamic feedback between structure and function and suggest that its study requires integrating various sources of knowledge into a consistent modelling framework. Photosynthesis is the essential pre-requisite of plant growth and an important question is how to define its dynamics and potentially integrate that understanding in FSPMs. This is a challenge because models for leaf photosynthesis are most frequently designed to simulate instantaneous or short term changes of environmental conditions whereas many FSPMs are designed for longer terms when additional influences must be considered, e.g., sink control (Paul and Foyer 2001). We consider two related problems. First: How can we measure and model the dynamics of photosynthesis? Increasingly research is showing variation in parameters of standard light saturation and A/Ci curves over daily and seasonal periods. We introduce some techniques used in the analysis of control systems that can aid in understanding such variation. We consider the types of question that may be asked using these techniques, the experiments and measurements that might be made and models that can be used to understand variation found in dynamic responses. Second: What type of feedback might be expected in the control of photosynthesis? When we say a system is “dynamic” we frequently imply that it responds to change in some form of self-correcting way, which implies some form of “feedback”. Engineers have developed theories of the control of dynamic systems and we examine how they may be applied to study of photosynthesis dynamics. THE DYNAMICS OF PHOTOSYNTHESIS Photosynthesis can be defined by its dependence on light and carbon dioxide concentration. There is well established theory that explains these relationships (Taiz and Zeiger 2010): production of ATP and NADPH by light reactions and their utilization in the Calvin-Benson cycle by which carbon from CO2 is incorporated into organic compounds. The response of foliage photosynthesis to light can be fitted with the non- rectangular hyperbola model (Lambers et al. 1998, p27): dR AQAQAQ A − ⋅⋅⋅⋅−+⋅−+⋅ = θ θφφφ 2 4)( max 2 maxmax (1) in which Q is the available incident PPFD, A is the CO2 assimilation rate, Amax is the assimilation rate at saturating light, φ is the apparent quantum efficiency (the initial slope of the linear part of the curve), θ is the convexity of the curve, and Rd is the dark respiration. Equation 1 represents photosynthesis as an instantaneous system—the output of the process, A, the photosynthesis rate, depends upon light. The equation does not take into account whether prior conditions 122 may affect current photosynthesis rate. More complete analyses incorporating the components of gaseous diffusion through stomata, mesophyll and cell have been developed (e.g., Farquhar et al. 2001) but these too consider photosynthesis as a more complex but still an instantaneous system. Studies of the effects of sunflecks on photosynthesis rate illustrate it does not respond instantaneously to increase in light but that there is an induction period (Way and Pearcy 2012). For example, when sunflecks are simulated experimentally as a step increase in light there is a generally curvilinear increase in photosynthesis rate. Investigators (see Way and Pearcy 2012) have described this rate of increase by calculating a time constant of response. The time constant equation for increase of photosynthesis from base value of zero is: A = Amax * (1 – e(-t/τ) ) ( 2) where Amax is an estimated asymptotic value for maximum photosynthesis rate attained following the step increase in light, t is time, usually measured in seconds, and τ is the time constant and which represents the time it takes for the step response to reach 63.2% of the asymptotic maximum. We present results and analyses showing that the response described by Eqn 2 is just one example of change in response to changing conditions. Different patterns of increasing photosynthesis in response to step functions of light for shade grown Abies amabilis and Tsuga heterophylla show leaves to be in different dynamic states associated with the ambient light they are receiving before the step increase. A frequently encountered pattern is represented by addition of two time constant equations one with τ in the range of 8 to 20 seconds and the other with τ in the range of 80 to 150 seconds. Another pattern is overshoot, where A increases to a maximum before settling to a lower value. These are well known response types found in engineering analyses of dynamic systems. For these species control of photosynthesis through variation in stomatal conductance, gs, tends to occur over considerably longer time intervals with τ ~ 600 s. DYNAMIC SYSTEMS AND FEEDBACK Porcar-Castell and Palmroth (2012) draw attention to the requirement for models that take account of the dynamic response of photosynthesis to changing conditions. However, they draw attention to an important problem: “While dynamic models present a substantial improvement compared to steady state models, their parameterization remains a challenge … because parameters change across time and space …” Dynamic models of leaf photosynthesis are based on theories of chloroplast and leaf function and define pool sizes and conductance of precursors, enzyme characteristics and how these change in response to changes in the environment, particularly light. While recognizing the heuristic value of such models we present a complementary approach with two components: (a) examining the plant through different conditions of its growth and exposing it to changes in weather; while (b) applying step functions and other patterns of changing conditions used in the analysis of dynamic systems (e.g., Franklin et al. 2009). The purpose of this approach is to define variation in the photosynthesis system directly in systems terms i.e., using properties such as time constants of response to changes of different types and estimates of capacitance and resistance to flows of basic components. Models representing photosynthesis as a series of metabolic pools and processes can make a priori assumptions about the type of control system that exists. These are typically open-loop control systems in which control action is dependent on fluctuations in resources and removal of products. This can be contrasted with active control systems such as controlled by transcription processes or removal of enzyme inhibitors which may be analogous to closed-loop control systems in which the control action is dependent on the output. For engineers: “Feedback is a property of closed-loop systems which permits the output to be compared with the input to the system so that appropriate control action may be formed as some function of output and input” (Distefano et al. 2011). An interesting question for study of dynamics of FSPMs in general and photosynthesis in particular is the extent to which the system can be represented as either a linked collection of open-loop systems with no active control or an active control system, e.g., through sink regulation (Paul and Foyer 2001). We will discuss over what time scales and conditions control of photosynthesis may be considered active or passive. 123 REFERENCES Bauerle WL, Oren R, Way DA, Qian SS, Stoy PC, Thornton PE, Bowden JD, Hoffman FM, Reynolds RF. 2012. Photoperiodic regulation of the seasonal pattern of photosynthetic capacity and the implications for carbon cycling. Proceedings of the National Academy of Sciences USA 109: 8612-8617. Distefano J, Stubberud A, Williams I. 2011. Schaum’s Outline of Feedback and Control Systems. Second edition. Ohio, McGraw-Hill. Farquhar GD, voin Caemmerer S, Berry JA. 2001. Models of photosynthesis. Plant Physiology 125: 42-45. Franklin GF, Powell JD, Emami-Naeini A. 2009. Feedback Control of Dynamic Systems. Sixth edition. New York, Pearson. Godin C, Sinoquet H. 2005. Functional-structural plant modelling. New Phytologist 166: 705-708. Mäkelä A, Hari P, Berninger F, Hänninen H, Nikinmaa E. 2004. Acclimation of photosynthetic capacity in Scots pine to the annual cycle of temperature. Tree Physiology 24: 369-376. Paul MJ, Foyer CH. 2001. Sink regulation of photosynthesis. Journal of Experimental Botany 52: 1383-1400. Pearcy RW, Gross LJ, He D. 1997. An improved dynamic model of photosynthesis for estimation of carbon gain in sunfleck light regimes. Plant, Cell and Environment 20: 411-424. Porcar-Castell A, Palmroth S. 2012. Modelling photosynthesis in highly dynamic environments: the case of sunflecks. Tree Physiology 32: 1062-1065. Taiz L, Zeiger E. 2010. Plant Physiology. Fifth Edition. Sunderland MA, Sinauer. Way DA, Pearcy RW. 2012. Sunflecks in trees and forests: from photosynthetic physiology to global change biology. Tree Physiology 32: 1066-1081. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 124 Revealing the relative importance of photosynthetic limitations in cucumber canopy Tsu-Wei Chen1*, Michael Henke2, Katrin Kahlen3, Pieter H.B. de Visser4, Gerhard Buck-Sorlin5, and Hartmut Stützel1 1Institute of Biological Production Systems, Leibniz Universität Hannover, Herrenhäuser Straße 2, 30419 Hannover, Germany, 2Department Ecoinformatics, Biometrics and Forest Growth, Georg- August University of Göttingen, Göttingen, Germany, 3Geisenheim University, Von-Lade-Straße 1, 65366 Geisenheim, Germany, 4Greenhouse Horticulture, Wageningen UR, Droevendaalsesteeg 1, 6708 PB Wageningen, the Netherlands and 5UMR 1345 Institut de Recherche en Horticulture et Semences (IRHS), AGROCAMPUS OUEST Centre d’Angers, 2 rue André le Nôtre, 49045 Angers Cedex 01, France *correspondence: chen@gem.uni-hannover.de Highlights: We identified that in a two meter high greenhouse grown cucumber canopy, photosynthesis is mostly light-limited, and light interception and biochemical capacity are the major factors limiting photosynthesis. The diffusion pathways, stomatal and mesophyll conductance, are minor restrictions. Keywords: Digitizing, photosynthesis, photosynthetic limitations, FvCB model, Cucumis sativus, GroIMP INTRODUCTION Improving the crop photosynthesis is important for increasing yield. To achieve this goal, methods to identify and to quantify the factors restricting photosynthesis are required. Several approaches to analyse the relative or quantitative magnitude of diffusional (stomatal and mesophyll resistance to CO2) and non-diffusional (biochemical and light) limitations of photosynthesis are proposed in the literature (Jones, 1985; Wilson et al., 2000; Grassi and Magnani, 2005; Grassi et al., 2009). The method proposed by Grassi and Magnani (2005), by which the restriction of photosynthesis (% of maximum photosynthesis) can be quantitatively partitioned to the stomatal, mesophyll and biochemical components of limitations, is based on the Farquhar von Caemmerer and Berry model (FvCB model, Farquhar et al., 1980) and considered to be a ‘more complex’ but ‘more realistic’ approach (Grassi et al., 2009). However, Grassi´s approach can only be applied at light-saturated conditions (Rubisco-limited), and plants in nature, especially at canopy level, should be more often grown under non-saturated light conditions (RuBP-limited). Therefore, modification of Grassi´s approach is required if the limitation analysis should be conducted at canopy level. The objective of this work is to quantify the relative importance of the photosynthetic limitations. We used digitized data to reconstruct a static 3D greenhouse cucumber canopy using the interactive modelling platform GroIMP. A modified version of the limitation analysis of Grassi and Magnani (2005) was conducted. This modification allows the limitation analysis to be conducted at non-saturated light conditions, which correspond to the plant conditions in greenhouse. MATERIALS AND METHODS Reconstructing a 3D cucumber canopy using GroIMP Whole plant architecture of cucumbers with 21 mature leaves grown in a greenhouse experiment was digitized as described by Wiechers et al. (2011b). Each leaf was represented by a predefined set of triangles and it was reconstructed using the commands FloatList and PolygonMesh in GroIMP (Kniemeyer, 2008). For reconstructing the virtual canopy structure, 18 cucumber plants with density 1.33 (plants per m2) were distributed in 3 rows. Distance between plants in one row and distance between rows were 0.5 m and 1.5 respectively. The corresponding set-up was used in the virtual reconstruction. 125 Model description and limitation analysis The light environment was simulated based on the approach of Buck-Sorlin et al. (2010) assuming the photosynthetic photon flux density (PPFD) above the virtual canopy is 600 µmol photon m-2s-1, diffuse/direct light ratio is 1:4 and sun position is on 1 July at 12:00. For computing the light distribution an advanced GPU-based ray-tracer, integrated into GroIMP, was used, with 10 million rays and a recursion depth of 10 reflections (Buck-Sorlin et al., 2010). A modified version of limitation analysis according to Grassi and Magnani (2005) was used to identify and quantify the stomatal (SLj), mesophyll (MCLj), biochemical (JBL) and light (JLL) limitation of to photosynthesis (Chen et al., in preparation): 𝐴max ref −𝐴 𝐴max ref ≅ 𝑆Lj + 𝑀𝐶Lj + 𝐽𝐵L + 𝐽𝐿L = 𝑙sj ∙ d𝑔cs𝑔csref + 𝑙mcj ∙ d𝑔m𝑔mref + 𝑙j ∙ d𝐽b𝐽cmaxref + 𝑙j ∙ d𝐽light𝐽cmaxref (1) where lsj, lmcj and lj, are the relative limitations of stomatal and mesophyll conductance and the electron transport rate, 𝑔csref, 𝑔mref and 𝐽cmaxref are their maximum values. The limitations are expressed in percentages of the potential photosynthesis (𝐴maxref ) . For this analysis, the intercepted light intensity at leaf level and the parameters of FvCB model and stomatal conductance for cucumber (Wiechers et al. 2011a) are used. Here, temperature is assumed to be 25°C. RESULTS AND DISCUSSION Photosynthesis is RuBP-regeneration limited If the chloroplastic CO2 concentration (Cc) was larger than the intersection point of FvCB model (Cctr), photosynthesis was limited by RuBP-regeneration. Under light-saturated conditions, at which Cc < Cctr, limitations were from CO2-diffusion. In cucumber, Cc remained constantly around 200 µmol mol-1 (Fig. 1A and 1B) and at 600 PPFD Cctr was below 150 µmol mol-1 (Fig. 1C). This indicated that under the simulated conditions the photosynthesis of the whole canopy was light-limited. Fig. 1. (A) Influence of irradiance on the intercellular (Ci) and chloroplastic (Cc) CO2 concentrations of cucumber leaves. (B) Under light saturated condition (1500 PPFD), Ci ranged between 300-320 µmol mol-1 and Cc were (n=3). (C) Simulated values of the intersection point of FvCB model (Cctr) in cucumber canopy are between 0-150 µmol mol-1, which is lower than Ci and Cc. Fig. 2. Visualization of the light limitation (A) and biochemical limitation (B) within a 2 m high cucumber canopy. Light intensity above the canopy is assumed to be 600 µmol photon m-2s-1. Sources of photosynthetic limitation The sources of photosynthetic limitation changed dramatically with the canopy depth (Fig. 2A, 2B). The CO2-diffusion pathways only restrict about 3-7 % of photosynthesis (Fig. 3A). The stomatal restriction increased with the leaf rank and mesophyll resistance only reduced less than 2% of the 126 photosynthesis capacity. Light interception and biochemical capacity were the most important factors reducing photosynthesis (Fig. 3B). At the lower canopy, about 68% of photosynthesis was limited by the biochemical capacity and 12% was limited by the light. At the upper canopy, 47% of the photosynthesis was restricted by light, without any biochemical limitation. Interestingly, although older leaves receive less light than the younger leaves, whereas older leaves are less light-limited than the youger leaves. This can be explained by the fact that the decrease in electron transport rate of the older leaves is mainly due to the reduction of biochemical capacity and improving the light interception of the leaves below rank 10 may only increase their photosynthesis rate up to 20%. Fig. 3. Photosynthetic limitation. (A) The diffusion pathways of CO2 restrict 4-6% of photosynthesis. Stomata limitation is 4% higher at upper part (higher leaf rank) than the lower part of the canopy. Above the rank 19, mesophyll limitation drops to zero. (B) Biochemical limitation of older leaves is about 70% and drops to zero at rank 20. Light limitation increases with leaf rank (n = 5). Here we only demonstrate the simulation assuming that the PPFD above the canopy is 600 µmol photon m-2s-1. It will be fruitful to apply this analysis with different light intensities. Further simulations with different canopy structures (e.g. isometric or V-shape training system) and plant densities would also be helpful in discovering the influence of these factors on the photosynthetic limitation. Furthermore, it is known that temperature influences stomatal, mesophyll and electron transport rate. Therefore, a more complex description of the temperature response to these physiological processes would aid in revealing the interaction of temperature and photosynthetic limitation. Using a dynamic structural model (Kahlen and Stützel, 2011; Wiechers et al. 2011a) would enable us to explore the effect of developmental stage on photosynthetic limitation at canopy level. These analyses could help greenhouse farmers to determine the strategy for supplemental light. LITERATURE CITED Buck-Sorlin GH, Hemmerling R, Vos J, de Visser PHB. 2010. Modelling of spatial light distribution in the greenhouse: description of the model. In: Li B, Jaeger M, Guo Y, eds. Plant growth modeling, simulation, visualization and applications, Proceedings – PMA09. IEEE Computer Society Conference Publishing Services, 79–86. Farquhar G, Caemmerer S von, Berry J. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149: 78–90. Grassi G, Magnani F. 2005. Stomatal, mesophyll conductance and biochemical limitations to photosynthesis as affected by drought and leaf ontogeny in ash and oak trees. Plant Cell & Environ 28: 834–849. Grassi G, Ripullone F, Borghetti M, Raddi S, Magnani F. 2009. Contribution of diffusional and non- diffusional limitations to midday depression of photosynthesis in Arbutus unedo L. Trees 23: 1149–1161. Jones HG. 1985. Partitioning stomatal and non-stomatal limitations to photosynthesis. Plant Cell & Environ 8: 95–104. Kahlen K, Stützel H. 2011. Modelling photo-modulated internode elongation in growing glasshouse cucumber canopies. New Phytologist 190: 697–708. Wiechers D, Kahlen K, Hartmut Stützel. 2011a. Dry matter partitioning models for the simulation of individual fruit growth in greenhouse cucumber canopies. Ann. Bot. 108: 1075–1084. Wiechers D, Kahlen K, Stützel H. 2011b. Evaluation of a radiosity based light model for greenhouse cucumber canopies. Agricultural and Forest Meteorology 151: 906–915. Wilson K, Baldocchi D, Hanson P. 2000. Spatial and seasonal variability of photosynthetic parameters and their relationship to leaf nitrogen in a deciduous forest. Tree Physiol 20: 565–578. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 127 Integrating architecture and physiological perspectives in fruit development Mikolaj Cieslak1^*, Michel Génard2, Frédéric Boudon3, Valentina Baldazzi2, Christophe Godin3, and Nadia Bertin2 1Department of Computer Science, University of Calgary, 2INRA, UR 1115 Plantes Systèmes de Culture Horticoles, 3INRIA project-team Virtual Plants, with CIRAD and INRA, UMR AGAP ^The presented work was done as part of a postdoctoral fellowship with INRA2 and INRIA3 *correspondence: msciesla@ucalgary.ca Highlights: Architectural properties of a fruit, such as its shape, vascular patterns, and skin morphology, play a significant role in determining the distributions of water, carbohydrates, and nutrients inside the fruit. Understanding the impact of these properties on fruit quality is difficult, because they develop over time and are highly dependent on both genetic and environmental controls. We developed a 3D fruit model that can be used to investigate effects of the principle architectural properties on fruit quality. Keywords: Fruit quality, water and carbon transport, fruit vasculature, skin microcracking, Prunus persica INTRODUCTION Fruit size, shape, composition and texture are all major qualities that determine consumer preference. Understanding the factors that regulate the development of these qualities is challenging, because they result from the interplay between physical and physiological processes that are under the control of both genetic and environmental factors. In the last 15 years, fruit quality has been largely investigated by using process- based models that treat the fruit as one large, homogeneous compartment, neglecting the fruit’s internal structure (Bertin et al., 2006). The architectural properties of a fruit, such as its size, shape, internal structure (number of carpels) and pattern of vasculature, however, can be remarkably diverse among varieties (Rodriquez et al., 2011). Since water and carbon are delivered to fruit tissues through a complex vasculature system, these architectural properties may have a significant impact on the distribution of water and carbon inside the fruit. For example, vascular patterns may account for the preferential supply of metabolites to specific tissues, and for causing physiological disorders such as blossom-end-rot (apical tissue necrosis) and shrivelling of the fruit’s skin. Also, there is a positive relationship between the distribution of sugars inside the fruit and the morphology of its skin. Water loss due to transpiration depends on both the pattern and density of cuticular cracks (Gibert et al., 2007, 2010) and the microclimate surrounding the fruit (Li et al., 2001), which increases the soluble solids content (sugar level) inside the fruit. The aim of this work was to investigate effects of fruit architectural properties on fruit quality by means of a 3D functional-structural fruit model that integrates architectural and physiological perspectives in fruit quality development, under the control of the environment. Existing 3D fruit models focus on the external shape of the fruit and treat its interior as homogeneous, without differentiation into tissue types (Saudreau et al., 2007, Mebatsion et al., 2011). Additionally, these fruit models do not consider the vascular tissue that supplies the fruit with resources and how the supply and other physiological processes affect fruit growth. In the following, we describe our generic 3D fruit model, which accounts for fruit shape, tissue compartmentalization, and vascular patterns, and use it to investigate the impact of fruit structure on sugar composition and distribution within a nectarine fruit. RESULTS AND DICUSSION We present a generic 3D fruit model that integrates architectural features and physiological processes of fruit development, with effects of the environment. For the fruit architecture, the geometry of the various fruit tissues is represented using 3D geometric shapes and the topological connections between them. For the physiological processes, we consider only those that are involved in the balance of water and carbon flows between the fruit, plant, and environment, as these drive fruit growth. In addition, we consider how this balance is modulated by exogenous factors like the availability of resources from the plant and the environmental conditions, such as temperature and humidity, and by endogenous factors that control the transport and accumulation of water and carbon to various fruit tissues via the xylem vessels and phloem 128 sieve tubes. The challenge is to represent the different fruit architectures as seen in nature, and to integrate the physiological processes that modulate fruit quality development. A generic 3D model of fruit development To construct a generic functional-structural fruit model, we developed a modelling pipeline in the OpenAlea platform (Pradal et al., 2009) that involves three steps: (a) creating a 3D volumetric mesh representation of the internal and external fruit structure, (b) generating a complex network of vasculature that is embedded within this mesh, and (c) integrating aspects of the fruit’s function, such as water and carbon transport, with the fruit’s structure. The model describes the late phase of fruit development when fruit growth is mostly due to cell expansion, once cell division has stopped. Most methods for generating 3D fruit geometry represent the external shape of the fruit using equation- based techniques (Saudreau et al., 2007), or using reconstructions from images (Mebastion et al., 2011), and assume the fruit has a homogeneous internal structure. For that reason, in a previous work (Cieslak et al. 2012), we developed a procedure for generating a 3D volumetric representation of fruit architecture, including the external shape and internal structure. To generate the geometry of the large tissues, such as the pericarp, the reconstruction algorithm uses Delaunay refinement that produces high quality tetrahedral meshes from 3D image data (Alliez et al., 2011), where each tetrahedron is labelled according to the part of the fruit tissue it represents. To generate the geometry of the vascular tissue, we used an algorithmic approach based on the assumption that vascular bundles are competing for space within the fruit, which was originally proposed for synthesizing leaf venation patterns (Runions et al., 2005). Figure 1 shows architectural models of nectarine and peach fruit that were constructed using this procedure. Based on this procedure, we made a generic model of fruit development by incorporating a model of water and carbon transport, which includes the flow of water and carbon in the fruit’s vasculature. This was achieved by extending a previously developed process-based model of fruit growth (Fishman and Génard, 1998) with features of recently developed phloem-xylem transport models that can handle branched architectures (Lacointe and Minchin, 2007). In this approach, the tetrahedral elements of the mesh are treated as compartments that represent a collection of cells within the fruit, and the model captures the aggregated response of those cells to changes in water and carbon content. The transport of water and carbon through the vasculature is based on the hypothesis of osmotically driven bulk flow, where a hydrostatic pressure gradient (due to differences in local sugar concentrations) drives the flow of water and carbon between regions of sugar loading and unloading. In our model, we assume loading of sugar occurs outside of the fruit’s vasculature so that sugar concentration in the pedicel is taken as input, whereas unloading may occur at any point inside the fruit that is linked by vasculature. Fig 1. Architectural model of nectarine and peach fruit. The images (A,C) show a photograph of a longitudinal section of a nectarine and peach fruit, respectively, that were used to generate 3D volumetric meshes (B,D). The user-defined blue and green lines highlight the exocarp and endocarp, respectively, which are used to define two polyhedral surfaces (one for the stone and another for the fruit’s surface) that serve as input into the mesh generation procedure. The green- line defines the main ventral and dorsal vascular bundles on the endocarp, whereas the branching secondary bundles are generated algorithmically according to the competition for space (Runions et al., 2005). Application to modelling sugar distribution inside nectarine fruit In nectarine fruit (Prunus persica), the spatial pattern of cuticular cracks on the fruit skin varies between the polar regions (stylar and peduncle ends) and equatorial regions (Gibert et al., 2007). This pattern changes the rate of water loss due to transpiration on different parts of the skin (Gibert et al., 2010), which may have an effect on the sugar concentrations inside the fruit. To analyse how such a pattern can cause a heterogeneous distribution of sugar inside a nectarine fruit, we used our functional-structural fruit model to perform simulations on the basis of our own experiments and on the work of Gibert et al. (2007, 2010). The percentage of microcracks on 32 regions (four transversal and eight longitudinal sections) of the 129 fruit’s skin has been measured by image analysis using a similar procedure as Gibert et al. (2007). For each of the 32 regions, the sugar content (degrees Brix) in the internal and external section of the fruit’s mesocarp (for a total of 64 measurements) was assessed. A linear relationship was found between the percentage of microcracks and sugar content (degrees Brix) for both the external and internal regions of the fruit (Fig. 2A,B). A 3D visualization of the results shows a gradient of sugar concentration from the fruit interior towards the fruit surface (Fig. 3A). We then created a functional-structural nectarine model using our modelling pipeline (Fig. 1B) and used it to simulate nectarine growth from 60 to 140 days after full bloom (dafb), because the heterogeneity in sugar distribution arises over time as the microcracks appear during the last 20 days of growth. During this time, the increase in fresh weight may be as much as 125 g (Gibert et al., 2007). The initial fresh mass was set to 25 g (Gibert et al., 2007) whereas the values of input variables (including temperature and humidity) and parameters were taken from a model of peach fruit growth (Fishman and Génard, 1998). However, the stomatal, cuticular, and crack components of conductance were modelled according to equations and parameters developed by Gibert et al., (2010). The percentages of cuticular cracks on the 32 regions of the fruit surface were taken from our own experiments, but the total cuticular crack surface area per fruit surface area was modelled as a function of the fruit fresh weight (g) according to data from Gibert et al., (2007). At the end of the simulation (140 dafb), the sugar concentrations of the 64 exterior and interior regions of the fruit were compared with sugar content (degrees Brix) data from our own measurements. In qualitative agreement, the model output showed a direct linear relationship between sugar content and the percentage of microcracks (Fig. 2C,D). A 3D visualization of the model output also shows a gradient of sugar concentration from the interior to the exterior of the fruit (Fig. 3B). Furthermore, simulations with no microcracking (not shown) resulted in a decrease in sugar content for the whole fruit, which is in agreement with the observed outcome of covering fruit with clear plastic film (Li et al., 2001). Although the parameter values have not yet been fitted to data, these results show that our model is capable of simulating the observed effects of architectural features, like skin microcracking, on the quality of the fruit. CONCLUSIONS We integrated architectural and physiological perspective in fruit development to construct an integrative computational model of fruit. The result was a dynamic system that gives us the ability to model fruit growth driven by resource availability and exogenous factors like temperature and humidity. With this type of functional-structural model, it is possible to investigate the important architectural features that affect fruit quality. We demonstrated this by examining the role of skin microcracking on determining the distribution of sugar content in nectarine fruit. This model will lead to more work on quantifying the effects of architectural features on fruit quality, such as examining effects of asymmetric vascular structure on nutrient distribution in tomato fruit. LITERATURE CITED Alliez P, Rineau L, Tayeb S, Tournois J, Yvinec M (2011) 3D Mesh Generation. In CGAL User and Reference Manual. 3.8 ed: CGAL Editorial Board. Bertin N, Bussières P, Génard M (2006) Ecophysiological models of fruit quality: a challenge for peach and tomato. Acta Horticulturae 718: 633-645. Cieslak M, Boudon F, Kenouche S, Zanca M, Goze-Bac C, et al. (2012) Generating 3D volumetric meshes of internal and external fruit structure. Acta Horticulturae 957: 239-245. Fishman S, Génard M (1998) A biophysical model of fruit growth: simulation of seasonal and diurnal dynamics of mass. Plant, Cell and Environment 21: 739-752. Gibert C, Chadœuf J, Vercambre G, Génard M, Lescourret F (2007) Cuticular Cracking on Nectarine Fruit Surface: Spatial Distribution and Development in Relation to Irrigation and Thinning. Journal of the American Society for Horticultural Science 132: 583-591. Gibert C, Génard M, Vercambre G, Lescourret F (2010) Quantification and modelling of the stomatal, cuticular and crack components of peach fruit surface conductance. Functional Plant Biology 37: 264-274. Lacointe A, Minchin PEH (2008) Modelling phloem and xylem transport within a complex architecture. Functional Plant Biology 35: 772-780. Li SH, Génard M, Bussi C, Huguet JG, Habib R, et al. (2001) Fruit quality and leaf photosynthesis in response to microenvironment modification around individual fruit by covering the fruit with plastic in nectarine and peach trees. Journal of Horticultural Science & Biotechnology 76: 61-69. Pradal C, Dufour-Kowalski S, Boudon F, Fournier C, Godin C (2008) OpenAlea: a visual programming and 130 component-based software platform for plant modelling. Functional Plant Biology 35: 751-760. Rodriguez GR, Munos S, Anderson C, Sim SC, Michel A, et al. (2011) Distribution of SUN, OVATE, LC, and FAS in the Tomato Germplasm and the Relationship to Fruit Shape Diversity. Plant Physiology 156: 275-285. Runions A, Fuhrer M, Lane B, Federl P, Rolland-Lagan AG, et al. (2005) Modeling and visualization of leaf venation patterns. ACM Transactions on Graphics 24: 702-711. Saudreau M, Sinoquet H, Santin O, Marquier A, Adam B, et al. (2007) A 3D model for simulating the spatial and temporal distribution of temperature within ellipsoidal fruit. Agricultural and Forest Meteorology 147: 1-15. Fig. 2. Sugar content in nectarine fruit as a function of the percentage of microcracks at 140 dafb. The two graphs on the top show the results of measurements on the percentage of microcracks and sugar content (degrees Brix) in the exterior region (A) and interior region (B) of a nectarine fruit. The two graphs on the bottom show the simulations results of sugar content (g soluble sugars / g FW) in the exterior region (C) and interior region (D) obtained by modelling increased surface conductance due to microcracks. Fig. 3. A 3D visualization of sugar content in a nectarine fruit at 140 dafb. Each tetrahedron is coloured according to measured sugar content in degrees Brix (A), or to the model output in g soluble sugars / g FW (B). The visualization shows the whole fruit from the front and back, with corresponding longitudinal sections, and a transversal section. Dark brown indicates high sugar content while light yellow indicates low sugar content. The tetrahedra representing the stone are coloured black, as the sugar content is assumed not to change. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 131 Up-scaling salt effects in cucumber: trade-off between photosynthesis and toxic ion accumulation Tsu-Wei Chen1*, Katrin Kahlen2 and Hartmut Stützel1 1Institute of Biological Production Systems, Leibniz Universität, Herrenhäuser Straße 2, 30419 Hannover, Germany, 2Geisenheim University, Von-Lade-Straße 1, 65366 Geisenheim, Germany *correspondence: chen@gem.uni-hannover.de Highlights: A dynamic cucumber FSPM, describing the effects of salinity on the plant morphology and the pattern of sodium accumulation in leaves, is parameterized and evaluated. This model is a first step in exploring mechanisms which improve plant tolerance and WUE at canopy level under salinity stress. Keywords: Salinity stress, Na+ accumulation, toxic effect, L-Cucumber, photosynthesis, transpiration INTRODUCTION Under salinity stress, concentrations of Na+ and Cl- ions in the xylem sap increase significantly (Wolf and Jeschke, 1987) and these two ions accumulate excessively in mature leaves (Munns and Tester, 2008). Once the cells in leaves become incapable of compartmentalising those ions in the vacuole, chlorosis or even necrosis appears (Stępień and Kłobus, 2006). Plants attempt to maximize carbon assimilation and minimize water loss, but there is a trade-off between transpiration and carbon assimilation. Optimization of this trade- off can be interpreted mathematically as the maximization of water use efficiency (WUE, assimilation per unit of water loss). Since the toxic ions are transported by the transpiration stream, an increase in WUE indicates a lower uptake of toxic ions per unit of carbon assimilated under salinity. This means that plants with higher WUE may delay the accumulation of ions to a toxic level which is in line with experimental results showing an inverse relation between Na+ accumulation and WUE in a comparison of tomato cultivars (Al‐Karaki, 2000). Moreover, inhibition of photosynthetic ability caused by accumulated toxic ions diminishes WUE further (Stępień and Kłobus, 2006). Therefore, a low WUE under salinity stress may even result in a negative feedback on plant growth. Since WUE and transpiration is closely related to leaf morphology and leaf distribution within canopy, functional-structural plant models (FSPM) should be a proper tool to study how WUE can be improved under salinity stress. The aim of this work is to construct and to parameterize the first FSPM describing Na+ accumulation and its toxic effect on physiological functions. MATERIALS AND METHODS Experiments and measurements Cucumber (Cucumis sativus L.), a salt sensitive crop, was chosen. Cucumber seedlings (‘Aramon’ Rijk Zwaan, De Lier, the Netherlands) were grown in three growth chambers in the Institute of Biological Production Systems, Leibniz Universität, Hannover, Germany. Cucumber plants were grown hydroponically under a 12-h photoperiod of 350 µmol m-2s-1 PPFD (photosynthetic photon flux density) with 24/20°C day- night temperature and 380 ppm CO2 concentration with four salinity levels, 0, 28, 56 and 84 mM NaCl in solution. In experiment 1, light response curves of gas-exchange parameters (photosynthesis, stomatal conductance and transpiration) were measured between days 8-10 after salinity start using a Li-6400 gas analyzer (LI-COR Inc., Lincoln, NE, USA). Final organ size (leaf, petiole and internode) was measured and dry masses of plant materials were weighed after drying at 70°C for 72 hours. Thereafter, plant samples were ground for Na+ analysis. Sodium concentration in the transpirational stream was estimated by total Na+ accumulated in the shoot over total transpiration. These data were used for model parameterization. In the experiment 2, cucumber plants were grown at the same environmental condition and data were used to evaluate the model. Model description Cucumber architecture model is based on L-Cucumber (Kahlen and Stützel, 2011). Influences of salinity stress on plant morphology and physiology are sketched in Fig. 1. Final internode length (FIL) is reduced proportionally with salinity level Ss: FIL(Ss) = FIL(1-0.0017Ss) (1) 132 Stomatal conductance (gs) is a function of PPFD (IInc) with additional influence by Ss and ion concentration in leaves (Sleaf): gs = f(Sleaf)(gs_min + b IInc)(1-αSs) (2) where minimum gs (gs_min) is 0.26, b and α are 0.0001 and 0.0065 respectively. f(Sleaf) is the function described in Fig.2. Light conversion efficiency (LCE) is influenced by IInc, osmotic restriction and Sleaf LCE = f(Sleaf)f(IInc)(1-βSs) (3) where f(Sleaf) is the function described in Fig. 2, f(IInc) is described in Wilson et al. (1992) and β (0.0047) is the osmotic effect on LCE derived from measured data. Transpiration (E) is linearly related to gs (E = 8.93gs + 0.08), and ion accumulation (Sacc) is the product of the ion concentration in the xylem sap (Sxy) and E. Sxy is calculated by Ss: Sxy = 0.51e(0.05 Ss) (4) and 38% of Sacc was partitioned to the supporting tissues. The relationship between the Na+ concentration and gas-exchange parameters was derived by normalizing and refitting corresponding published data (James et al., 2002, Fig. 2). The reduction of leaf area due to salinity is determined by the dry weight partitioned to the leaves and specific area (290 cm2 g-1, not influenced by salinity). Fig. 1 Model structure representing effects of different components of salinity on morphology and function. RESULTS AND DISCUSSION In this model, a reduction of leaf area under salinity stress is due to the decrease of light conversion efficiency and then the dry mass partitioned to the leaves. In comparison with the control plants, leaf area at slight and high salinity stress (28 and 56 mM NaCl) was reduced about 15-20% and 50-60% respectively. The simulated results are quite in agreement with the measurements (Fig. 3). Fig. 2 Effects of Na+ concentration on stomatal conductance and light conversion efficiency. The equations are obtained by refitting the data from James et al. (2002), which are normalized by the threshold Na+ concentration of cucumber (1.84 mmol Na+ g DW-1). Fig. 3 Measured and simulated reduction of leaf area at 28 and 56 mM NaCl (n=3). The patterns of Na+ accumulation in the 6th leaves after leaf appearance (Fig. 4A) and the patterns of Na+ concentration along the leaf rank after exposing to salinity for 28 days (Fig. 4B) can be simulated, but not very accurately, especially at high salinity level. Interestingly, the Na+ concentration was overestimated at higher leaf rank but underestimated at lower leaf rank in both salinity levels (4B). Two arguments stated in 133 the literature could explain this model error: 1) Sxy should not be constant but decrease along the leaf rank, as described in the literature (Wolf and Jeschke, 1987) or 2) Na+ reaching young leaves could be transported to old leaves via the phloem (Wolf et al., 1991). However, the changes of Sxy along the stem are difficult to estimate accurately and could be influenced by the plant age and the length of stem (Wolf et al., 1991). To estimate the re-translocation of Na+ from young leaves to old leaves experimentally is even more difficult. Munns and Tester (2008) stated that this re-translocation is an important mechanism to avoid the damage of young leaves, but some authors suggest that Na+ export has no significant contribution to the reduction of leaf Na+ (Wolf et al., 1991, Watson et al., 2001). Our model framework could allow us to answer the following questions: 1) what are important mechanisms of Na+ transport in plant? 2) How important is the Na+ re-translocation to salt tolerance? 3) How to improve WUE by plant management strategies to avoid the toxic ion accumulation in leaves. To our knowledge, this is the first model up-scaling the Na+ accumulation from leaf level to whole plant level and we expect that model improvement could provide insight to the and plant tolerance to ionic stress. ACKNOWLEDGEMENTS This work is supported by the German Research Foundation (DFG). Fig. 4 Measured and simulated Na+ concentration in the cucumber leaves at 28 and 56 mM NaCl. (A) Increase of the Na+ concentration in the 6th leaves with days after leaf appearance and (B) the Na+ concentration along the leaf rank after exposing to salinity for 28 days. LITERATURE CITED Al‐Karaki GN. 2000. Growth, water use efficiency, and sodium and potassium acquisition by tomato cultivars grown under salt stress. J. Plant Nutri. 23: 1–8. James RA, Rivelli AR, Munns R, Caemmerer S von. 2002. Factors affecting CO2 assimilation, leaf injury and growth in salt-stressed durum wheat. Functional Plant Biol. 29: 1393. Kahlen K, Stützel H. 2011. Modelling photo-modulated internode elongation in growing glasshouse cucumber canopies. New Phytologist 190: 697–708. Munns R, Tester M. 2008. Mechanisms of salinity tolerance. Annu. Rev. Plant Biol. 59: 651–681.. Stępień P, Kłobus G. 2006. Water relations and photosynthesis in Cucumis sativus L. leaves under salt stress. Bio. Plant. 50: 610–616. Wilson J, Hand D, Hannah M. 1992. Light interception and photosynthetic efficiency in some glasshouse crops. J. Exp. Bot. 43: 363–378. Watson R, Pritchard J, Malone M. 2001. Direct measurement of sodium and potassium in the transpiration stream of salt-excluding and non-excluding varieties of wheat. J Exp Bot 52: 1873–1881. Wolf O, Munns R, Tonnet ML, Jeschke W. 1991. The role of the stem in the partitioning of Na+ and K+ in salt-treated barley. J Exp Bot 42: 697–704. Wolf O, Jeschke W. 1987. Modelling of sodium and potassium flows via phloem and xylem in the shoot of salt- stressed barley. J. Exp. Bot. 128: 371–386. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 134 A model of mechanics and gas exchange in a neighborhood of a single stoma Ansgar Bohmann1,* and Andrés Chavarría Krauser1 1Interdisciplinary Center for Scientific Computing & Center for Modelling and Simulation in the Biosciences, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany *correspondence: ansgar.bohmann@uni-hd.de Highlights: The interplay of stomatal behaviour, epidermis mechanics, water flow, and diffusion is modeled dynamically with a system of ordinary and partial differential equations based on mechanical and thermodynamic principles. Simulation results of the discretised equations are shown. Keywords: Stomata, mechanics, turgor, diffusion, model, simulation. To gain insight in the physics and regulation of gas exchange (water vapour, carbon dioxide, and oxygen) in plant leaves we propose a dynamical first-principle model for a small disc-shaped section of a leaf around a single stoma (see Fig. 1). We consider different layers of tissues starting from the lower surface: the lower epidermis with a perfectly impermeaple cuticule and stomata controlled by guard cells, the interstitial air space, and the photosynthetically most active tissues (spongy and palisade parenchyma cells lumped together). The upper epidermis with its cuticule is assumed to contain no stomata and is treated as impermeable. We focus on the mechanical interaction between epidermis cells and guard cells, coupled to water transport driven by water potential gradients and diffusion of solvents in the symplastic and apoplastic compartments of the epidermis, as well as evaporation into and diffusion within the interstitial air space. Vapour exchange with the ambient air is controlled by stomatal aperture which in turn is determined by the mechanics and the guard cell solute content. During opening and closing of stomata solvents are pumped between the guard cell symplast and apoplast. The underlying physical processes, along with typical parameter values are described in standard literature (e.g. Nobel, 2005). The structure of the resulting model is a coupled system of ordinary and parabolic partial differential equations (reaction diffusion equations). This provides a more detailed description in particular with respect to spatial resolution as compared to resistor network models. It also captures dynamic effects and links microscopic physical properties, such as known diffusion constants, to observable quanities such as stomatal aperture and net transpiration rates. It provides a physically accurate explanation to the inverse behaviour of stomatal aperture after sudden changes in ambient parameters such as ambient moisture (see Mott et al., 1997). A finite volume approach was applied for space discretisation and computational results are shown. This model is intended to serve as a building block for a more comprehensive model of the leaf. LITERATURE CITED Mott KA, Denne F, Powell J. 1997. Interactions among stomata in response to perturbations in humidity. Plant, Cell & Environment, 20: 1098–1107, 1997. Nobel, PS. 2005. Physicochemical and environmental plant physiology. Elsevier, 3rd edition. Fig. 1.a) Section through leaf centered around a single stoma b) Steady state profiles for apertures 0 – 10 µm Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 135 A mechanistic model for the estimation of the quantum yield of photochemistry based on light, temperature, and chlorophyll a fluorescence Beñat Olascoaga and Albert Porcar-Castell Department of Forest Sciences, PO Box 27, 00014 University of Helsinki, Finland *correspondence: benat.olascoagagracia@helsinki.fi Highlights: By studying chlorophyll a fluorescence emissions from a range of light intensities in Scots pine saplings acclimated to different temperatures, we aim to build a model to interpret chlorophyll a fluorescence capable of estimating the quantum yield of photochemistry (𝞍P). Keywords: chlorophyll a, fluorescence, Scots pine, Pinus sylvestris L. INTRODUCTION The analysis of the chlorophyll a fluorescence emitted from vegetation is an approach to estimate the light use efficiency (LUE), a term used for the estimation of gross primary productivity (GPP) by remote sensing, and the measurement of changes in fluorescence can be used to infer information about changes in 𝞍P, which is a good proxy of LUE. Nevertheless, fluorescence is only one of the possible pathways in which the absorbed excitation energy can be used, and it competes with two other pathways: photochemistry, and thermal energy dissipation. The link between photochemistry and fluorescence is not trivial, and variations in fluorescence can be caused by both changes in photochemical or in non-photochemical energy utilization. This difficulty can be solved by studying chlorophyll a fluorescence by a saturating light pulse technique, which momentarily saturates the photochemical pathway and allows 𝞍P estimation from fluorescence parameters. But this active technique cannot be implemented from large distances as those of remote sensing, where the sun-induced passive fluorescence is used instead. Thus, linking fluorescence to LUE in the absence of saturating pulse technique still remains to be improved. The aim of this study is to develop a mechanistic model capable of bypassing the lack of saturating pulse capabilities in sun-induced fluorescence measurements by estimating the status of the reactions centres and quinone pools, the dynamics of photochemical capacity and non-photochemical quenching (NPQ), and energy fluxes from variations in fluorescence and using light and temperature to constrain photoinhibition and NPQ. MATERIAL AND METHODS In summer 2011, a total of 17 Scots pine (Pinus sylvestris L.) saplings growing in the field were transferred to a weather chamber and acclimated to different temperatures ranging from -5 to 40 °C. For each temperature, current-year needles were exposed to different light treatments ranging from 50 to 1500 µmol photons m-2 s-1 during an hour, and fluorescence emissions were recorded every second by a monitoring- PAM system (Heinz Walz GmbH, Germany). Fluorescence emissions were also recorded during sapling recovery in the darkness after the light treatments. During the whole process, a series of saturating light pulses (1s, 4000 µmol photons m-2 s-1 actinic light) were also given in order to get fluorescence parameters necessary to estimate 𝞍P. RESULTS AND DISCUSSION The maximum quantum yield of the photosystem II (Fv/Fm) was highest around 20 °C, and decreased gradually towards cooler temperatures. Fv/Fm decreased drastically towards warmer temperatures. NPQ building under light reached higher values towards the highest light treatments, and reached faster a constant value under warm conditions, except in the coldest temperatures studied. NPQ relaxation in the darkness reached faster its initial values under warmer conditions except under -5 °C, where it was kept steady or even increased slightly. The results concerning parameterization and model development are being developed and will be presented in the 7th International Conference on Functional-Structural Plant Models. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 136 Simulated interaction between tree structure and xylem and phloem transport in 3D tree crowns using model LIGNUM Eero Nikinmaa1,*, Risto Sievänen2, Jari Perttunen2, and Teemu Hölttä1 1Department of Forest Sciences, PO Box 27, 00014 University of Helsinki, Finland, 2Vantaa Res. Ctr, Finnish Forest Research Institute, PO Box 18, 01301 Vantaa, Finland *correspondence: eero.nikinmaa@helsinki.fi Highlights: We have implemented xylem and phloem transport model (Hölttä et al. 2006) with 3D tree model LIGNUM to study how structural traits in tree crown influence the transport in branched architecture with observed transpiration and photosynthetic response to driving environmental variables. We study how structural traits in tree crown influence the xylem and phloem transport and associated pressure gradients when observed transpiration and photosynthetic response to driving environmental variables are applied in branched architecture. Keywords: phloem translocation, sap flow, photosynthesis, transpiration, tree architecture Transpiration of tree crowns is directly connected to xylem pathway conductivity from soil to transpiring leaves. Assimilate transport in phloem is closely connected to xylem transport (Hölttä et al. 2006). Low water potential in leaves will slow down phloem transport or cause even reversal of flow (Hölttä et al. 2006). The environmental variables that drive photosynthesis and transpiration vary a lot within tree crowns and canopies influencing the attainable photosynthetic and transpiration rates. The hydraulic architecture of a tree crown along with the environmental conditions at each site within the canopy will influence local (and thus global) assimilation and transpiration rates (Nikinmaa et al. 2012). We combined the assimilation and transpiration model (Mäkelä et al. 2006), xylem and phloem transport model (Hölttä et al. 2006) with 3D tree model LIGNUM (Sievänen et al. 2008) for Scots pine trees. The xylem and phloem transport model deals with water pressure in xylem (Px) and phloem (Pp) and the amount of sugar solute in phloem (Np). In LIGNUM, the woody parts of trees consist of internodes. We formulate the transport model as differential equations for each internode as 𝑑𝑃𝑖 𝑑𝑡 = 𝑎𝑖�𝑄𝑖,𝑎𝑥,𝑖𝑛 − 𝑄𝑖,𝑎𝑥,𝑜𝑢𝑡� + 𝐸𝑥𝑝 − 𝑆𝑖 (𝑖 = 𝑥,𝑝) 𝑑𝑁𝑝𝑑𝑡 = 𝑎𝑛�𝑄𝑖,𝑎𝑥,𝑖𝑛 − 𝑄𝑖,𝑎𝑥,𝑜𝑢𝑡�𝑁𝑝 + 𝐿 − 𝑈 where Qi,ax,in and Qi,ax,out are axial inflow and outflow of water, Exp is accounting for flow of water between xylem and phloem in the internode, Si is sink of water depending on transpiration rate of the internode, ai and an are coefficients depending on physical conditions and the properties of the internodes (including volume and elastic modulus), and L and U are rates of loading and uploading of sugars. L is proportional to photosynthetic rate and U is proportional to growth and respiration rates of the internode. We solve the equations using fourth order Runge-Kutta method with time step of order of seconds and follow daily patterns of environmental drivers (radiation, temperature and water vapor deficit). We study how vertical variation in xylem conductivity, variation in leaf-area vs. sapwood area relation in different branching orders and variation in phloem cross-sectional area reflect to diurnal within crown water and assimilate transport rates and water potentials and discuss the results against know features of tree transport. We use the results to evaluate feasible crown structure and its ecological significance. LITERATURE CITED Hölttä T, Vesala T, Sevanto S, Perämäki M, Nikinmaa E. 2006. Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis. Trees 20, 67–78. Mäkelä A, Kolari P, Karimäki J, Nikinmaa E, Perämäki M, Hari P. 2006. Modelling five years of weather-driven variation of GPP in a boreal forest. Agricultural and Forest Meteorology 139, 382-398. Nikinmaa E, Hölttä T, Hari P, Kolari P, Mäkelä A, Sevanto S, Vesala T. 2012. Assimilate transport in phloem sets conditions for leaf gas exchange. Plant Cell and Environment First published online : 11 OCT 2012, DOI: 10.1111/pce Sievänen R, Perttunen J, Nikinmaa E, Kaitaniemi P. 2008. Toward extension of a single tree functional structural model of Scots pine to stand level: effect of the canopy of randomly distributed, identical trees on development of tree structure. Functional Plant Biology 35(9/10): 964-975. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 137 Integrating water transport into L-kiwi using an aspect-oriented approach Helge Dzierzon and Alla N. Seleznyova The New Zealand Institute for Plant &Food Research Limited, Palmerston North 4442, New Zealand *correspondence: Helge.Dzierzon@plantandfood.co.nz Highlights: A simple as well as transparent soil-vine water transport model was created and integrated into the functional model L-kiwi using L-Systems and the aspect-oriented approach. The model will play an important part in modelling variability of the fruit quality within the vine canopy. Keywords: Water transport, Actinidia deliciosa, kiwifruit, plant model, aspect-oriented approach Water transport from the soil into the plant canopy plays an essential role in plant growth and development; it brings nutrients from the soil and root-produced hormones from the roots and influences many physiological processes. In kiwifruit, effects of manipulations such as use of rootstocks and root pruning on water potential and water transport are of considerable interest. Hence, our aim was to integrate the water transport into an existing model of a kiwifruit vine, L-kiwi (Cieslak et al. 2011a). We chose a version of L-kiwi (Cieslak et al. 2011b) which uses an aspect-oriented approach based on multi-modules. Namely, each element of the plant structure is represented by a sequence of L-system modules with each module representing an aspect of the element’s function. Separate sets of productions are used for modelling each aspect, with context-sensitive rules facilitated by local lists of modules to consider/ignore. The biological system comprised a kiwifruit vine grafted on a rootstock. The initial model (Cieslak et al. 2011b) included sub-models for architecture, carbon transport, auxin transport and biomechanics. In the water transport sub-model, we used transpiration fluxes from the leaves as boundary conditions for the water transport system. We used an empirical model of daily variation of leaf transpiration rate and included a feedback of leaf water potential on transpiration as suggested by Jarvis (1976). Another boundary condition for the vine transport system was set by the soil water potential based on the soil relative water content (Thornley et al. 1990). The root/soil space was represented by a two dimensional finite element system (Blendinger 1996). Effect of soil water content on the soil conductivity was implemented as suggested by Thornley & Jonson (Thornley et al. 1990). At each derivation step of the model, the computation of water transport included three phases: calculating the water flux in the plant structure based on the transpiration fluxes from the leaves, calculating water potentials of the plant modules, and adjusting the values of the water fluxes to take into account feedback impacting water content in the soil and evaluating errors. The resulting model is simple and transparent. The aspect-oriented approach allowed the addition of the water transport sub-model without changes to other aspects of the system. Compared to L-peach (Allen et al. 2005), which uses an electric circuit analogy for implementation of water transport, the current model is more straightforward and each of its variables has a direct physiological interpretation. In particular, we do not use a notion of electromotive force to represent transpiration of leaves, but rather use the transpiration directly as boundary conditions. Further, the soil component of the model is more comprehensive as it allows adding variation of the soil water potential on the root soil boundary. The model is able to represent the patterns of water potential distribution within the plant and responses to irrigation and soil drying. In the future, the model will include a sub-model of fruit fresh weight and dry weight which requires carbon concentration and water potential as boundary conditions at the point of fruit attachment. This will allow to model variability of the fruit quality within the vine canopy. LITERATURE CITED Cieslak M, Seleznyova AN, et al. 2011. A functional-structural kiwifruit vine model integrating architecture, carbon dynamics and the effects of the environment. Annals of Botany 107: 1025-1041. Cieslak, M, Seleznyova AN, et al. 2011. Towards aspect-oriented functional-structural plant modelling. Annals of Botany 108: 1025-1041 Allen MT, Prusinkiewicz P, et al. 2005. Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. New Phytologist 166(3): 869-880. Jarvis PG 1976. The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Philosophical Transactions of The Royal Society of London, B 273(927): 593-610. Thornley JHM, Johnson IR. 1990. Plant and crop modelling: a mathematical approach to plant and crop physiology. Caldwell, NJ: The Blackburn Press. Blendinger, Ch. 1996. Eine Approximation des gesättigt-ungesättigten Darcy-Flusses in dünnen Gebieten. Dissertation, Rheinische Friedrich-Wilhems-Universität zu Bonn. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 138 Integration of a mechanistic biochemical and biophysical leaf gas exchange model in L-PEACH Inigo Auzmendi1,*, Romeo Favreau2, David Da Silva2 and Theodore DeJong2 1National Wine and Grape Industry Centre, Charles Sturt University, Locked Bag 588, Wagga Wagga, NSW 2678, Australia and 2Department of Plant Sciences, University of California Davis, Davis, CA 95616, USA *correspondence: iauzmendi@csu.edu.au Keywords: Photosynthesis, transpiration, L-PEACH, plant growth simulation L-PEACH is a functional structural model that simulates the growth of peach trees based on carbon partitioning between organs. Further development incorporated water transport, through transpiration and water potential, allowing studies of the effect of water stress on carbon partitioning (Da Silva et al. 2011). Our first approach to model leaf photosynthesis and transpiration with environmental sensitivity at an hourly time step, based on Kim and Lieth (2003), was not validated or computationally optimised. To overcome these issues we used the LEAFC3 model published by Nikolov et al. (1995). This model was computationally optimised and validated for forest trees and annual crops and it has been included in functional structural barley models. Even though LEAFC3 has been validated at the leaf level, this was done using an enclosed chamber, hence avoiding issues corresponding to whole plant estimations. Nikolov’s model assumed that the leaf temperature was an input of the model or it was estimated from the bi- directional short and long-wave radiation absorbed by the leaf, which can be easily determined in an enclosed leaf chamber but is complex to determine in an open canopy. Instead, we employed an empirical function obtained from measurements of canopy temperature in peach trees growing in a well irrigated orchard (Glenn et al. 1989). This function connected the difference between leaf and air temperature to vapour pressure deficit, which can be estimated from air temperature and relative humidity. Hence, using this function is simpler and more computationally efficient than the energy balance previously used (Nikolov et al. 1995). The leaf sub-model was developed as a stand-alone module that was integrated into L-PEACH as shown in Figure 1. The model was successfully used to simulate the effects of relative humidity on peach growth. This model integration is an important step for using functional-structural plant models in further studies to investigate long term effects of different environmental variables on canopy photosynthesis, transpiration, structure and yield characteristics, thus improving our understanding on the interactions of perennial plants with the environment. Fig. 1. Schematic representation of the integration of the mechanistic biochemical and biophysical leaf gas exchange model (leaf model) and the interactions with other sub-models in L-PEACH. LITERATURE CITED Da Silva D., Favreau R., Auzmendi I. and DeJong T.M. 2011. Linking water stress effects on carbon partitioning by introducing a xylem circuit into L-PEACH. Annals of Botany 108: 1135-1145. Glenn D.M., Worthington J.W., Welker W.V. and McFarland M.J. 1989. Estimation of peach tree water use using infrared thermometry. Journal of the American Society for Horticultural Science 114: 737-741. Kim S.H. and Lieth H.J. 2003. A coupled model of photosynthesis, stomatal conductance and transpiration for a rose leaf (Rosa hybrida L.). Annals of Botany 91: 771-781. Nikolov N.T., Massman W.J. and Schoettle A.W. 1995. Coupling biochemical and biophysical processes at the leaf level: an equilibrium photosynthesis model for leaves of C3 plants. Ecological Modelling 80: 205-235. T, RH, u Leaf incident light (IRad) Carbon Water Weather data Solar Radiation (Rad) Temperature (T) Relative humidity (RH) Wind speed (u) Canopy model Leaf light interception Leaf model Photosynthesis and transpiration L-system model Carbon allocation Structural growth Respiration Yield Water Potential Rad Structure T Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 139 Towards integrating primary C-N metabolism and physiology of crop growth across different plant scales: the ProNet-CN model – a multiscale approach for functional-structural plant modeling Johannes Müller*, André Eschenröder, and Olaf Christen Institute of Agricultural and Nutritional Sciences, University of Halle-Wittenberg, D-06900 Halle, Germany *correspondence: johannes.mueller@landw.uni-halle.de Highlights: ProNet-CN is a new multiscale process network integrating biophysical, metabolic, and physio- logical processes of biomass formation across plant scales. It combines the LEAFC3-N model describing the exchange of CO2, water vapor, and energy with a new model of the dynamics of mass balances of main carbon and nitrogen metabolites and its allocation between interacting compartments or organs. Keywords: Model, multiscale, photosynthesis, carbon, nitrogen, biomass INTRODUCTION The understanding of biological systems may be greatly enhanced by multiscale modeling approaches that span several structural and temporal scales and enable predicting emergent properties of the system using information from – respectively models of – more basic levels (Dada and Mendes 2011; Weinan, 2011). During last years, functional structural plant models were refined by integrating classical process- based plant models (review: de Reffye et al. 2009). On the other hand, current efforts in systems biology have triggered the development of detailed kinetic models of carbon and nitrogen metabolism (e.g., Poolman et al. 2004, Foyer et al. 2006; Rasse and Tocquin 2006; Uys et al. 2007; Nägele et al. 2010). Bridging the gap between these modeling domains could facilitate integrating the knowledge on plant processes across different scales. Here we present a first version of such a multiscale modeling framework. MODEL ProNet-CN calculates the dynamics of mass balances of main carbon (C) and nitrogen (N) metabolites, accounting for major biochemical conversions, allocation, and biomass formation. These processes are coupled across four nested scales: (i) metabolic scale, (ii) reaction compartments, (iii) organs, and (iv) plant (Fig. 1). To keep the complexity of the model manageable and consistent with the analytical capabilities, for the present we consider plants represented by only one shoot. Photosynthetic C input and transpiration (Tr) are calculated by the LEAFC3-N model (Müller et al. 2005; Braune et al. 2009). The water uptake and flux through the plant is assumed equal to Tr. Limiting soil water availability and plant water storage are not considered. N uptake is reduced to a passive influx of nitrate with the water stream. Mass balance and rate equations are formulated in terms of moles C and N associated with the considered metabolites. Concen- trations are defined per projected organ area. Both individual steps and lumped sequences of biochemical reactions or transport are modeled phenomenologically in terms of Michaelis-Menten kinetics or as driven by a concentration gradient, respectively. If appropriate, extensions were introduced to account for control by concentrations of C or N metabolites. The formation of organic N-compounds is condensed to the stoichio- metry of proteins and formally included into the C and N balances of the cytosol. The calculation of respiratory C losses relies on the concept of growth and maintenance respiration (McCree 1970). Leaf area growth is assumed proportional to the rate of synthesis of cellulose and hemicelluloses in leaves. MATERIAL AND METHODS Data were gathered on spring barley (Hordeum vulgare L.) grown in partially (glasshouse, exp. 1) or fully climatized (climate chamber, exp. 2) conditions at different levels of N supply (Müller et al. 2009). In exp. 1, lateral shoots were cut immediately after emergence to get a simplified plant structure. This enables to mea- sure twice a week the CO2 exchange and transpiration rates on all leaves and the characteristics listed below on all ’organs’ comprising visible parts of the individual leaf blades, pseudo-stem (pooled nodes, internodes, leaf sheaths, enclosed parts of leaf blades, and ear before heading), ear after heading, and roots of the entire plant. The analyses involved dry mass, leaf area, chlorophyll (leaf blades), total C, C bound to soluble carbo- hydrates and to fiber substances, total N, N bound to nitrate, amino acids and amids, and to proteins. In exp. 140 2, main shoots were analyzed in similar way, whereas lateral shoots were pooled and analyzed for overall dry mass, total C, and total N. For parameterizing the LEAFC3-N photosynthesis model, light and CO2 response curves of net photosynthesis rate were recorded in exp. 1 on all leaves and in exp. 2 on leaves of rank 4 and the leaf below the flag leaf (Braune et al. 2009; Müller et al. 2009). As additional information, data were available on the content of glucose, fructose, sucrose, starch, fructans (M.-R. Hajirezaei, IPK Gatersleben, Germany), and cell wall compounds (B. Usadel, MPI Potsdam-Golm, Germany) in barley leaves, as well as on the diurnal dynamics of main carbon metabolites in grasses grown under different N supply and CO2 concentration (Isopp et al. 2000). Matlab-Simulink (The Mathworks®) was used as simulation environment. Simulation studies covered the development of barley plants from leaf emergence until ripeness. The environmental data recorded at plant height in exp. 1 were used in the simulation studies (time step 5 min). RESULTS AND DISCUSSION Generally, the simulated dynamics of the conversion and transport rates of the considered metabolites and of the related mass balances were in good agreement with both the expected response and the experimental data. As an example of the simulations, the net rate of the interconversion of two central metabolites of the carbon metabolism, namely of cytosolic hexose (Hex) and sucrose (Suc) for leaves 1 to 10 during plant onto- genesis are shown in Fig. 2 (in terms of mol C). This simulation output reflects that leaves 2 to 10 during their early phase of development are sinks for C (import of Suc and thus Suc → Hex dominates) and thereafter act as a source of C (export of Suc and thus Hex → Suc dominates). This is mirrored by similar patterns of the net transport rate of Suc into/out of the phloem (simulation not shown). Skipping a large number of analogous simulation results for other C and N metabolites, the growth patterns are shown in Fig. 3. Again, the simulation results were generally in good agreement with the data. A more detailed comparison with data is planned after further refinement of the model and improved calibration. Simulink was proved to represent a powerful tool for developing a multiscale dynamic systems model that integrates C and N metabolism, organ based C and N mass balances, and process up-scaling to biomass formation. Fig. 1. Model scheme. Model inputs: Ca − ambient CO2 concentration, ha − air humidity, N − nitrogen bound to nitrate in soil water, Oa − ambient oxygen concentration, Ta − air tempera- ture, Qi − incident irradiance, u − wind speed, W − water. Carbon entities: Cel − C in cellu- lose and hemicelluloses, CNo − C in organic N compounds (mol), Fru − C in fructans (mol), Hex − C in hexoses (mol), Sta − C in starch (mol), Suc − C in sucrose (mol), Tri − C in trioses (mol). Organs and compartments: see figure. Composite symbols as in the following examples: HexCs − C in hexoses in the cytosol (mol), rTriHexCs − rate of C flux from triose phosphate to hexoses due to transformation of triose phos- phate to hexoses in the cytosol (mol s-1), tTriClCs − rate of C flux due to transport of trioses from chloroplast into the cytosol (mol s-1). Other symbols: rRespCs: rate of release of C from the sucrose pool in leaf cytosol due to growth and maintenance respiration. (2) VaCs Leaf (Lf) 1-10 Ear (Ea) Cell wall (Cw) (4) Vacuole (Va) (3) tSucVaCs tHexCsCw H2O tWXyLf (1) Qi Ca Oa Ta ha u rTriCl Photosynthesis (LEAFC3-N) Transpiration (LEAFC3-N) CO2 all organs CO2 Chloroplast (Cl) tHexClCs tTriClCs Stem (St) Root (Ro) Soil (So) N, W tNSoXy tWSoXy tNXyLf Xy le m (X y) WXy NXy tSucCsPh tCNoCsPh CNoPh tC N oE a tS uc Ph Ea CNoEa StaEa Ph lo em (P h) SucPh Cytosol (Cs) 141 ACKNOWLEDGEMENT This research was supported by the Federal Ministry for Education and Research (contract No. 0315426B). The authors thank two unknown reviewers for critics and helpful comments. LITERATURE CITED Braune H, Müller J, Diepenbrock W. 2009. Integrating effects of leaf nitrogen, age, rank, and growth temperature into the photosynthesis-stomatal conductance model LEAFC3-N parameterised for barley (Hordeum vulgare L.). Ecological Modelling 220:1599-1612. Dada JO, Mendes P. 2011. Multi-scale modelling and simulation in systems biology. Integrative Biology 3:86-96. De Reffye P, Heuvelink E, Guo Y, Hu B-G, Zhang B-G. 2009. Coupling process-based models and plant archi- tectural models: a key issue for simulating crop prodiction. In: Cao W, White JW, Wang E (Eds.): Crop Modeling and Decision Support. Berlin Heidelberg/Beijing: Springer/Tsinghua University Press, 130-146. Foyer CH, Noctor G, Verrier P. 2006. Photosynthetic carbon-nitrogen interactions: modellinfg inter-pathway control and signalling. In: Plaxton WC, McManus MT. 2006. Control of Primary Metabolism in Plants. Annual Plant Reviews 22:325-347. McCree KJ. 1970. An equation for the rate of respiration of white clover plants grown under controlled conditions. In: Setlik, I (Ed.): Prediction and Measurement of Photosynthetic Productivity. Pudoc, the Netherlands, pp. 221-229. Isopp H, Frehner M, Almeida JFP, et al. 2000. Nitrogen plays a major role in leaves when source-sink relations change: C and N metabolism in Lolium perenne growing under free air CO2 enrichment. Australian Journal of Plant Physiology. 27:851-858. Müller J, Wernecke P, Diepenbrock W. 2005. LEAFC3-N: a nitrogen-sensitive extension of the CO2 and H2O gas exchange model LEAFC3 parameterised and tested for winter wheat (Triticum aestivum L.). Ecological Modelling 183:183-210. Müller J, Braune H, Diepenbrock W. 2009. Complete parameterisation of photosynthesis models – an example for barley. In: Cao W, White JW, Wang E, eds. Crop Modeling and Decision Support. Berlin Heidelberg/Beijing: Springer/Tsinghua University Press, 12-23. Nägele T, Henkel S, Hörmiller I, Sauter T, Sawodny O, Ederer M, Heyer AG. 2010. Mathematical modeling of the central carbohydrate metabolism in arabidopsis reveals a substantial regulatory influence of vacuolar invertase on whole plant carbon metabolism. Plant Physiology 153:260–272. Poolman MG, Assmus HE, Fell DA. 2004. Applications of metabolic modelling to plant metabolism. Journal of Experimental Botany 55:1177-1186. Rasse DP, Tocquin P. 2006. Leaf carbohydrate controls over Arabidopsis growth and response to elevated CO2: an experimentally based model. New Phytologist 172:500–513. Uys L, Botha FC, Hofmeyr J-HS, Rohwer JM. 2007. Kinetic model of sucrose accumulation in maturing sugarcane culm tissue. Phytochemistry 68:2375–2392. Weinan E. 2011. Principles of Multiscale Modeling. Cambridge University press, 488 p. Fig. 2. Simulated ontogenetic courses of the rate of conversion hexose ↔ sucrose (rHexSucCs) in the cyto- sol of leaves of rank 1 to 10 (in terms of mol C s-1). The fluctuations represent the diurnal cycles. Fig. 3. Ontogenetic courses of dry mass of the whole plant (m Plant) and plant organs (Ro: root, St: fiber substances of the stem, m Ph: substances transported via phloem). 120 Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 142 Modelling zinc uptake and radial transport in roots Juliane Claus1*, Ansgar Bohmann1 and Andrés Chavarría-Krauser1 1Interdisciplinary Center for Scientific Computing & Center for Modelling and Simulation in the Biosciences, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany *correspondence: juliane.claus@bioquant.uni-heidelberg.de Highlights: Modelling of zinc radial transport in roots was undertaken to understand the experimentally observed pattern of zinc accumulation near the central cylinder of the root. The model confirms the hypothesis that low abundance of the efflux transporter HMA4 produces this radial gradient in zinc concentration, but surprisingly, transpiration was found also to be a key parameter. Keywords: zinc, radial transport, regulation, diffusion, root Zinc is an essential micronutrient in green plants, yet toxic at high concentrations. Only specialized hyperaccumulator plants can tolerate high zinc doses and are therefore of special interest for their potential application in phytoremediation and crop development (Clemens et al., 2002). Zinc ions are taken up from the soil along with water and are transported radially towards the root's vascular bundle in two parallel pathways: the cell wall (apoplast) and the cytoplasm (symplast). Cross-membrane transport into and out of the cytoplasm is mediated by ZIP and HMA transporter proteins, respectively (Fig. 1). Experimental results show a pattern of zinc accumulation close to the centre of the root, which disappears at high levels of HMA (Hanikenne et al., 2008). Using a computational model, we study the roles of ZIP regulation, HMA level and water flow velocity in creation of this radial pattern. A comprehensive one-dimensional dynamical model of radial zinc transport is developed to conduct simulations (Claus et al., 2012). This model accounts for the structure of the root consisting of symplast and apoplast and includes effects of water flow, diffusion, and cross-membrane transport via transporters. It also incorporates the radial geometry and varying porosity of root tissues, as well as regulation of ZIP transporters. We use existing biological data to estimate parameters and analyze the properties of the model in numerical simulations. In the steady state, the model reproduces the zinc gradient found in experiments as well as its loss at increased levels of HMA. Surprisingly, water flow velocity is found to be also a key parameter for producing this gradient. Simulations in time and space show short adaptation times to changes in external conditions. Since a slow ZIP regulation lead in these scenarios to high-amplitude oscillations, our results suggest that the time scales of regulation and transport need to be similar in the order of seconds to minutes. LITERATURE CITED Claus J, Bohmann A, Chavarría-Krauser A. 2012. Zinc uptake and radial transport in roots of Arabidopsis thaliana: a modelling approach to understand accumulation. Annals of Botany, doi: 10.1093/aob/mcs263 Clemens S, Palmgren MG, Krämer U. 2002. A long way ahead: understanding and engineering plant metal accumulation. TRENDS Plant Sci. 7:309-315s. Hanikenne M, Talke IN, Haydon MJ, et al. 2008. Evolution of metal hyperaccumulation required cis-regulatory changes and triplication of HMA4. Nature 453:391-395. Fig. 1. Schematic description of zinc transport in roots from the medium towards the xylem. Arrows indicate the direction of transport. Equations on the right describe the radial transport of zinc in symplastic and apoplastic compartments (see Claus et al., 2012 for details). Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 143 Simulating the impact of (“long-distance” or “root-to-shoot”) hormonal signaling and non-uniform soil water distribution on plant transpiration K. Huber1,*, J. Vanderborght1, M. Javaux1,2, N. Schroeder1,3, I. Dodd4, H. Vereecken1 1Agrosphere (IBG-3), Forschungszentrum Juelich GmbH, Germany; 2Earth and Life Institute, Université Catholique de Louvain, Belgium; 3Juelich Supercomputing Centre, Forschungszentrum Juelich GmbH, Germany; 4The Lancaster Environment Centre, Lancaster University, UK *correspondence: k.huber@fz-juelich.de Highlights: In response to non-uniformly distributed soil water, root water uptake and actual (whole plant) transpiration was simulated using R-SWMS as part of the soil dried. These variables varied widely (reduction between 10 and 55 percent) between plants with different controls of stomatal conductance, i.e. controlled by leaf pressure and/or by the concentration of a hormonal signal triggered by low root water potentials in dry soil regions. Hormonal regulation of transpiration was effective only for a limited time, when water flow out of drying soil regions was sufficient to transport hormones to the shoot. Keywords: R-SWMS, hormonal signaling, transpiration reduction, stomatal conductance THEORY Low soil water availability causes most plants to reduce their actual transpiration, Tact, via stomatal closure. Tardieu and Simmoneau [1998] classified stomatal adjustments for several different species and distinguished between isohydric and anisohydric plant types, the first type keeping leaf water pressure hleaf constant via stomatal closure during drying and the latter type showing decreasing hleaf for higher transpiration rates and lower soil water contents. The triggers for stomatal closure that reduceTact compared with the potential transpiration, Tpot can be driven either by plant hydraulics, hormonal signaling or a combination of both (Equation 1) [Tardieu and Davies, 1993]. 𝛼 = � 𝑔𝑠,𝑚𝑖𝑛 + �𝑔𝑠,𝑚𝑎𝑥 − 𝑔𝑠,𝑚𝑖𝑛� 𝑒𝛽[𝑠𝑖𝑔𝑛𝑎𝑙]𝑒𝛿ℎ𝐿𝑒𝑎𝑓 � 1𝑔𝑠,𝑚𝑎𝑥 (1) where gs,min and gs,max are minimal and maximal stomatal conductances [µmol cm-2 d-1], [signal] is the hormone concentration in the leaf [µmol cm-3], hLeaf [cm] is the pressure head in the leaves, and β [cm3 µmol- 1] and δ [cm-1] are empirical parameters. The reduction factor α [-] is the ratio between Tact and Tpot and takes values between 0 and 1. The most common studied plant hormone that is responsible for stomatal closure is abscicid acid (ABA) [Davies et al., 2005]. As the soil dries, the rate of ABA produced by the roots increases and is proportional to the root water pressure [Simonneau et al., 1998]. It is assumed that the ABA is transported with the xylem water flow towards the leaves to trigger stomatal closure. SIMULATIONS Virtual experiments were simulated using R-SWMS, which describes the water flow in the soil, towards, and in the 3-D network of roots mechanistically and based on basic laws of fluid dynamics [Javaux et al., 2008]. This model simulates the soil, root, and leaf water pressure heads. To model the hormonal signal concentrations in the leaf, [signal], a transport equation in the root network with signal mass production rate at the root tips, Msignal [µmol d-1], and advection terms in the root xylem segments that are derived from the flow equation was solved using a particle tracking algorithm. MSignal is a function of the pressure head at the root tips, hroot (Eq. 2). 𝑀𝑠𝑖𝑔𝑛𝑎𝑙 = 0 𝑓𝑜𝑟 |ℎ𝑅𝑜𝑜𝑡| < |ℎ0| (2) a ℎ𝑅𝑜𝑜𝑡 − 𝑏 𝑓𝑜𝑟 |ℎ𝑅𝑜𝑜𝑡| ≥ |ℎ0| where a [µmol cm-1 d-1] and b [µmol d-1] are production factors and h0 is a threshold potential that triggers the signal production. The particle tracking algorithm simulates the mass flux of the signal at the root collar 144 which is divided by the transpiration stream to obtain the signal concentration in the leaf. The signal concentration may also be calculated by assuming that all produced signal arrives instantaneously at the root collar by dividing the sum of the signal production rates at the root tips by the transpiration stream (Eq. 3) [𝑠𝑖𝑔𝑛𝑎𝑙] = ∑𝑀𝑠𝑖𝑔𝑛𝑎𝑙 𝑇𝑎𝑐𝑡 (3) Stomatal conductance is not modeled explicitely but as a reduction factor (varying between 0 and 1) for Tpot using Equation 1. Simulations were conducted in a virtual split root setup in a soil domain of 15.5 cm depth and 21 cm² soil surface with a top soil boundary condition (irrigation) of 10 cm3d-1 and an upper root boundary condition (Tpot) of 9.9 cm3d-1. Initial soil water content was uniformy distributed over depth. The irrigation was uniform over the total soil domain for the first 5 days. Then the same irrigation rate was applied only to one side of the soil domain. Hence only the water distribution changed; the plants had always sufficient water to maintain Tpot. Five different cases were compared (Table 1). For the first case, denoted as ’PH (pressure head)’, the upper root boundary condition (hleaf) cannot be lower than a critical water potential hcrit. If hleaf reaches hcrit the type of the upper boundary condition is switched from flow to constant water potential. For ’Signal’, Tact is calculated with Equation 1 and δ zero so that the leaf water pressure has no influence on stomatal closure. For ’PH+Signal’ also the influence of of hleaf on stomatal conductance is considered. To compare the impact of signal transport towards the leaf ’PH+Signal’ is also calculated assuming an instantaneous signal without simulating transport (’PH+Sign inst.’). Those four cases are compared with ’No Regulation’, where stomata remain fully open. Table 1. Model parameters* PH Signal PH+Signal |ψCrit| -7100 - - β - 1*10-3 1*10-3 δ - 0 1*10-5 a - 1.5*10-4 1.5*10-4 b - 1.065 1.065 |ψ0| - -7100 -7100 * Orders of magnitude from Tardieu and Davies [1993] RESULTS AND DISCUSSION Fig. 1. Comparison of actual (whole plant) transpiration rate for the five different cases Fig. 2. Rates of signal mass arriving at the root collar and originating from the dry and irrigated side for PH+Signal case: left axis; relative signal mass rates normalized by the total signal mass rates, right axis: absolute signal mass rates. 145 Figure 1 shows that the onset of transpiration reduction is earlier for the purely hydraulic regulation (’PH’). Transpiration for the signaling cases with transport first decreases but start to increase around day 9. This seems counter-intuitive as the stress for the drying part of the soil system is still increasing. Through comparison with the’PH+Sign.inst.’ case, this effect can be related to particle transport. Initially the relative signal mass (solid lines in Figure 2) arriving at the root collar from the dry side is higher than that arriving from the wet side. But around day 9 the ratios change and about 75% of the signal arriving at the leaves originates from the irrigated part of the root system. After four days of drying there is no more water uptake from the dry soil part. Therefore the water velocity inside the dry roots is close to zero so that produced signal is not transported anymore. This leads to a distinct maximum in the signal concentration when plotted versus water content in the dry soil compartment (Figure 3). This behavior was reported previously in plants exposed to partial [Dodd et al., 2008, Figure 5] or alternated root zone soil drying [Stoll et al., 2000]. However, the relation between leaf signal concentration and root zone water content is expected to depend on the soil water distribution. Due to internal water redistribution within the plant from deeper roots located in wet soil, flow velocities might not reach zero even in some very dry parts of the root system. Also the diurnal dynamics of the transpiration rates were not considered in the simulation. During the night when transpiration is diminished, water can redistribute within the root system (according to plant water potential gradients), increasing signal transport in the morning when stomata re-open and the redistributed water is transported from dry root zones to the shoot. Simulations using R-SWMS to evaluate these effects are currently being carried out. Fig. 3. Relationship between hormone concentration arriving in the leaves and soil water content of the drying part of the soil domain LITERATURE CITED Davies, W. J., G. Kudoyarova, and W. Hartung 2005. Long-distance ABA signaling and its relation to other signaling pathways in the detection of soil drying and the mediation of the plant's response to drought, Journal of Plant Growth Regulation, 24(4), 285-295. Dodd, I. C., G. Egea, and W. J. Davies 2008, Abscisic acid signalling when soil moisture is heterogeneous: decreased photoperiod sap flow from drying roots limits abscisic acid export to the shoots, Plant Cell Environ., 31(9), 1263- 1274. Javaux, M., T. Schröder, J. Vanderborght, and H. Vereecken 2008. Use of a Three-Dimensional Detailed Modeling Approach for Predicting Root Water Uptake, Vadose Zone Journal, 7(3), 1079-1079. Simonneau, T., P. Barrieu, and F. Tardieu 1998, Accumulation rate of ABA in detached maize roots correlates with root water potential regardless of age and branching order, Plant Cell Environ., 21(11), 1113-1122. Stoll, M., B. Loveys, and P. Dry (2000), Hormonal changes induced by partial rootzone drying of irrigated grapevine, Journal of Experimental Botany, 51(350), 1627-1634. Tardieu, F., and W. J. Davies 1993., Integration of Hydraulic and Chemical Signaling in the Control of Stomatal Conductance and Water Status of Droughted Plants, Plant Cell Environ., 16(4), 341-349. Tardieu, F., and T. Simonneau 1998, Variability among species of stomatal control under fluctuating soil water status and evaporative demand: modelling isohydric and anisohydric behaviours, Journal of Experimental Botany, 49, 419- 432. ACKNOWLEDGMENTS K.H. is funded by the SFB TR32: Transregional Collaborative Research Center 32 (www.tr32.de). Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 146 Modelling Spatial and Temporal Leaf Temperature Dynamics A focus on the leaf boundary layer Marc Saudreau 1,2,*, Boris Adam 1,2, Amélie Ezanic 3 and Sylvain Pincebourde 3 1INRA, UMR547 PIAF, F-63100 Clermont-Ferrand, France, 2UBP, UMR547 PIAF, F- 63000 Aubière, France, 3IRBI, IRBI UMR CNRS 7261, Université de Tours, Tours, France *correspondence: marc.saudreau@clermont.inra.fr Highlights: A 3D leaf temperature model is proposed to estimate dynamics of temperature gradients at leaf surface. The 3D leaf shape, the leaf physiology, and the microclimate are accounted for. Computational Fluid Dynamics was used to simulate realistic spatial evolution of the sensible heat flux at the leaf surface. Keywords: 3D Leaf Model, Heat balance, Nusselt Number, Free Convection, Boundary Layer INTRODUCTION Leaf temperature is an important factor involved in many biological processes such as leaf transpiration and photosynthesis (Gates 1968), leaf – pathogen interactions (Bernard et al. 2013) or insect development rates (Beck 1983). Within a plant canopy, leaves can exhibit a wide variety of temperature dynamics (frequency, amplitude, spatial gradients) related to the leaf position within the canopy (sunlit vs shaded leaf), the leaf shape and orientation (small vs large, downward vs upward), the leaf physiology (stomatal regulation), and the variability in microclimatic conditions (wind, light, air temperature and air relative humidity). Such variability in leaf temperature dynamics result from changes in heat energy exchanges between the leaf and its local environment. The underlying physics is well known and the temperature dynamics can be inferred by solving a heat balance equation where microclimate and leaf physiology are taken into account through radiation (R), convection (C), evapotranspiration (λE) and diffusion (G) terms: R + C + λE + G = 0 (Monteith and Unsworth 1990). Among these terms, the convective term (C) is definitively the more difficult to estimate because it describes the heat transfer process due to the leaf boundary layer. Many leaf energy models have been developped so far and have been integrated in crop and plant canopy models (Sinoquet et al. 2001; Brisson et al. 2003) but they only simulate the dynamics of the spatially average leaf temperature. Our aim was to build up a flexible and fast 3D leaf temperature model to predict main trends of spatial temperature patterns dynamics at leaf surface. Both leaf geometry, leaf physiology and microclimate were accounted for (Fig. 1). Based on theoretical and Computational Fluid Dynamics (CFD) results, forced and free laminar boundary layers were implemented for the convective term. The free convective boundary layer implementation and the 3D model are presented and discussed. THE 3D LEAF TEMPERATURE MODEL Among the different terms of the heat balance equation presented above, the diffusion term and the leaf thickness are neglected (G ≈ 0), based upon values of the leaf thickness (∼10-4 m) and the leaf thermal conductivity (0.4 W.m-1.K-1 (Vogel 1983)), and the time step used (from 30 minutes to one hour). Thus, the leaf volume is assumed to be zero and the surface is decomposed into n triangles. On each triangle, the heat balance equation is solved following Monteith and Unsworth (1990): R + C + λE = 0. The radiation heat flux is split into a direct and a diffuse component, and PAR and NIR wavebands are considered. The convective and evapotranspirative heat fluxes are modelled using classical relationships (Monteith and Unsworth 1990). The Jarvis model is used for the leaf stomatal conductance (Damour et al. 2010). The entire leaf temperature model is written in Python. Numerical integrations and the iterative procedure used to solve the heat balance equation are based upon numpy and scipy libraries (Jones et al. 2001). Both theoretical (plates) and real (3D scanned apple leaves) surfaces were used to assess the model and to perform temperature computations. 147 THE BOUNDARY LAYER Loss of energy by the leaf boundary layer is highly dependent on the main force driving the flow (Schuepp 1993). For a leaf, two forces could induce a movement of the air at its surface: the inertial force due to the main outer flow (i.e. the wind speed U), and the buoyancy force due to temperature gradient between the leaf surface (Tleaf) and the air (Tair). If the flow imposed by the external wind is weaker than the flow induced by the temperature difference between the leaf and the surrounding air, the convection is defined as ”free”. On the contrary if the boundary layer is driven by the external wind flow the convection is defined as ”forced”. The flow pattern and thus the heat exchange coefficient pattern dramatically change from a ”free” to a ”forced” convection The convective heat transfer per unit of surface is defined by h(Tleaf – Tair) where h is the heat transfer coefficient (W.m-2.K-1). For convenience of scaling, the Nusselt number (Nu) defined as k h.LNu = , where L is a characteristic length scale (m), and k is the thermal conductivity of air (W.m-1.K-1), is used instead of h (Monteith and Unsworth 1990). The intensity of free and forced convection can be estimated with the Grashof number (the ratio of buoyancy force to viscous force - Gr=βgL3(Tleaf-Tair)/ν2) and the Reynolds number (the ratio of inertial force to viscous force - Re=UL/ν) (Monteith and Unsworth 1990) where β (K-1) is the thermal expansion coefficient of the air, g (m.s-2) is the acceleration of the gravity, and ν (m².s-1) the kinematic viscosity of the air. Theoretical and experimental results have shown that the Nusselt numbers for free and forced convections are proportional to Gra and Reb respectively (Schuepp 1993). The use of CFD (Comsol Multiphysics v4.3a) enables us to estimate the exponent coefficients a and b for a wide variety of driving force intensity and surface geometry. Based on simple geomerical considerations (distance from the leaf leading edge according to the wind direction, distance from the leaf edge, main surface inclination angle) and estimates of Nusselt numbers from CFD, both kind of convection type were implemented in the 3D Leaf model. RESULTS AND DISCUSSION Figure 2a shows the effect of Grashof number on average Nusselt numbers for a horizontal thin plate. For both faces the Nusselt number exibits an exponential relationship with the Grashof number: Nu ~ m.Gra with a ≈ 0.186 ,m ≈ 0.325 for the lower face, and a ≈ 0.152, m ≈ 0.498 for the lower faces. These values are in agreement with the study of Wei et al. (2002) who performed numerical simulations of the natural convection heat transfer for an uniformly heated plate with metallic physical properties: a ≈ 0.2, m ≈ 0.317 and a ≈ 0.16, m ≈ 0.675 for the lower and upper faces respectively. Some heat transfer observations from uniformly heated metallic leaf models are available from early studies of Knoerr and Gay (1965) and Dixon and Grace (1983). They reported values of a between 0.1 and 0.2. For several Grashof numbers i.e. free convection intensities, the ratio between the local Nusselt number Nux and the average Nusselt number Nuavg (see figure 2a) along the main axis of the plate is plotted in figure 2b. For the range of Grashof numbers investigated, the ratio Nux/Nuavg do not change with Gr except at the edge of the upper face. The Nusselt number presents different patterns between faces with a quasi flat curve at the lower face except at the edge, and with increasing values from the plate center to the edge for the Fig. 1. Schematic view of the main features of the 3D leaf model Fig. 2. Free convection – CFD results: (a) Average Nusselt number function of the buoyancy force intensity: Nuavg =1/L ∫LNuxdx, and (b) Local Nusselt number Nux/Nuavg along the main axis for several Grashof numbers (X/L = 0 corresponds to the plate center and X/L = 0.5 to the edge of the plate). (a) (b) 148 upper face. The ratio Nux/Nuavg can be fitted with 5th and 6th order polynomial functions with R² coefficient up to 0.94 for lower and upper faces respectively. The above CFD results show that some simple and robust relationships of heat transfer coefficients can be found for a free laminar convective boundary layer. Of course leaf boundary layers could exhibit local and sudden patterns for high inclination angle of the surface or when high wind velocity promotes the transition to turbulence of the leaf boundary layer, and the creation of large energetic structures in the trailing edge of the leaf. Such situations cannot be handled with the above relationships. Above relationships of local and average heat transfer coefficients Nux (x/L) and Nuavg(Gr) of free laminar convective boundary layer for both lower face and upper face were implemented in the 3D leaf model (figure 3a). Based upon such results and when all features of the 3D leaf model are used together, leaf temperature heterogeneity can be revealed (Figure 3b). In the future, a sensitivity analysis of the main parameters of the model and a model assessment based on IR infra-red camera measurements will be performed. LITERATURE CITED Beck SD. 1983. Insect Thermoperiodism Annual Review of Entomology 28:91-108 Brisson NC, Gary et al. 2003. An overview of the crop model stics. European Journal of Agronomy 18(3–4): 309-332. Bernard F, Sache I, Suffert F and Chelle M. 2013. The development of a foliar fungal pathogen does react to leaf temperature! New Phytologist, 198: 232–240 Damour G, Simonneau T, Cochard H, Urban L. 2010. An overview of models of stomatal conductance at the leaf level, Plant Cell and Environment, 33(9):1419-38 Dixon M and Grace J. 1983. Natural convection from leaves at realistic Grashof numbers. Plant, Cell & Environment 6(8): 665-670. Gates D. M. 1968. "Transpiration and Leaf Temperature." Annual Review of Plant Physiology 19(1): 211-238 Jones E, Oliphant T., Peterson P et al. 2001. SciPy: Open Source Scientific Tools for Python, http://www.scipy.org Knoerr KR and Gay LW. 1965. Tree Leaf Energy Balance, Ecology 46: 17-24 Monteith J and Unsworth MH. 1990. Principles of environmental physics, 2nd edn. Edward Arnold, London, pp. 291. Schuepp PH. 1993. Tansley review no. 59: Leaf boundary-layers. New Phytologist 125(3): 477-507. Sinoquet H, Le Roux X, Adam B, Ameglio T, Daudet FA. 2001. RATP: a model for simulating the spatial distribution of radiation absorption, transpiration and photosynthesis within canopies: application to an isolated tree crown. Plant, Cell and Environment 24: 395–406. Vogel S. 1983. The lateral thermal conductivity of leaves, Canadian. Journal of Botany, 62:741-744 Wei JJ, Yu B, et al. 2002. Numerical study of simultaneous natural convection heat transfer from both surfaces of a uniformly heated thin plate with arbitrary inclination. Heat and Mass Transfer 38(4): 309-317. ACKWNOLEDGEMENT This work was funded by the French National Research Agency project MicroCliMite No ANR-10-BLAN-01706-02 Fig. 3. Illustrations of (i) the Nusselt number implementation for a free convection for an horizontal 3D leaf model (a), and of (ii) a simulated temperature pattern according to given microclimate characteristics (b). (a) (b) Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 149 Hydraulic constraints influence the distribution of canopy photosynthetic properties Mikko Peltoniemi1,2,3, *, Remko Duursma4 and Belinda Medlyn3 1Finnish Forest Research Institute (METLA), Vantaa, Finland.2Department of Forest Sciences, University of Helsinki, Helsinki, Finland.3Department of Biological Sciences, Macquarie University, North Ryde, NSW, Australia.4Hawkesbury Institute for the Environment, University of Western Sydney, Penrith, NSW, Australia. *correspondence:mikko.peltoniemi@metla.fi Highlights: We showed that limited water transport capacity to upper canopy leaves leads to sub-optimal photosynthetic performance of a tree. In these cases, the widely applied assumption of optimal N distribution that follows irradiance distribution does not hold. Hydraulically constrained optimum N distribution would be flatter than the distribution of irradiance. We further showed that in order to maximize canopy photosynthesis, trees should allocate water transport capacity and N co-optimally, which means allocating both of them according to irradiance distribution. Keywords: Canopy, Hydraulic conductance, Nitrogen, Optimal, Photosynthesis, Resource allocation Leaf properties vary significantly within plant canopies, due to the strong gradient in light availability through the canopy. Leaves near the canopy top have high nitrogen (N) and phosphorus content per unit leaf area, high leaf mass per area, and high photosynthetic capacity, compared to leaves deeper in the canopy. Variation of leaf properties has been explained by the optimal distribution of resources, particularly nitrogen, throughout the canopy. Studies of the optimal distribution of leaf nitrogen (N) within canopies have shown that, in the absence of other constraints, the optimal distribution of N is proportional to light. This is an important assumption in the big-leaf models of canopy photosynthesis and widely applied in current land- surface models. However, measurements have shown that the gradient of N in real canopies is shallower than the optimal distribution. One thing that has not yet been considered is how the constraints on water supply to leaves influence leaf properties in the canopy. Leaves with high stomatal conductance tend to have high transpiration rate, which suggests that for the efficient operation of canopy, high light leaves should be serviced by more water. The rate of water transport depends on the hydraulic conductance of the soil-leaf pathway. We extend the work on optimal nitrogen gradients by considering the optimal co-allocation of nitrogen and water supply within plant canopies. We developed a simple “toy” two-leaf canopy model and optimised the distribution of N and hydraulic conductance (K) between the two leaves. We asked whether the hydraulic constraints to water supply can explain shallow N gradients in canopies. We found that the optimal N distribution within plant canopies is proportional to the light distribution only if hydraulic conductance is also optimally distributed. The optimal distribution of K is that where K and N are both proportional to incident light, such that optimal K is highest to the upper canopy. If the plant is constrained in its ability to construct higher K to sun exposed leaves, the optimal N distribution does not follow the gradient in light within canopies, but instead follows a shallower gradient. We therefore hypothesize that measured deviations from the predicted optimal distribution of N could be explained by constraints and costs on the distribution of K within canopies. Distribution of N in tall canopies would be particularly constrained unless these trees were unable to invest in the construction and maintenance of high hydraulic conductance to peripheral leaves. Further empirical research is required to the extent to which plants can construct optimal K distributions, and whether shallow within-canopy N distributions can be explained by sub-optimal K distributions. Future development of ecosystem carbon and water exchange models could benefit from integration of water supply and other constraints influencing canopy N distribution. LITERATURE CITED Peltoniemi MS, Duursma RA, Medlyn BE. 2012. Co-optimal distribution of leaf nitrogen and hydraulic conductance in plant canopies. Tree Physiology 32: 510-519 Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 150 Reliable estimation of parameters of the Farquhar-Von Caemmer-Berry Biochemical model cannot be obtained by fitting An/Ci curves Qingguo Wang1,3, David H. Fleisher2, Jong Ahn Chun3, Jonathan Resop2, Dennis Timlin2 and V.R. Reddy2 1Wye Research and Education Center, University of Maryland, Queenstown, MD 21658 USA; 2USDA-ARS System Crops and Global Change Lab, Beltsville, MD 20705 USA, 3APEC Climate Center, 12 Centun 7 ro, Haeundae-gu, Busan 612 020, Republic of Korea. *correspondence: qingguo.wang@apcc21.org Highlights: Because of the limited accuracy and limited number of data points of an An/Ci curve, the parameters of the Farquhar-von Caemmerer-Berry photosynthesis model cannot be reliably estimated by analysis of An/Ci datasets with the data measured from currently available commercial gas exhange device. However , the fitted parameters remains useful to predict photosynthesis. Keywords: FvCB model, prameters, fitting, An/Ci curve, The Farquhar-von Caemmerer-Berry (FvCB) leaf photosynthesis model for C3 plants (Farquhar et al, 1980) has been widely used to simulate CO2 assimilation and the response of plant to climate change from leaf to canopy scales due to its solid theoretical basis and simplicity. The fitting methods can be divided into two types: type I method fits parameters with the original FvCB model (Sharkey et al. 2007). Type II fits parameters with the quadratic equation (Gu et al., 2010). Each method relies on different assumptions and has technical limitations. Depending on the methods used, the estimated parameters can be substantially different. To the best of our knowledge, there is no publication on testing the fitting methods with generated ideal data sets and data sets superimposed by possible measurement errors, an essential step for fully evaluating the fitting methods because the true parameter values are known and the An/Ci curves can be stimulated under all possible conditions. The objectives are to verify the reliability of parameterization approaches for fitting An/Ci curves by three approaches. One was from type I, a commonly used method of Sharkey et al. (2007); the second is from type II methods, which have been stated to overcome some major issues of extant methods (Gu et al., 2010); and the third is the analytical method that assumes the errors in An/Ci data are negligible. Two groups of data sets with different accuracies are generated for examining the reliability of three different methods. One group of datasets are generated with 15 data points with three different fixed accuracies: (1) data with high accuracy of 9 decimal places (DSH-15); (2) data with the same accuracy of the currently available commercial gas exchange device (DSL-15) without measurement error; (3) data with the same accuracy of the currently available commercial gas exchange device and with measurement error imposed (DSE-15). Another group of datasets are generated with either varied accuracy or varied number of data points. All three methods cannot estimate reliable parameters of the FvCB model by analyzing An/Ci curves with the same accuracy of the measured data produced from the currently available commercial gas exchange device. The method of Sharkey et al. (2007) cannot obtain accurate parameters even with highly accurate datasets because one equation used is theoretically incorrect and has unrealistic assumptions. Analytical methods and the method of Gu et al. (2010) can estimate reliable parameters from highly accurate datasets with enough data points. However, the resulting fitted parameter set by methods of Sharkey et al. (2007) and Gu et al. (2010) remains useful to predict An under the same conditions under which the An/Ci curves were derived. LITERATURE CITED Farquhar GD, Von Caemmerer S, Berry JA. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149, 78–90. Gu L, Pallardy SG, Tu K, Law BE, Wullschleger SD. 2010. Reliable estimation of biochemical parameters from C3 leaf photosynthesis–intercellular carbon dioxide response curves. Plant, Cell & Environment 33:1852-1874. Sharkey TD, Bernacchi CJ, Farquhar GD, Singsaas EL. 2007. Fitting photosynthetic carbon dioxide response curves for C-3 leaves. Plant, Cell & Environment 30, 1035–1040. DISTRIBUTION OF RESOURCES AND GROWTH IN PLANTS Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 153 Stem diameter variation: endogenous regulation versus environmental dynamics and its implication for functional modelling Maurits Vandegehuchte1, Adrien Guyot2, David Lockington2 and Kathy Steppe1 1Laboratory of Plant Ecology, Faculty of Bioscience Engineering, Ghent University, Coupure links 653, 9000 Gent, Belgium, 2National Centre for Groundwater Research and Training- School of Civil Engineering, The University of Queensland, 4072 Brisbane, Australia *correspondence: maurits.vandegehuchte@ugent.be Highlights: Stem diameter variations are generally modelled based on the time lag between transpiration and root water uptake. However, small differences in endogenous osmotic regulation of the storage tissue can result in significant changes in stem diameter variation. This endogenous control needs to be taken into account in functional-structural plant models to accurately predict growth. Keywords: stem diameter variation, Rhizophora, Avicennia, growth, osmotic regulation INTRODUCTION When interpreting and modelling the plant water status, radial transport between xylem and surrounding storage tissues is of crucial importance as it allows turgor to build up which ultimately leads to plastic growth, providing a specific threshold pressure is overcome (Lockhart, 1965). Moreover, water in the storage tissue buffers discrepancies between water demand and supply, avoiding hydraulic failure in the xylem. As such, it has been commonly accepted that a clear time lag exists between the transpiration at leaf level and the water uptake at root level, caused by the hydraulic resistance between the two (e.g. Zweifel et al., 2000, Peramaki et al., 2001, Sevanto et al., 2002, Steppe et al., 2006). This time lag causes a decrease in stem diameter in the morning as then the water supply from the roots lags behind the transpiration at leaf level, necessitating water flow from the storage compartments (Hinckley and Bruckerhoff, 1975). In the afternoon, when xylem water potential rises because of a decreased atmospheric water demand, water again flows back to the storage tissues, resulting in a diameter increase (Molz and Klepper, 1973). In functional plant models, diameter changes are modelled based on the in- and outflow of water in the storage tissues from and to the xylem. In these models, the single cell approach is often applied, considering the stem storage as a single volume separated from the xylem by a water permeable membrane with a specific resistance (e.g. Génard et al., 2001, Steppe et al., 2006). Water transport to this storage compartment then increases turgor, resulting in dynamic diameter changes or plastic growth if a threshold value is exceeded. In these models, however, endogenous osmotic activity is not taken into account. Our aim was to assess possible differences in diameter variations and coupled endogenous osmotic regulation between two representatives of the two most dominant mangrove genera, Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa Griff. These species are known to thrive in saline, and, hence, drought inducing conditions, requiring specific water use strategies. MATERIALS AND METHODS Measurements were conducted at the west coast of North Stradbroke Island, Queensland, Australia (S27°27.061’ E135°25.806’), a vegetated sand dune island. The island is characterized by sandy soils and acidic waterbodies intertwined by a complex mix of groundwater-fed lakes, swamps and creeks (Page et al., 2012). On this field site, three full grown trees of both Avicennia marina (Forssk.) Vierh. and Rhizophora stylosa Griff. were chosen, located in proximity of each other to avoid tidal effects and spatial salinity gradients. The field site was subjected to tidal movement, flooding the site approximately twice every 24 hours. Air temperature, relative humidity, solar radiation, rainfall and windspeed were measured and recorded every ten minutes at 2 m above soil surface (HOBO weather station, Onset, Cape Cod, Massachusetts, USA). Vapour pressure deficit (VPD, kPa) was inferred from measured air temperature (Tair) and relative humidity (RH) according to Buck (1981). Soil salinity and water table depth were determined with in situ pressure sensors (Aqua Troll 200, In-Situ Inc., Fort Collins, CO, USA) installed in piezometers, located close to the measured trees at depths of 25 and 180 cm. All trees were equipped with a dendroband 154 (DRL26 – Logging Band Dendrometer, ICT international, Armidale, NSW, Australia), continuously recording stem diameter variations, and Sapflow+ sensors, registering sap flux density (Vandegehuchte and Steppe, 2012). Stem water potentials were recorded with stem psychrometers (PSY-1 Stem Psychrometer, ICT International, Armidale, NSW, Australia). Besides these continuous measurements, stomatal resistance was measured for four days (DOY 241, 247, 251 and 254) throughout the measurement period, applying a dynamic porometer (AP4 dynamic porometer, Delta-T Devices Ltd, Cambridge, UK). By slightly modifying the mathematical flow and storage model of Steppe et al. (2006) based on the work of De Swaef et al. (2012), a mechanistic model was obtained to assess dynamics in xylem and storage water potentials based on stem sap flux density and stem diameter variations. This model was applied as a tool to synthesise the conducted measurements and derive trends in osmotic potential of the stem storage tissue. Modelled xylem water potentials were compared with psychrometric measurements. RESULTS AND DISCUSSION Contrary to what is expected from literature, stem diameter of Rhizophora increased during the morning and decreased in the afternoon. Even though a similar pattern has been shown for CAM plants (Gouws et al., 2005, Matimati et al., 2012), stomatal closure was measured during the night, indicating that the CAM mechanism was not applicable for Rhizophora. As sap flux density and stem water potential showed similar patterns for Avicennia and Rhizophora and these trees were subjected to the same environmental conditions, the differences in diameter variations patterns are likely due to endogenous osmotic regulation. Our model outputs based on stem diameter input suggest that, unlike what is generally expected, xylem water potential lags behind the storage water potential for Rhizophora (Figure 1b), due to an earlier decline in storage osmotic potential compared to Avicennia (Figure 2a). When decoupling the volumetric effect and the presence of osmotic active compounds on storage osmotic water potential, it is clear that, while both species seem to endogenously regulate the amount of osmotic compounds present in the storage tissues, Rhizophora manages to increase this amount earlier during the day than Avicennia (Figure 2b). Figure 1 Model results showing the diameter input and xylem and storage water potential output for both Avicennia (a) and Rhizophora (b). These results indicate that stem diameter variations, and, hence, growth, may not only be determined by environmental dynamics but may also be strongly influenced by endogenous control. This implies that also these endogenous adaptations need to be included in functional-structural plant models to allow correct predictions of plant behaviour. Our results indeed show that very small differences in osmotic active compound regulation may have drastic influences on important plant physiological variables such as stem diameter. A more thorough knowledge on how these features influence stem diameter variations will result 246.0 246.5 247.0 247.5 248.0 248.5 249.0 W at er p ot en tia l ( M Pa ) -4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 22.998 23.000 23.002 23.004 23.006 23.008 23.010 Day of the year 246.0 246.5 247.0 247.5 248.0 248.5 249.0 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 Stem diam eter (cm ) 16.191 16.192 16.193 16.194 16.195 16.196 Xylem WP Storage WP Stem diameter (a) (b) 155 in new insights into why species differ in growth patterns and, hence, which strategies are more beneficial, depending on the environmental conditions. Moreover, it will allow to assess the relative importance of endogenous regulation and environmental dynamics to long-term growth. LITERATURE CITED Buck AL. 1981. New Equations for Computing Vapor Pressure and Enhancement Factor. Journal of Applied Meteorology, 20: 1527-1532. De Swaef T, Hanssens J, Cornelis A, Steppe K. 2012. Non-destructive estimation of root pressure using sap flow, stem diameter measurements and mechanistic modelling. Annals of Botany. Génard M, Fishman S, Vercambre G, Huguet JG, Bussi C, Besset J, Habib R. 2001. A biophysical analysis of stem and root diameter variations in woody plants. Plant Physiology, 126: 188-202. Gouws LM, Osmond CB, Schurr U, Walter A. 2005. Distinctive diel growth cycles in leaves and cladodes of CAM plants: differences from C(3) plants and putative interactions with substrate availability, turgor and cytoplasmic pH. Functional Plant Biology, 32: 421-428. Hinckley TM, Bruckerhoff DN. 1975. The effects of drought on water relations and stem shrinkage of Quercus alba. Canadian Journal of Botany, 53: 62-72. Lockhart JA. 1965. An analysis of irreversible plant cell elongation. Journal of Theoretical Biology, 8: 264-275. Matimati I, Musil CF, Raitt L, February EC. 2012. Diurnal stem diameter variations show CAM and C-3 photosynthetic modes and CAM-C-3 switches in arid South African succulent shrubs. Agricultural and Forest Meteorology, 161: 72-79. Molz FJ, Klepper B. 1973. On the Mechanism of Water-Stress-Induced Stem Deformation1. Agronomy Journal, 65: 304-306. Page TJ, Marshall JC, Hughes JM. 2012. The world in a grain of sand: evolutionarily relevant, small-scale freshwater bioregions on subtropical dune islands. Freshwater Biology, 57: 612-627. Peramaki M, Nikinmaa E, Sevanto S, Ilvesniemi H, Siivola E, Hari P, Vesala T. 2001. Tree stem diameter variations and transpiration in Scots pine: an analysis using a dynamic sap flow model. Tree Physiology, 21: 889- 897. Sevanto S, Vesala T, Peramaki M, Nikinmaa E. 2002. Time lags for xylem and stem diameter variations in a Scots pine tree. Plant Cell and Environment, 25: 1071-1077. Steppe K, De Pauw DJW, Lemeur R, Vanrolleghem PA. 2006. A mathematical model linking tree sap flow dynamics to daily stem diameter fluctuations and radial stem growth. Tree Physiology, 26: 257-273. Vandegehuchte MW, Steppe K. 2012. Sapflow+: a four-needle heat-pulse sap flow sensor enabling nonempirical sap flux density and water content measurements. New Phytologist, 196: 306-317. Zweifel R, Item H, Hasler R. 2000. Stem radius changes and their relation to stored water in stems of young Norway spruce trees. Trees-Structure and Function, 15: 50-57. Figure 2 Osmotic potential of the storage tissue (a) and derived osmotic equivalents of the entire storage volume (b) for Avicennia and Rhizophora Ψ Π (M Pa ) A vi ce nn ia -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2 Ψ Π (M Pa) R hizophora -4.2 -4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 Day of the year 246.0 246.5 247.0 247.5 248.0 248.5 249.0 O sm ot ic e qu iv al en ts A vi ce nn ia (m ol ) 24 26 28 30 32 34 O sm otic equivalents R hizophora (m ol) 24 26 28 30 32 34 Avicennia Rhizopora (a) (b) Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 156 Crop load effects on stem diameter variations in peach evaluated with an integrated plant and fruit model Tom De Swaef1*, Carmen D. Mellisho2, Annelies Baert1, Veerle De Schepper1, Wenceslao Conejero2 and Kathy Steppe1 1Laboratory of Plant Ecology, Ghent University, Ghent, Belgium, 2 Dpto. Riego. Centro de Edafología y Biología Aplicada del Segura (CSIC). Murcia, Spain *correspondence: tom.deswaef@ugent.be Highlights: Integrating a mechanistic carbon and water flow model with a model of peach fruit water and carbon accumulation enabled to quantify plant carbon relations with varying crop load. Physiological processes at the plant level could as such be related to effects on fruit growth. Keywords: water relations, carbon relations, stem diameter, fruit growth INTRODUCTION Peach fruit production and quality (Prunus persica (L.) Batsch.) are substantially affected by physiological processes related to whole-plant water and carbon relations (e.g. Fishman and Génard, 1998; Conejero et al., 2010). To enhance the understanding of water and dry matter accumulation in peach fruit, it is therefore essential to assess the link with plant water and carbon status. In recent years, some effort has already been done to unravel and interpret variations in stem diameter (Dstem) with respect to the plant water and carbon status (e.g. Sevanto et al., 2003; Daudet et al., 2005; De Schepper and Steppe, 2011; De Swaef et al., 2012). Recorded variations in Dstem are an overall result of several distinct mechanisms which are (in)directly related to water and carbon status: irreversible radial growth, reversible shrinking and swelling (in relation to varying levels of hydration) of living cells and expansion or contraction of dead conducting xylem elements due to the increase or relaxation of internal tensions (Daudet et al., 2005). The present study aims at unravelling the quantitative effects of crop load on Dstem, the plant carbon status and fruit growth. Therefore, the dynamic water and carbon flow and storage model of De Schepper and Steppe (2010) was coupled to the fruit water and carbon accumulation model of Fishman and Génard (1998) and was used to describe Dstem for three different crop loads. MATERIALS AND METHODS The experiment was performed in 2008, in a seven-year-old early maturing peach orchard (Prunus persica (L.) Batsch, cv. Flordastar grafted on GF-677 peach rootstock) at the CEBAS-CSIC experimental station in Santomera (Murcia, Spain) (38°06’N, 1°02’W, elevation 110 m). Trees were irrigated daily above the estimated crop evapotranspiration (156% ETc) to assure non-limiting soil water availability. On 10 March (DOY 70) the peach trees were thinned to obtain three different crop load treatments. In a control treatment (Commercial crop load) fruits were hand-thinned to leave 25 cm between the fruits to obtain a commercial crop load. In a second treatment, fruits were not thinned, leaving all fruits on the tree (High crop load). In a third treatment, all fruits were removed by hand (Zero crop load). Three trees were monitored per treatment. On 30 April (DOY 121) fruits of the Commercial and High crop load treatments were harvested. Solar radiation, air temperature, relative humidity and wind speed at 2 m above the soil surface were measured by an automatic weather station located near the experimental site and stored every 30 min. In addition, stem diameter (Dstem) variations were measured throughout the experimental period on three trees per treatment. Therefore, a set of linear variable displacement transducers (LVDT) (Model DF 2.5, accuracy 10 µm, Solartron Metrology, Bognor Regis, UK) was used. MODEL DESCRIPTION We extended the tree model of De Schepper and Steppe (2010) with a fruit model (Fishman and Génard, 1998) as demonstrated in Fig. 1. Climatic data were used as input variables to estimate transpiration rate 157 based on Penman-Monteith (Allen et al., 1998). In the model, vertical water transport within the conductive xylem (X) or phloem (Pc) is driven by pressure potential gradients, because such transport does not require membranes to be crossed. In the case of radial flow or flow to the fruits, membranes need to be crossed and, consequently, flows were described based on total water potential gradients. Within the phloem, dissolved sugars were assumed to be transported by the flowing water according to the principle of mass flow. Unloading at the root level (U) was defined to be dependent on the sucrose concentration. Loading in the crown (L) was simplified to a single parameter which was calibrated using Dstem data. Transport of carbon and water from the xylem and phloem compartment in the crown towards the fruits was calculated using the model of Fishman and Génard (1998). The number of fruits varied between the different treatments and this was included in the model by multiplying the fruit carbon and water accumulation by the number of fruits. Fig. 1. Diagram with model compartments (H, heartwood; X, conductive xylem; Pc, conductive phloem; S, storage cells; Cz, cambial zone; Fruit) and water (full line) and sugar (dashed line) transport. This transport can occur in both directions: the flow is positive when it is in the direction of the arrow and negative when it is in the opposite direction. L represents loading of sugar in the phloem, U represents unloading of sugar in the storage cells. Thick lines represent flows calculated with the Fishman and Génard model (1998). The concurrent water and carbon transport causes changes in water content in the different tissues. In the stem and fruit compartment these were converted to volume and corresponding stem and fruit diameter changes (Steppe et al., 2006). Finally, respiration and starch conversion are taken into account in order to close the carbon balance. More details on the model description and equations can be found in De Schepper and Steppe (2010). The model, consisting of a set of algebraic and differential equations, was implemented and solved numerically using the modelling and simulation software package PhytoSim (Phyto-IT BVBA, Mariakerke, Belgium). This environment allows model implementation, simulation, calibration, sensitivity analysis, identifiability analysis and data acquisition. RESULTS AND DISCUSSION The three treatments (zero, commercial and maximum crop load), varied in the number of fruits at the start of the simulation (DOY 70): on average 0, 547, 3114 fruits per tree, respectively. From harvest on (DOY 121), the number of fruits was zero for all treatments. Apart from the number of fruits, model parameters for all treatments were equal. A set of parameters was optimised using measured data on three treatments, with three trees per treatment. Model simulations and measurements of stem diameter are presented in Fig. 2. Simulations of diurnal variations and overall growth rate of Dstem corresponded very well with measurements on all three treatments. 158 Fig. 2. Measured and simulated stem diameter for the three treatments: zero cop load (top), commercial crop load (middle) and maximum crop load (low). Measured and simulated data are the mean of three trees per treatment. The vertical dashed line indicates harvest of the fruits. Before harvest, Dstem growth rate of the zero crop load treatment exceeded the growth rate in other treatments because of a relatively higher availability of sugars in the phloem tissue, which were laterally used for growth in the cambial zone of the stem (Fig. 2). Dstem growth rate increased after harvest for the commercial and maximum crop load treatments, as a result of an increased amount of sugars available in the phloem tissue after fruit removal. During the fruit growth period, the enhanced fruit number in the maximum crop load treatment increased the competition for sugars between different individual fruits. Consequently, the amount of sugars in the phloem decreased, causing a reduced growth of individual fruits. As such, the average fruit weight in the commercial crop load was 123.5 g, whereas for the maximum crop load the average was 30.23 g (Conejero et al., 2010). LITERATURE CITED Allen RG, Pereira LS, Raes D, Smith M. 1998. Crop evapotranspiration: guidelines for computing crop water requirements. Irrigation and Drainage 56, FAO, Roma. Conejero W, Ortuño MF, Mellisho CD, Torrecillas A. 2010. Influence of crop load on maximum daily trunk shrinkage reference equations for irrigation scheduling of early maturing peach trees. Agricultural Water Management 97: 333-338. Daudet FA, Améglio T, Cochard H, Archilla O, Lacointe A. 2005. Experimental analysis of the role of water and carbon in tree stem diameter variations. Journal of Experimental Botany 56: 135–144. De Schepper V, Steppe K. 2010. Development and verification of a water and sugar transport model using measured stem diameter variations. Journal of Experimental Botany 61: 2083-2099. De Schepper V, Steppe K. 2011. Tree girdling responses simulated by a water and carbon transport model. Annals of Botany 108: 1147-1154. De Schepper V, van Dusschoten D, Copini P, Jahnke S, Steppe K. 2012. MRI links stem water content to stem diameter variations in transpiring trees. Journal of Experimental Botany 63: 2645–2653. De Swaef T, Driever SM, Van Meulebroek L, Vahaecke L, Marcelis LFM, Steppe K. 2012. Understanding the effect of carbon status on stem diameter variations. Annals of Botany doi: 10.1093/aob/mcs233 Fishman S, Génard M. 1998. ) A biophysical model of fruit growth: simulation of seasonal and diurnal dynamics of mass. Plant, Cell and Environment 21: 739–752. Sevanto S, Vesala T, Peramaki M, Nikinmaa E. 2003. Sugar transport together with environmental conditions controls time lags between xylem and stem diameter changes. Plant, Cell and Environment 26: 1257–1265. Steppe K, De Pauw DJW, Lemeur R, Vanrolleghem PA. 2006. A mathematical model linking tree sap flow dynamics to daily stem diameter fluctuations and radial stem growth. Tree Physiology 26: 257–273. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 159 Physiological growth model CASSIA predicts carbon allocation and wood formation of Scots pine Pauliina Schiestl-Aalto1, Liisa Kulmala2*, Harri Mäkinen2, Tuomo Kalliokoski1,2 and Annikki Mäkelä1 1Department of Forest Sciences, PO Box 27, 00014 University of Helsinki, Finland, 2Vantaa Res. Ctr, Finnish Forest Research Institute, PO Box 18, 01301 Vantaa, Finland *correspondence: liisa.kulmala@metla.fi Highlights: The dynamic, intra-annual model CASSIA combines detailed models of wood formation and properties with a process-based growth simulation system. It predicts the daily growth of wood, needles, shoots and roots of Scots pine based on weather variation and photosynthetic production. Keywords: dynamic modeling, Pinus sylvestris L, sink, source, xylogenesis INTRODUCTION The growth of trees varies according to genetic origin, tree age and environmental drivers like tree position in the stand, the weather conditions of the current and previous years, and soil characteristics (Oleksyn et al. 2001, Salminen and Jalkanen 2005, Chuine et al. 2006, Pinto et al. 2011). Mechanistic understanding of the external and internal control of growth is needed to understand the effects of changing environment on tree growth and wood formation. Drew et al. (2010), for example, has developed a process- based approach to model wood property variation but dynamic model CASSIA (Carbon Allocation Sink- Source Interaction Analysis) is one of the first attempts to combine detailed models of intra-annual wood formation (xylogenesis) with a process-based growth simulation system in a whole-tree carbon balance framework. It predicts the daily growth of wood, needles, shoots and roots of Scots pine (Pinus sylvestris L.) based on weather variation and photosynthetic production. It also includes a description of wood formation at time scales ranging from days to several years, in a whole-tree carbon balance framework. Especially, the model is able to describe how the sink and source relationships interact through various time scales in tree growth. THE MODEL In the model, the state variables are the storages of short chain sugars (sucrose), long chain sugars (starch), and the biomasses of needles, primary wood, secondary wood and fine root (Fig. 1). The model further divides the cambial growth to enlarging, wall forming and mature tracheids. The model projects the states of growth at any point in time with a time step of one day. Fig. 1. A schematic presentation of the model. The photosynthesis is the source of carbon whereas the growth of needles, wood and roots and respiration act as carbon sinks. The arrows represent flows of carbon and the shapes stand for the environmental effects of factors. Sucrose Starch Photosynthesis Secondary wood Needles Roots Enlargement Cell wall Growth = Soil moisture = Air temperature = Soil temperature Division Storage Carbon flow Influence Growth respiration Maintenance respiration Primary wood 160 The daily change in the pool of sugars without the exchange between sucrose and starch storages (dS/dt, g C day–1) depends on photosynthesis, P(t), and maintenance respiration, 𝑅𝑀(𝑡), growth, 𝐺𝑡𝑜𝑡(𝑡), and growth respiration, 𝑅𝐺(𝑡): 𝑑𝑆 𝑑𝑡 = 𝑃(𝑡)− 𝑅𝑀(𝑡)− 𝐺𝑡𝑜𝑡(𝑡) − 𝑅𝐺(𝑡), (1) The photosynthesis, P(t), is calculated according to Mäkelä et al. (2008). The maintenance respiration, 𝑅𝑀(𝑡), depends on the biomass and ambient temperature that is the air temperature for the aboveground parts and soil temperature for the roots. The empirical temperature dependence of each part is obtained from continuous measurements at the SMEARII station. The growth respiration, 𝑅𝐺(𝑡), is linearly dependent on growth according to Running and Coughlan (1988). The potential growth i.e. growth sink is based on external environment. The most important environmental factor for the above ground growth is the air temperature whereas soil temperature and moisture determine the potential growth of roots. The potential growth follows the annual cycle of tree activity in terms of thermal time, which is assumed to progress with daily mean temperature (Hänninen and Kramer 2007). In the model, the thermal time is an accumulation of a sigmoid function of temperature (Hänninen 1990). The active growth period begins and ends when the accumulation of thermal time reaches threshold values. The level of growth proceeds with the accumulated thermal time as a sine function for shoots, needles and roots whereas the cambial growth follows a square root function of the accumulated thermal time. The potential growth occurs when carbon is not a limiting factor, i.e., sink strength regulates the growth. If photosynthetic input exceeds the sinks, the sugars are converted and stored as starch. The carbon storages are used to supplement the growth, if the carbon bound in photosynthesis is insufficient to cover the need of the sinks entirely. If the carbon storage is low, the growth becomes source-limited and it is lower than the potential growth. MEASUREMENTS We measured the tree growth in middle-aged Scots pine stands in Norhern Finland at SMEARI (67°46′N, 29°35′E) and in Southern Finland at SMEARII (61°52′N, 24°17′E) and in Ruotsinkylä (60°21′N, 25°00′E). We took microcore samples at SMEARI and SMEARII during 2007–2009 and in Ruotsinkyla during 2002– 2010 for the timing of tracheid formation and differentiation. The length growth of needles and branches in different parts of the canopy were measured 2–3 times in a week during the growing seasons. Because measurements were not made every day, an average daily growth of the measuring days was calculated. The shoot growth was measured in SMEARI during 2007–2009 and in SMEARII in 2003–2009. Needle growth was measured at SMEARII in 2003–2009. We estimated the model parameters using the measurements in SMEARII in 2008 and used them for the model runs of the other sites and years. PRELIMINARY RESULTS The model runs for SMEARII during 2002–2009 reveal that the growth was mainly sink-driven, except for the late growing season in 2006 and the early season in 2007. The growth was suppressed by a prolonged drought in August 2006 that decreased the photosynthetic input. The model succeeded to predict the growth of shoots (Fig. 2A) in years 2006, 2008 and 2009, whereas in years 2005 and 2007, the onset and cessation were consistent with the measurements but the final shoot length was overestimated. In general, the model succeeded to predict the timing of growth (Fig. 2B) and average final length of needles, apart from years 2005–2007 when the model accurately estimated onset and growth cessation but overestimated the final needle length. Moreover, the model succeeded to predict the dynamics of cambial growth (Fig. 2C), except for the year 2009, when the estimated number of cells was lower and the onset of cambial growth later than the observed ones. With the parameters estimated for SMEARII stand in year 2008, the model succeeded to predict the timing of cambial growth in Värriö and in Ruotsinkylä in years 2007–2008 but in year 2009, the model resulted in an underestimation similar to Hyytiälä in 2009. The model accomplished to predict the final ring 161 width in Värriö, but in Ruotsinkylä that is a more fertile site, the model underestimated the final ring width indicating a need to tune the fertility-specific parameters. In future, we will develop the model by refining the description of uptake, allocation, and transport processes of sugars and water within trees to improve understanding of stress responses, especially the effects of prolonged drought on tree growth. Fig. 2: The modeled (lines) and measured (circles) daily average relative growth of shoots (A1-A2), needles (B1-B2) and the stem radius (C1-C2) at SMEARII in 2007 (left panels) and in 2008 (right panels). LITERATURE CITED Chuine I, Rehfeldt GE, Aitken SN. 2006. Height growth determinants and adaptation to temperature in pines: a case study of Pinus contorta and Pinus monticola. Canadian Journal of Forest Research 36: 1059-1066. doi:10.1139/X06-005 Drew DM, Downes GM, Battaglia M. 2010. CAMBIUM, a process-based model of daily xylem development in Eucalyptus. Journal of Theoretical Biology 264: 395–406 Hänninen H. 1990. Modeling dormancy release in trees from cool and temperate regions. In: Dixon, R.K.,Meldahl, R.S., Ruark, G.A. & Warren, W.G. (eds.). Process modeling of forest growth responses to environmental stress. Timber Press, Portland p. 159-165. Hänninen H, Kramer K. 2007. A framework for modelling the annual cycle of trees in boreal and temperate regions. Silva fennica 41(1): 167-205. Mäkelä A, Pulkkinen M, Kolari P, Lagergren F, Berbigier P, Lindroth A, Loustau D, Nikinmaa E, Vesala T, Hari P. 2008. Developing an empirical model of stand GPP with the LUE approach: analysis of eddy covariance data at five contrasting conifer sites in Europe. Global Change Biology 14: 92-108. DOI: 10.1111/j.1365- 2486.2007.01463.x Pinto CA, Henriques MO, Figueiredo JP, David JS, Abreu FG, Pereira JS, Correia I. 2011. Phenology and growth dynamics in Mediterranean evergreen oaks: Effects of environmental conditions and water relations. Forest Ecology and Management 262: 500–508. doi:10.1016/j.foreco.2011.04.018 Oleksyn J, Reich PB, Tjoelker MG, Chalupka W. 2001. Biogeographic differences in shoot elongation pattern among European Scots pine populations. Forest Ecology and Management 148:207-220. DOI: http://dx.doi.org/10.1016/S0378-1127(00)00537-5 Running SW, Coughlan JC. 1988. A general model of forest ecosystem processes for regional applications I. Hydrologic balance, canopy gas exchange and primary production processes. Ecological Modelling 42: 125-154. Salminen H, Jalkanen R. 2005. Modelling the effect of temperature on height increment of scots pine at high latitudes. Silva Fennica 39(4): 497-508. Proceedings of the 7th International Conference on Functional-Structural Plant Models, Saariselkä, Finland, 9 - 14 June 2013. Eds. Risto Sievänen, Eero Nikinmaa, Christophe Godin, Anna Lintunen & Pekka Nygren. http://www.metal.fi/fspm2013/proceedings. ISBN 978-951-651-408-9. 162 Understanding and evaluating some allometric relationships useful for functional-structural plant modeling M. Paulina Fernández1 1Faculty of Agronomy and Forest Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile *Correspondence: pfernan@uc.cl Highlights: The dynamic process of development and growth of Pinus radiata trees was studied during an entire growing season and the allometric relationship between foliage biomass and the supporting conductive area of tissues analyzed. Changes in the stem through time of this relationship suggest that the use of a constant and fixed value for modeling purposes leads to wrong results. This subject is discussed and illustrated by means of simulations. Keywords: Plant allometry; pipe model; foliage development; wood formation. INTRODUCTION When new structures are formed two important principles seem to operate: economy and optimization. Economy in the sense of minimal use of energy or material to obtain the goal; optimization, in the sense of optimal configuration in order to achieve multiple goals or attain a balance between physiological and structural demands. As a result we observe an harmonic structure so designed as to maintain those principles throughout the lifespan of the individual. We perceive an optimal equilibrium, even if we do not fully understand the commanding forces behind it, as allometric relationships between organs, tissues, between structure and function, as studied by Niklas (1994) among others. If these rules apply to stem building during tree growth it should conduct water and metabolic products as a pipe system but at the same time it will have to withstand the increasing weight and mechanical forces acting on the crown and bole. These goals are to be achieved at a minimal cost and as an optimized solution. Already Shinozaki (1964) and later many other authors like Mäkelä (2002) have analyzed the allometry involved in this pipe system, and Matheck and Kluber (1997), Niklas (1992) among others, the bio- mechanical balance of these at times huge structures. In functional-structural modeling one of the key factors that concerns us is the way in which growth is allocated. After photosythesis and respiration have been taken care of, surplus material may be sent to new organs or to enlarge existing ones. Particularly, when modeling the stem growth of the trees, key questions are the amount of material that is used to build the new mantle of wood and the kind of structure derived therefrom. Leaves require a continuous supply of water from roots to replace that lost in transpiration. So, a relationship should exist between the amount of foliage (leaf biomass) and the cross section of the trunk or branches that support it in order to satisfy the required flow of water. To solve this matter a common solution in various models is to use an allometric relation between the mass of transpiring foliage and the pipe system that has to be constructed to supply it. Such a relationship has actually been documented for different species (Mäkelä, 2002) and has been used in structural-functioning models. Obviously, it is not only the area of cross sections that are involved in the flow, but also the inherent conducting capacity, which in turn depends on the density of the wood (Santiago (1) (2) as1=s1·s2 as2=s3·s4 as1=as2 Sap flux s1 s2 s3 s4 aflux1j aflux2j bf1 bf2 aw1j aw2j ρ1> ρ2 Aflux1=∑aflux1j Aflux2=∑aflux2j Aflux1Aw2 => bf1