Comparison of marginal and mixed-effects complementary log-log regression models for predicting planted silver birch mortality

Abstract

Mortality is a key process in forest succession, yet modelling individual tree mortality presents significant challenges. In this study, tree mortality models for silver birch (Betula pendula Roth.) were developed to address these complexities. The modelling data comprised thinning trials for planted silver birch established between 1981 and 1991 in southern and central Finland. Thirteen experiments were established on former agricultural land and eight experiments were on forest land. The test data comprised planted silver birch stands of a spacing trial established on agricultural land in the early 1970s. The modelling options included four different types of models based on different random effect structures: a marginal model without random effects, a random site as RND_SITE, a random plot nested within the site designated as RND_PLOT(SITE), and a random year nested within the site designated as RND_YEAR(SITE) in a linear mixed-effects complementary log-log (CLL) regression. The CLL models were evaluated according to fit statistics, with the RND_YEAR(SITE) model demonstrating the best results. Furthermore, all mortality models were implemented into the MOTTI simulator to evaluate the development of planted silver birch stands in terms of stem number (N, trees ha−1) and stand basal area (G, m2 ha−1). In the MOTTI evaluation, unthinned stands were selected, and the data were divided into density groups: initially dense (N > 2000 trees ha−1), normal density stands (1000 trees ha−1 ≤ N ≤ 2000 trees ha−1), and sparse stands (N < 1000 trees ha−1). The independent dataset demonstrated optimal performance with the RND_YEAR(SITE) model. The current MOTTI model performed generally well but underestimated N and G for the normal density stands compared to the new model options. Finally, when examining the compatibility of the RND_YEAR(SITE) model with the existing and recently introduced stand self-thinning models, the recent model demonstrated high compatibility, while the existing model showed a clear underestimation.