Marine Ecology Progress Series Volume 764:213–236 Published July 15, 2025 https://doi.org/10.3354/meps14886 1. INTRODUCTION The rapid pace of environmental change presents unprecedented challenges for monitoring and man- aging wildlife populations (Berkes et al. 2008, Waltner- Toews et al. 2008, Chapin et al. 2009). Conventional approaches often rely on long-term historical trends, and are increasingly insufficient as populations are exposed to novel conditions that result in unfamiliar dynamics (Chapin et al. 2009, Marolla et al. 2021). Management actions in response to changing con- ditions are frequently delayed until a more complete © The authors 2025 Publisher: Inter-Research · www.int-res.com *Corresponding author: jarno.vanhatalo@helsinki.fi Integrated population model reveals human- and environment-driven changes in Baltic ringed seal Pusa hispida botnica demography and behavior Murat Ersalman1, Mervi Kunnasranta2,3, Markus Ahola4,5, Anja M. Carlsson5, Sara Persson5, Britt-Marie Bäcklin5, Inari Helle3, Linnea Cervin5, Jarno Vanhatalo1,6,* 1Department of Mathematics and Statistics, Faculty of Science, University of Helsinki, 00014 Helsinki, Finland 2Department of Environmental and Biological Sciences, University of Eastern Finland, 80100 Joensuu, Finland 3Natural Resources Institute Finland, 00790 Helsinki, Finland 4Marine Environment Research Group, Sustainable Environment Unit, Turku University of Applied Sciences, 20520 Turku, Finland 5Department of Environmental Monitoring, Swedish Museum of Natural History, 104 05 Stockholm, Sweden 6Organismal and Evolutionary Biology Research Programme, Faculty of Biological and Environmental Sciences, University of Helsinki, 00014 Helsinki, Finland ABSTRACT: Integrated population models (IPMs) are a promising approach to test ecological theories and assess wildlife populations in dynamic and uncertain conditions. By combining multi- ple data sources into a unified model, they enable the parametrization of versatile, mechanistic models that can predict population dynamics in novel circumstances. Here, we present a Bayesian IPM for the ringed seal Pusa hispida botnica population inhabiting the Bothnian Bay in the Baltic Sea. Despite the availability of long-term monitoring data, traditional assessment methods have fal- tered due to dynamic environmental conditions, varying reproductive rates, and recently re-intro- duced hunting, thus limiting the quality of information available to managers. We fit our model to census and various demographic, reproductive, and harvest data from 1988 to 2023 to provide a comprehensive assessment of past population trends, and predict population response to alter- native hunting scenarios. We estimated that 20 000–36 000 ringed seals inhabited the Bothnian Bay in 2024, increasing at a rate of 3–6% yr–1. Reproductive rates have increased since 1988, leading to a substantial increase in the growth rate up until 2015. However, the re-introduction of hunting has since reduced the growth rate, and even minor quota increases are likely to reduce it further. Our results also support the hypothesis that a greater proportion of the population hauls out under lower ice cover circumstances, leading to higher aerial survey results in such years. In general, our study demonstrates the value of IPMs for monitoring wildlife populations under changing environ- ments and for supporting science-based management decisions. KEY WORDS: Integrated population model · IPM · State-space model · Bayesian · Pinniped · Environmental change · Haulout · Long-term monitoring · Wildlife management https://crossmark.crossref.org/dialog/?doi=10.3354/meps14886&domain=pdf&date_stamp=2025-07-15 Mar Ecol Prog Ser 764: 213–236, 2025 understanding is achieved through research, yet the urgency of these problems seldom allows for lengthy deliberation (Chapin et al. 2009, Dietze et al. 2018). There is thus a growing need for versatile, mech- anistic population models capable of testing alter- native hypotheses on the development of natural populations and accommodating uncertainties in pop - ulation assessments. The integration of such models with long-term monitoring data can lead to efficient generation of explanatory and anticipatory predic- tions (Mouquet et al. 2015, Maris et al. 2018, Marolla et al. 2021). The repeated application of short-term predictions, combined with informed management decisions and continuous monitoring, can facilitate testing and refining model assumptions and acceler- ate the pace of research — a process that is at the heart of adaptive management (Holling 1978, Lahoz- Monfort et al. 2014, Dietze et al. 2018). The demand for mechanistic, data-driven popula- tion models was among the key motivations behind the development of integrated population models (IPMs), which combine multiple data sources in a sin- gle, unified model to simultaneously infer key demo- graphic parameters and population processes (Bes- beas et al. 2002, Buckland et al. 2004, Schaub & Abadi 2011, Zipkin & Saunders 2018). This is in contrast to traditional approaches where independent empirical estimates for model parameters are typically incorpo- rated into a population projection matrix such as a Leslie matrix (Caswell 2001). The main advantages of IPMs include their flexibility, their ability to separate process variability from observation error, and their ability to more precisely estimate a larger number of parameters by leveraging synergies between multiple data sources (Abadi et al. 2010, Schaub & Abadi 2011, Zipkin & Saunders 2018). Additional information can also be incorporated under the Bayesian framework in the form of prior distributions, which can be deter- mined based on previous empirical work on similar species or expert opinions (Buckland et al. 2004). Suf- ficiently developed IPMs could potentially function as ‘digital twins’ of their target populations, where the data are continuously updated and the model recal- ibrated in a way that enables managers to swiftly respond to changing conditions (de Koning et al. 2023, Trantas et al. 2023, Lecarpentier et al. 2024). Despite the great promise of IPMs as digital twins of wild animal populations, their potential has yet to be fully realized. To demonstrate the value of IPMs in monitoring and managing animal populations in dynamic and uncertain conditions, we developed a Bayesian IPM for the Baltic ringed seal Pusa hispida botnica popula- tion inhabiting the Bothnian Bay, the northernmost region of the Baltic Sea and home to over 75% of all Baltic ringed seals (Härkönen et al. 1998, Sundqvist et al. 2012, Halkka & Tolvanen 2017). We adopted a state-space formulation for our model (Buckland et al. 2004) and parametrized it using count data obtained from aerial transect surveys, demographic data from hunted and bycaught seals, hunting records from Fin- land and Sweden, and assessments of reproductive status in sampled females. The ringed seal population in the Bothnian Bay is a notable example of an ice- dependent pinniped population for which long-term monitoring data are available. However, despite the abundance of data, uncertainties stemming from a multitude of changing conditions have precluded assessments of population size and growth for over a decade (HELCOM 2023a). The population size of Baltic ringed seals had plum- meted from an estimated 100 000–450 000 in the year 1900 to about 5000 by the late 1970s, driven largely by unsustainable bounty hunting practices and extremely low reproductive rates caused by organochlorine con- tamination (Helle et al. 1976, Durant & Harwood 1986, Härkönen et al. 1998, 2008, Harding & Här- könen 1999, Kokko et al. 1999). Both seal hunting and the use of PCB and DDT were subsequently prohib- ited, and the Bothnian Bay population has shown signs of recovery since the late 1980s. Aerial transect surveys conducted in 1988–2012 suggested an an - nual growth rate of approximately 5% (Sundqvist et al. 2012). However, more recent census estimates have shown unusually high variability and systematic deviations from historical trends, casting uncertainty over the current status of the population (HELCOM 2023a). In the Bothnian Bay, aerial transect surveys are con- ducted annually around the third week of April, and ringed seals are counted when they are visible while molting on the sea ice (i.e. ‘hauled out’) after having abandoned their subnivean lairs (Härkönen & Lunne- ryd 1992). Aerial survey results have traditionally been used as an index of population size and trend, based on the assumption that approximately the same proportion of the population hauls out on ice during the surveys each year (Härkönen & Lunneryd 1992). It has been speculated, however, that a substantially larger fraction of seals may haul out when aerial sur- veys coincide with low ice cover or early ice breakup, resulting in extremely large population counts that are not comparable to typical results (HELCOM 2023a). Moreover, previous analyses of survey esti- mates have often assumed constant population growth, implying constant demographic rates (Sundqvist et 214 Ersalman et al.: Integrated population model for ringed seal al. 2012). However, reproductive rates of Baltic ringed seals have likely been improving since the use of PCB and DDT was banned (Helle 1980b, Kauhala et al. 2019, HELCOM 2023b). Unsurprisingly, the popula- tion growth rate may have been increasing as well (HELCOM 2023a). Thus, we hypothesized that the atypical aerial survey estimates observed over the past decade stem from a combination of improve- ments in reproductive rates and a higher visibility of seals on ice following mild winters. The challenges of managing the ringed seal pop- ulation in the Bothnian Bay are amplified by the recent re-introduction of seal hunting in Finland and Sweden in an attempt to mitigate the rising tension between fisheries and the growing seal population. The effectiveness of hunting as a strategy for alleviat- ing seal–fishery conflicts hinges on achieving a com- promise between conservation goals and the interests of coastal fisheries (Oksanen et al. 2014, Cummings et al. 2019). This requires reliable assessments of pop- ulation size, growth rate, and demography, an under- standing of seal–human interactions, and the ability to predict population responses to alternative man- agement decisions. However, due to the ongoing dif- ficulties with monitoring ringed seals in the Bothnian Bay, the impact of hunting on ringed seal demogra- phy is unknown. The growing conflict between seals and fisheries, and the dynamic and uncertain conditions brought on by climate change, improving reproductive rates, and the re-introduction of hunting highlight the need for mechanistic models of ringed seal population dynamics, and an increasingly holistic analysis of the available data. Using a Bayesian IPM, we provide a solution to the challenges that have crippled ringed seal monitoring efforts in the Bothnian Bay through- out the last decade. In addition to the population size and growth rate, we estimate a large number of eco- logically important parameters and make short-term predictions regarding population response to changes in hunting quotas. 2. MATERIALS AND METHODS 2.1. Study population The Baltic ringed seal is a subspecies of ringed seal endemic to the Baltic Sea (Rice 1998; but see Palo et al. 2001). Recognized sub-populations inhabit the Bothnian Bay, the Archipelago Sea, the Gulf of Riga, and the Gulf of Finland (Härkönen et al. 1998, Halkka & Tolvanen 2017). Our study focused on the Bothnian Bay population, which comprises over 75% of all Bal- tic ringed seals (Sundqvist et al. 2012). The Bothnian Bay is the northernmost region of the Baltic Sea, with a surface area of approximately 37 000 km2 (Fig. 1). Since the southern sub-populations in the Archipel- ago Sea, the Gulf of Finland, and the Gulf of Riga are small (Sundqvist et al. 2012), and ringed seals show high breeding site fidelity (Härkönen et al. 2008, Kelly et al. 2010), we treated the dynamics of the Bothnian Bay population independently of the other sub-populations. Ringed seals are among the smallest and most strongly ice-associated pinnipeds in the world (Smith et al. 1991). Their annual life cycle has been classified into 3 main ‘ecological seasons’ (Fig. 2): the foraging period, the subnivean period, and the molting period (Born et al. 2004, Kelly et al. 2010, Oksanen et al. 2015b). During the foraging period between June and Janu- ary, Baltic ringed seals spend over 90% of their time in the water, hauling out on land primarily at night for resting (Oksanen et al. 2015b). This phase is marked by intense feeding activities, as ringed seals seek to accumulate blubber reserves in preparation for the approaching winter (Oksanen et al. 2015b, Kauhala et al. 2019). Interactions with coastal fisheries are there- fore most common between late spring and late fall. During this period, bycatch mortality is most typical for young ringed seals (Oksanen et al. 2015a, Jounela et al. 2019). During the winter, ringed seals spend most of their time out of the water in subnivean lairs built on sea ice  (Kelly et al. 2010). Around February–March, a single pup is born inside the snow lair and is nursed for 5–8 wk (Helle 1979, Lydersen & Hammill 1993). The snow lair provides shelter to pups against harsh weather conditions and predators. Therefore, pups born without the protection offered by a stable lair are unlikely to survive (Smith & Stirling 1975, Ferguson et al. 2005, Sundqvist et al. 2012). Because whelping and nursing require sufficient ice and snow conditions, adult seals are often associated with stable pack ice during the breeding season, whereas juveniles are more commonly observed in productive foraging areas near the ice edge or in the open water (Crawford et al. 2012, Oksanen et al. 2015b). Mating is thought to take place within 1 mo of parturition (McLaren 1958, Stirling 1983), although the implantation of the embryo is delayed until around July (McLaren 1958). If females do not have enough blubber reserves, implantation may not occur (Boyd et al. 1999). The molting period begins as the snow cover starts to melt and subnivean lairs collapse, typically in April. 215 Mar Ecol Prog Ser 764: 213–236, 2025 Molting ringed seals spend a significant portion (50– 80%; Härkönen & Lunneryd 1992, Born et al. 2002, Kelly et al. 2010) of their time basking on the sea ice in order to increase blood flow to the skin and maintain elevated skin temperatures (Feltz & Fay 1966, Tho- metz et al. 2021). Sub-adults and adults often con- tinue molting until the ice melts, typically around late May in the Bothnian Bay (Helle 1980a, Härkönen et al. 2008), whereas pups typically complete their natal hair molt in lairs (Smith 1973, Lydersen & Hammill 1993). The molting period also marks the beginning of the ringed seal hunting seasons in Sweden and Finland, which were re-introduced in 2015 and in 2016, respec- tively. Some small-scale hunting took place earlier, mainly for research purposes (Nyman et al. 2003, Routti et al. 2009). Annual hunting quotas were ini- tially set to about 100 seals in each country and were gradually raised to 420 seals in Sweden and 375 seals in Finland as of 2022 (Section 2.2.2). Sweden then re - duced quotas to 350 seals in 2023, whereas the Finn- ish quota was kept the same. Hunting of ringed seals in Sweden is legal between 1 May and 15 January, although the actual distribu- tion of hunting activities is bimodal, with distinct spring and autumn seasons (Fig. 2). Sweden practices ‘protective’ hunting, which largely restricts hunting to within 200 m of fishing sites where seals have pre- viously caused damage to gear or taken catch. Pro- tective hunting is also allowed within the vicinity of fish farms, fish conservation areas, and fish release sites. Hunting in Sweden is therefore likely to be opportunistic. Hunting of ringed seals in Finland is legal between 16 April and 31 December. Finland allows recreational hunting of ringed seals, and hunters are therefore more likely to actively seek out seals. Hunting in Finland al- most exclusively takes place on sea ice, and the hunt- ing season effectively ends once sea ice melts (Fig. 2). The total harvest in Finland is influenced by the sever- 216 Fig. 1. (a) Study area (red square) and the extent of ice cover in (b) 2004, (c) 2015, and (d) 2018 around the third week of April. These 3 years respectively illustrate the median, minimum, and maximum ice extents observed during the study period Ersalman et al.: Integrated population model for ringed seal ity of winter. For example, following mild winters, seals tend to congregate in smaller areas of stable ice closer to land, making them more accessible to hunters (Här- könen & Lunneryd 1992, Harding & Härkönen 1999, Ministry of Agriculture and Forestry 2007). 2.2. Data 2.2.1. Aerial surveys The basking population size of ringed seals during the peak molting season was estimated by the Swe- dish Museum of Natural History (SMNH) using aerial strip surveys conducted in the Bothnian Bay in mid- to late April each year between 1988 and 2023. The 800 m wide strips were placed evenly over the study area, and the number of observed seals was recorded from an aircraft flying at 90 m altitude (Härkönen & Lunneryd 1992, Härkönen et al. 1998). The proportion of the total ice area covered by the surveys ranged from 13 to 53%, except for 2016, when only 7% of the total ice area was surveyed. The average density of seals over the surveyed transects was extrapolated over the whole ice-covered area to estimate the total size of the basking population, which is thought to account for 50–80% of the overall population (Här- könen & Lunneryd 1992, Born et al. 2002, Kelly et al. 2010). The precision of the estimates improves with increasing coverage, although the gain in precision begins to diminish beyond a coverage of about 13% (Härkönen & Lunneryd 1992). 2.2.2. Harvest totals and quotas Finnish hunting quotas and harvest totals from 2016–2022 were provided by the Finnish Wildlife Agency. Hunting records, quotas, and sampling pro- tocols from Sweden between 2015 and 2022 were pro- vided by the SMNH. 2.2.3. Demographic and reproductive data Demographic age and sex data on the ringed seal population and data on the reproductive status of female seals were obtained from the Natural Re - 217 Fig. 2. Baltic ringed seal annual life cycle. The density plots at the center show, in polar coordinates, the temporal distribu- tion of hunting and bycatch based on sampled seals (SW: Sweden; FI: Finland). The illustration was created with the aid of DALL-E 3 (https://openai.com/index/dall-e-3/) Mar Ecol Prog Ser 764: 213–236, 2025 sources Institute Finland (Luonnonvarakeskus, or Luke) and SMNH. These data were compiled from samples taken from hunted (2016–2021 for Finland and 2015–2021 for Sweden) and bycaught (years 1988–2021) seals sent to Luke or SMNH by hunters and fishermen. Age determination was done by count- ing the growth layer groups in the cementum of either canines or molars from the lower jaw (Stewart et al. 1996). We assumed that misidentifications of sex or age were negligible, and samples that were missing information on both age and sex were excluded from our analysis. The resulting number of samples per year ranged between 46 and 240 for Finland, and between 28 and 80 for Sweden. Among those, the number of samples missing either age or sex informa- tion ranged from 1 to 10 per year for Finland, and 1 to 9 per year for Sweden. Female ringed seals were examined for the pres- ence of a visible fetus and placental scar in the uterine horn, and a corpus albicans (CA) within the ovary. Because the implantation of embryos does not occur until July (McLaren 1958, Boyd 1991), we relied on evaluations of a visible fetus in samples obtained between August and January. Placental scars and CA  may both fade with time (Boyd 1984, HELCOM 2023b). In our samples, the proportion of seals with placental scars in recent years was nearly 20% lower in May than in April. In contrast, the proportion of seals with CA was similar between April and June. To minimize observation errors associated with fading in post-partum signs, we relied on placental scar data from April, and CA data from April through June. We used only samples of females that were 5+ yr old for the post-partum signs, and 4+ yr old for a vis- ible fetus (see Section 2.3.1). Samples that were not evaluated for any reproductive sign were excluded, resulting in yearly sample sizes ranging from 0 to 18 for visible embryos, 0 to 62 for placental scars, and 0  to 83 for CA (Fig. S2 in Supplement 1; all Supple- ments are available at www.int-res.com/articles/suppl/ m764p213_supp.pdf). From here on, we define the pregnancy rate as the proportion of 4+ yr old females carrying a fetus dur- ing the fall. To account for possible pregnancy losses, post-partum signs of pregnancy were modeled sep- arately. We define the birth rate as the proportion of  4+ yr old females that remained pregnant long enough to have a placental scar at the time of parturi- tion, as this is thought to be the closest measure available to assess the percentage of adult females that produced a live pup. Our definition of birth may include some late-term abortions and stillbirths, which are potentially common in pinnipeds (McKen- zie et al. 2005, Stenson et al. 2016) and treated as pup mortality in our analysis. 2.2.4. Sea ice extent data Weekly raster maps of ice concentration across the Baltic Sea between 1988 and 2023 were acquired from the Finnish Meteorological Institute. We used ice concentration data from north of 63° N latitude around the third week of April, when both aerial sur- veys and most of Finnish hunting take place (Här- könen & Lunneryd 1992). The ice cover was calcu- lated by multiplying the total sea area with the proportion of raster cells containing an ice concen- tration >0. 2.3. Population dynamics model 2.3.1. Structure of the population dynamics model We modeled the population dynamics of ringed seals using an age- and sex-structured model with demographic stochasticity in births and deaths. Be - cause female ringed seals typically begin reproduc- ing at the age of 5 yr (McLaren 1958, Lydersen & Gjertz 1987, Kauhala et al. 2019, Reimer et al. 2019), and reproductive senescence is rare (McLaren 1958, Ellis et al. 2018), we included 6 age classes in our model, grouping 5+ yr old individuals in a single age class. We refer to 0 yr old individuals as pups, 1–4 yr olds as sub-adults, and 5+ yr olds as adults. Note that while 4 yr old sub-adults can become pregnant in our model, they do not give birth until reaching adult- hood at age 5. As hunting quotas do not discriminate between males and females, and the sex ratio of the harvests does not necessarily reflect the sex ratio of the population, we included males in our population model but assumed that females were the limiting sex in reproduction. We assumed a post-breeding census, and formu- lated the dynamics of the population between each census in terms of 3 successive sub-processes: mortal- ity, aging, and birth (Fig. 3). Aging was assumed to occur immediately before parturition. We denote the state of the population at the census of year t by the vector nt. The elements of nt, denoted by ns,a,t, corre- spond to the number of seals of sex s ∈ {f,m} and age a ∈ {1,…, 5+} in the population immediately after par- turition. The states of the population after the mortal- ity and aging sub-processes are denoted respectively by the intermediate state vectors ut (1) and ut (2). Nota- 218 https://www.int-res.com/articles/suppl/m764p213_supp.pdf https://www.int-res.com/articles/suppl/m764p213_supp.pdf Ersalman et al.: Integrated population model for ringed seal tions for commonly referenced parameters are sum- marized in Table 1. 2.3.2. Survival and mortality In each year, the mortality sub-process was de - scribed as a multi-state transition model, where seals are assigned to 1 of 5 states: those that survived (S), were harvested in Finland (H fi), were harvested in Sweden either during the spring (Hsw(1)) or during the fall (Hsw(2)), or died due to other causes (D). Due to a lack of data on the magnitude of bycatch, it was included with other sources of mortality. Assuming mortality depends on sex and age and is mutually independent among seals, this process can be modeled stochastically using a multinomial distribution: (1) where ns,a,t is the total number of seals of sex s and age a at the census of year t; (2) is a vector of transition probabilities; and (3) is a vector of the number of seals that transition to each state. We modeled the mortality rates in the absence of hunting, μs,a, as constant throughout the years. We explicitly modeled only the mortality rates of female pups and adults. The mortality rates of sub-adult females were interpolated between the mortality rates of pups and adults, so that: | Multinomial ,u n n, , , , , ,s a t t s a t s a t 1 + t^^ hh , , , ,, , , , , , , , , , , ,s a t s a t S s a t D s a t H s a t H s a t Hsw( ) sw( ) fi1 2 t t t t tt = # - , , , ,u u u u u u, , , , , , , , , , , , , , , , ,s a t s a S t s a D t s a H t s a H t s a H t 1 1 1 1 1 1 sw( ) sw( ) fi1 2=^ ^ ^ ^ ^ ^h h h h h h% / 219 Fig. 3. Simplified model structure for female ringed seals. Colored circles represent unobserved state variables and blue squares represent observed data sources. Vertical ellipses indicate continuation across age classes. Arrows denote depen- dencies, with grey shading indicating groups of variables on which observations are conditioned. The dotted arrow indicates that reproductive signs are derived from harvested and bycaught seal samples. The dynamics of the population state between census points (yellow circles) are decomposed into three sub-processes: (1) individuals transition to mortality states (orange circles) based on whether they survive (S), are harvested (H), or die from other causes (D), with harvested individuals further grouped based on whether they were harvested in Finland, in Sweden during the spring, or during the fall (not shown); (2) sur- vivors age into the next class (green circles); and (3) adult females produce new pups, forming the population state at the next census. All variables are defined as in Table 1 and Section 2 Mar Ecol Prog Ser 764: 213–236, 2025 (4) where μf,a is the mortality rate of female seals of age a, and c is a param- eter that determines how quickly the mortality rate approaches that of adults as the seals age. Male survival rates were modeled in terms of deviations from female survival rates, so that a priori mortality rates were expected to be identical between the sexes, while allowing the data to in form us on potential differences (Supplement 2). The probability, fs,a, that a seal survives all sources of mortality other than hunting throughout the year is then given by the exponential function: (5) To be able to predict future population responses to al- ternative management decisions, we explicitly mod- eled the within-year dynamics of hunting as a function of hunting quotas. We assumed all Finnish hunting takes place in April and May when ringed seals are basking on sea ice, and that the harvest rate is pro- portional to the density of seals hauled out on ice. We estimated the density of seals along the Finnish coast, in each age and sex group, as ws,a,tns,a,t/Ct, where ws,a,t denotes the proportion of seals expected to be hauled out on sea ice in year t (see Section 2.3.3), and Ct is the ice extent across the Bothnian Bay during peak molting. We further assumed that the number of active hunters in Finland is proportional to the number of unused hunting licenses, implying a Holling Type I functional re sponse in the absence of a quota (Holling 1959). The within-year dynamics of hunting in Finland can therefore be expressed as a system of 2 ordinary differential equations: (6) (7) where denotes the expected number of seals of  sex s and age a that have been harvested in Finland, is the hunting quota for year t, is the total harvest in Finland at time x after the onset of the hunting season, ñs,a,t(x) is the number of seals that are alive at time x, and is the per capita harvest rate directed towards each demographic group in year t. We assumed that there was stochastic variation in per capita harvest rates across the years, without any temporal trends: (8) Here, Ês,a is the median per capita harvest rate, and is a noise term. Setting the initial har- vest to 0, an approximate closed-form solution to Eqs. (6) and (7) can be ob tained to estimate the ex - pected composition of the harvests, and hence the probability, , that a seal of sex s and age a is har- vested in Finland during year t (Supplement 3). Swe- dish hunting during both the spring and the fall were modeled similarly to Finnish hunting. However, unlike hunting in Finland which takes place almost entirely on sea ice, protective hunting in Sweden is likely to be opportunistic. We therefore assumed that the harvest rate in Sweden was proportional to the total number of ringed seals in the Bothnian Bay, rather than to the density of ringed seals on sea ice (Supplement 3). Spring hunting in Sweden was assumed to take place during May and June, and fall hunting during September and October (Fig. 2). Once estimates for , , and are obtained, the probability that a seal survives all sources of mortality is given by: (9) Note that while the expected harvests, as implied by Eqs. (6) and (7), are constrained by the hunting quotas, the realized harvests given by the stochastic model in Eq. (1) may exceed these quotas. This formulation not only simplifies the model considerably but also accounts for the possibility of illegal or unrecovered hunting. e, µ s a – ,s az = d dH E Q H C n–, , fi , , fi fi fi , , , ,s a t s a t t t t s a t s a t x x ~ x= u^ ^ ^hh h d dn n E Q H C n –µ – –, , , , , , , fi fi fi , , , , s a t s a s a t s a t t t t s a t s a t x x x ~ x =u u u ^ ^ ^ ^h h hh Hfi , ,s a t Qfi t / aH Hfi , , fi t s a tx x= ,s^ ^h h Efi , ,s a t E E e, , fi , fi s a t s a t= et ~N ,0t E 2 five ^ h , ,s a t Hfi t , ,s a t Hsw( )1 t , ,s a t Hsw( )2 t , ,s a t Hfi t 1– – –, , , , , , , , ,s a t S s a t H s a t H s a t H s a sw( ) sw( ) fi1 2 t t t t z= _ i a1 4# # ,( )c log – µ µ µ µ ( ) ( )log log loga 5 – , , , , f a f f f 0 0 5 = +^ ^h h6 @ 220 Symbol Description ns,a,t Number of seals of sex s and age a at the start of year t Nt Total population size at the start of year t ρX s,a,t Probability that a seal of sex s and age a transitions to mortality state X u(1) s,a,X,t Number of seals of sex s and age a that transition to mortality state X u (2) s,a,t Number of seals of sex s and age a at the end of year t Hi t Harvest totals of country i in year t μs,a Mortality rate of seals of sex s and age a in the absence of hunting fs,a Survival probability of seals of sex s and age a in the absence of hunting ws,a,t Haul out probability of seals of sex s and age a in year t w s,a Haul out probability of seals of sex s and age a when sea ice is abundant Ct Ice extent in the Bothnian Bay in late April bt Probability that an adult female gives birth at the start of year t Table 1. Notation for commonly referenced parameters Ersalman et al.: Integrated population model for ringed seal 2.3.3. Haul-out probability The proportion of seals that are visible on ice during the molting period depends on the frequency with which seals move into and out of the water. We assumed that during the molting period, seals of sex s and age a move onto the ice at a per capita rate of z1 s,a,t, and move back into the water at a per capita rate of z0 s,a,t. The pro- portion of seals hauled out on ice is then given by: (10) Although our assumption of constant movement rates implies exponentially distributed haul-out and forag- ing durations, Eq. (10) remains valid for any distribu- tion with a finite expectation (Janssen & Manca 2006). Deteriorating ice conditions may force seals to spend longer periods of time in the water or on land, as suitable haul-out sites on ice become increasingly less accessible (Härkönen et al. 1998, Thometz et al. 2021). We therefore assumed that the per capita rate at which seals move onto the ice follows a sigmoid function of ice availability, obtaining a value of 0 when no ice is present, and saturating at a maximum value when sea ice is abundant: (11) Here, f is a half-saturation constant. The value of ws,a,t in Eq. (10) is determined solely by the relative magni- tudes of z0 s,a,t and z1 s,a,t. Consequently, we have chosen to scale z1 s,a,t such that it asymptotically approaches 1 for all sex and age classes. To account for the possibility that a larger fraction of seals hauls out during low ice cover, we modeled the per capita rate at which hauled-out seals move into the water as a logistic function that decreases as ice cover approaches 0. In other words, we assumed that on average, seals remain on the ice for longer periods of time when sea ice is scarce: (12) Here, is the expected proportion of seals hauled out when sea ice is abundant, a0 and a1 are param- eters that determine the shape of the logistic curve, and d is the ratio between the lower and upper asymp- totes of z0 s,a,t. A non-0 lower asymptote for z0 s,a,t accounts for the fact that the maximum amount of time seals can spend on ice may be constrained by the need to forage or cool off. We assumed that on average, sub-adult and adult seals haul out with the same probability (i.e. ), but note that during the time of aerial surveys, sub-adults are typically thought to be underrepresented on ice compared to adults (Smith 1973). Hence, should be regarded as the average haul-out probability across sub-adults and adults. Pups largely complete molting by the time aerial sur- veys are conducted, and are significantly less likely to be on ice (Smith 1973, Lydersen & Hammill 1993). Thus, we assumed that the baseline haul-out probabil- ity of pups is a constant fraction of that for sub-adults and adults (i.e. ), with the effect of sea ice modeled in the same way as for sub-adults and adults using Eqs. (10)–(12). 2.3.4. Reproduction To account for the diminishing effects of organo- chlorine contamination on the reproductive rates of ringed seals, we modeled the probability that an adult female gives birth to a single pup in the absence of density-dependent effects as a time-varying logistic function increasing from a historic low of bmin to a theoretical maximum of bmax, so that: (13) where bt 0 is the expected birth rate in year t if popula- tion density were 0, and b0 and b1 are parameters that determine the shape of the logistic curve. Little is known about the mechanisms that regulate population density in marine mammals, although De- Master (1984) suggested that ringed seal populations in the Arctic may be predator-limited. Given the ab- sence of large predators in the Baltic Sea, we as sumed that Baltic ringed seals are resource-limited, with intra-specific competition primarily affecting fecun- dity. We assumed that fecundity would be more sensi- tive to changes in population size at high population densities, and modeled the rate at which pregnancies fail (e.g. due to abortions) as an exponentially increas- ing function of population size. The density-dependent birth rate, denoted by bt, can then be modeled as: (14) where is the total population size during the previous year, q0 is the average failure rate of pregnancies at 0 population density, and q1 is the rate at which such failed pregnancies increase with population size (Supplement 4). Pup production was then modeled using a multino- mial distribution: , , , , , , , , s a t s a t s a t s a t 1 0 1 ~ g g g= + f C C , ,s a t t t1 2 2 2 g = + d e d1 1 1– – , , , , s a t s a s a C 0 – t0 1 g ~ ~= + + a a+t t ^ h; E ,s a~t , a 0,s a 6 2~ ~=t t ~t ,0 1!d 6 @ ,s 0~ d~=t t b b e b b 1 – min max min t t 0 – 0 1 = + + b b+^ h b b et t e0 1– –N 0 t1 1 = i i -^ h ,s aN n , ,t s a t1 1– –=/ 221 Mar Ecol Prog Ser 764: 213–236, 2025 (15) where the sex ratio at birth is assumed to be at parity (McLaren 1958). Here, denotes the number of adult females immediately before pupping, and • is  a dummy variable for the number of mature fe - males that do not give birth, which occurs with prob- ability 1 – bt. 2.4. Observation models 2.4.1. Aerial survey estimates We modeled the estimated basking population size resulting from the aerial strip surveys as a negative binomial distribution with expectation equal to the true basking population size: (16) Here, ñt is the expected population state at the time of the aerial surveys (Section 2.3.2), wt is a vector of haul-out probabilities (Section 2.3.3), and r is a vari- ance parameter. The negative binomial distribution is commonly used to model biological count data and can be thought of as a Poisson distribution with a rate parameter that varies stochastically as a result of, e.g. changes in observability or demographic stochastic- ity on ñt that lead to overdispersion in the counts (Lindén & Mäntyniemi 2011). 2.4.2. Harvest totals and samples The total harvests for both Finland and Sweden are known exactly in principle, but we nonetheless assumed a small (~5% CV) variation around them because, in addition to having computational bene- fits, it accounts for the possibility of unrecovered or illegally hunted seals, as well as rare instances of misreporting: (17) where denotes the observed harvest totals and Ht denotes the actual harvest totals in either Finland or Sweden during year t. We used separate observation models for spring and fall hunting in Sweden, except in 2015 and 2016 when only the total harvest was known. Assuming that sampling of seals from the harvests is independent, the age and sex composition of the sampled seals from Finland and Sweden can be mod- eled using a multinomial distribution: (18) where is the demographic composition of the recov- ered samples in year t, is the composition of the harvests, vs,a is the relative probability that a seal of sex s and age a is sampled from the harvests, and denotes the element-wise, or Hadamard, product. We assumed that seals are sampled randomly from the harvests in Finland and in Sweden during the fall (i.e. ). However, sampling during the spring has not been ran- dom in Sweden since larger seals are specifically re- quested from hunters to assess reproductive health. The observation model to estimate v for spring hunting in Sweden is described in Supplement 5. Observation models for samples that were missing either sex or age information are described in Supplement 6. 2.4.3. Bycatch samples We assumed that bycaught seals were sampled ran- domly and independently. Because we included bycatch with other sources of mortality, we con- ditioned the observation model for bycaught samples on the number of seals that died due to causes other than hunting, and modeled the composition of bycaught samples using a multinomial distribution: (19) where is the demographic composition of the bycaught samples in year t, and y is a 12-simplex of weights accounting for possible deviations between the composition of bycatch and sources of mortality other than hunting (Supplement 2). Observation models for samples that were missing either sex or age information are presented in Supplement 6. 2.4.4. Observations of reproductive success Given reports of significant late-term pregnancy losses in other pinniped populations and the in - creased energetic demands of late-stage gestation (Pitcher et al. 1998, McKenzie et al. 2005, Stenson et al. 2016), we assumed the rate of pregnancy losses increased linearly from zero at conception to a maxi- mum at parturition. However, we note that there is lit- tle evidence of late-term pregnancy losses in Baltic ringed seals, and it has been suggested that the influence of nutritional factors on pinniped reproduc- tion is greatest at the point of implantation (Boyd u , ,f t5 1 2 –+ ^ h nt( ,rBinomial– ~ )t|y Negative nt t survey + Tu u | , .uy N H H0 05ht t t t t 1 2` _ ^^ h ih y ht t |y u v u v u Multinomialhs , , , hs , , Tt t s a s a t H t H t1 1 1 9 + / ,yf^ ^ ^ ph h h yhs t u ,H t 1^ h 9 ,s a6,1v ,s a = | Multinomial ,y u u u ybs , , , bs , , Tt t s a s a t D t D t1 1 1 9 + } } /f^ ^ ^ ph h h ybs t , , | ~ Multinomial , , , un n u b b b2 2 1– 2 2 :, , , , , , f t m t t f t t t t 0 0 1 5 1– – +b ^ ^ lh h" % , / 222 Ersalman et al.: Integrated population model for ringed seal 1991). Hence, for sensitivity analysis, we also consid- ered a model where the rate of pregnancy losses was assumed to decrease linearly (Supplement 4). Assuming the reproductive status of sampled fe - males is representative of the population as a whole, and there are no errors in the detection of fetuses, the number of observed pregnancies during the fall of year t can be modeled using a binomial distribution: (20) where: (21) is the pregnancy rate of the population, and is the average time, in years, between mating and the sampling of pregnant females (Supplement 4). In principle, all females that recently gave birth will possess both a placental scar and a CA. However, since both post-partum signs can fade with time, they might not always be identified (Boyd 1984, HELCOM 2023b). Moreover, the presence of a CA does not nec- essarily indicate recent birth. CA may also be present in females that had an infertile estrous cycle, and in some cases, it may even be a remnant of the previous reproductive season (Boyd 1984). We denote by zij k,t ∈ {0, 1} whether a sampled seal k had a placental scar evaluation of i and a CA eval- uation of j; for example, z10 k,t = 1 if a placental scar, but not a CA, was observed in a seal. The outcome of the reproductive assessment for each adult female can then be modeled using a categorical distribution with probability vector gt: (22) The probabilities gt ij for each assessment outcome will depend on the birth rate bt, the probability k that a seal that has not given birth has a CA, and the detec- tion probabilities for placental scars (ps) and CA (pc), respectively. Hence, for a randomly sampled seal, both a placental scar and a CA are observed (z11 k,t = 1) with probability gt 11 = bt ps pc, corresponding to sam- pling a seal that has recently given birth and success- fully detecting both the placental scar and the CA. If a placental scar is observed without a corresponding CA (z10 k,t = 1), it must be that a CA was present but not seen. Such an outcome will occur with probability gt 10 = bt ps (1 – pc). Finally, if a CA is observed with- out a corresponding placental scar (z01 k,t = 1), it means that either the female recently gave birth but the placental scar was not detected (i.e. because it faded), or the female did not recently give birth but none- theless had a CA which was detected. Such an as - sessment will occur with probability gt 01 = bt (1 – ps) pc + (1 – bt) k pc. The probability that neither a placental scar nor a CA is observed is then gt 00 = 1 – gt 11 – gt 10 – gt 01. Samples obtained in May and June, as well as those obtained before 2007, were only evaluated for the presence of CA. For these samples, we replaced the categorical distribution in Eq. (22) with the Bernoulli observation model: (23) An extension of the observation model described in this section to handle incomplete data is presented in Supplement 6. 2.5. Posterior inference and model assessment 2.5.1. Posterior inference Following standard practice in IPMs, we assumed the different data sources were independent and con- structed the joint likelihood as a product of the indi- vidual data likelihoods presented in Section 2.4 (Abadi et al. 2010). Prior distributions for model parameters are given in Supplement 2. Posterior infer- ence was conducted using Markov chain Monte Carlo methods implemented using Stan version 2.26.23 (Stan Development Team 2023), a probabilistic pro- gramming language that uses gradient-based methods to draw samples from the posterior distributions of the parameters. Because Stan relies on gradient infor- mation, it does not permit discrete valued parameters. As a result, all discrete valued parameters in our model, along with their corresponding probability distributions, were approximated using continuous numbers and distributions (Supplement 7). We simulated 4 Markov Chains and drew 4000 pos- terior samples with each chain. The first 2000 samples drawn from each chain were treated as the warm-up period and were discarded. The resulting effective sample size (Stan Development Team 2023) was greater than 1500 for all model parameters. Conver- gence checks were performed using the R-hat diag - nostic (Stan Development Team 2023) as well as visual inspection of trace plots. All R-hat values were less than 1.01, and the trace plots for each parameter appeared to be well-mixed, indicating that the model had converged. Model fit was assessed using poste- rior predictive checks (Supplement 1). A visual com- ~| Binomial ,y p y y ppregnant pregnant not pregnant t t t t t+_ i ep bt t e 1 1– p N2 0 t1 = x i + i_ i .0 5p .x , , , | ~Categorical , , ,z z z z, , , ,k t k t k t k t t t t t t 11 10 01 00 11 10 01 00c c c cc ^ h# "- , | ~Bernoulliz ,k t t t t 1 11 01• c cc +^ h 223 Mar Ecol Prog Ser 764: 213–236, 2025224 parison of the observed distribution of data with the distribution of simulated data showed no signs of model misfit. 2.5.2. Sensitivity analyses To examine how different data sources influenced posterior estimates of individual parameters, we refitted our model using various subsets of the avail- able data (Gelman et al. preprint doi.org/10.48550/ arXiv.2011.01808). We focused on aerial survey data, reproduction data, harvest totals, and dead samples. For each of the 4 data types, we refitted the model using only data from odd years. For aerial survey data, we also ran models with only pre- and post-2012 data, corresponding respectively to periods with low and high variability in the observed counts. For repro- duction data, we ran an additional model with only post-2007 data to determine if long-term reproductive trends could be estimated without direct observations of reproductive signs. In total, we fit our model to 8 different data sets: the full data set and 7 reduced ver- sions. For all models, we created prior–posterior com- parison plots of key parameters and calculated prior– posterior overlaps (Figs. S5–S9 in Supplement 1). For models using the reduced data sets, we also com- puted overlaps of posteriors with those from the full model (Table S1 in Supplement 1). Additionally, we computed Pareto-k statistics for each data type using Pareto smoothed importance sampling, implemented via the R package ‘loo’ (Veh tari et al. 2022), in order to assess their relative in fluence on overall model fit (Vehtari et al. 2017). The results of these analyses are presented in Supplement 1. We also ran prior sensitivity analyses for the base- line haul-out probability parameter , which plays a key role in estimating total population size and was assigned an informative prior in our model due to a lack of direct data (Section 2.3.3). We refitted our model with 2 alternative priors, each shifted by 0.1 to the left and right from the original, and compared the resulting estimates for key model parameters. All models were fitted and their sampling conver- gence assessed as described in Section 2.5.1. In 4 of the sensitivity analyses, 1 of the chains showed poor mix- ing and was therefore removed from consideration. 2.5.3. Demographic analysis Since asymptotic demographic analysis is of inter- est to practical management of Baltic ringed seals, we applied analytical methods for matrix population models to our demographic parameter estimates to calculate key asymptotic quantities, such as the intrinsic population growth rate, stable stage struc- ture, and critical harvest levels that would lead to population decline (Caswell 2001, Ersalman 2024). All demographic analyses were performed in R Statistical Software version 4.2.0 (R Core Team 2022). 2.5.4. Predictive simulations Using posterior samples of the model parameters, we projected the population dynamics of Baltic ringed seals in the Bothnian Bay over the next 15 yr. Since our model lacked an explicit link between demographic parameters and sea ice conditions, we chose not to include climate change projections in future simulations to avoid drawing misleading con- clusions. Instead, we focused on comparing the ef - fects of alternative hunting quota scenarios. We con- sidered 4 management scenarios: Scenario 1 maintains current hunting quotas; Scenarios 2 and 3 implement annual increases of 15 and 35 licenses, respectively, for both Finland and Sweden; and Scenario 4 intro- duces a one-time reduction of 270 licenses in each country, equivalent to a decrease of approximately 75%. These scenarios were applied starting from 2024. For each simulated year, the ice extent in April was randomly sampled from historically observed results. We ran 8000 simulations of each scenario, corresponding to each posterior sample of the model parameters, using R Statistical Software version 4.2.0 (R Core Team 2022). 3. RESULTS Posterior median estimates from our model indicate that the total number of ringed seals in the Bothnian Bay has increased from 4700 (95% CI: 3500–6600) in  1988 to 26 700 (20 200–36 300) in 2023 (Fig. 4a). Driven by an estimated rise in ringed seal birth rates from 0.32 (0.13–0.53) to 0.74 (0.66–0.81) (Fig. 4b), we estimated that the population growth rate increased from 1.7% (–1.7 to 4.5%) in 1988 to a peak of 6.8% (5.6–8.1%) in 2015 before declining to as low as 4.0% (2.5–5.5%) in 2021 due to the re-introduction of seal hunting (Fig. 4c). The dominant eigenvalue of the population projection matrix suggests that under ideal conditions, the Bothnian Bay population can achieve a maximum growth rate of about 7.0% (5.9– 8.8%) (Fig. 4c), with a corresponding net reproduc- ~t Ersalman et al.: Integrated population model for ringed seal tion rate of 3.3 (2.3–4.6) female pups produced per lifetime (Section 2.5.3). We estimated that pregnancy rates may have been as low as 0.27 (0.02– 0.56) during the 1970s and could reach a maximum of 0.83 (0.75–0.93) in a healthy Bothnian Bay population. Re - productive rates were primarily in - formed by direct data on reproductive signs, but the aerial survey data also provided some indication of an in - creasing trend in reproduction over time (Fig. S7 in Supplement 1). The current pregnancy rate was estimated to be 0.82 (0.74–0.89) (Fig. S2 in Sup- plement 1), although the birth rate in the spring was 0.74 (0.66–0.81). It is therefore possible that about 9% (1– 21%) of pregnancies are aborted between the fall and spring. However, the pregnancy estimates were some- what sensitive to assumptions about the importance of late-term abortions. When late-term abortions were as - sumed to be relatively rare, correspond- ing to the model with decreasing rate of pregnancy losses (Supplement 4), the estimated current pregnancy rate was 0.78 (0.72–0.84), with 4% (0–8%) of pregnancies failing between fall and winter. The choice of the model for the pregnancy losses was insignificant for other results. The reproductive status of ringed seals is commonly assessed using pla- cental scars and CA. We estimated that by late April, approximately 7% (1–15%) of placental scars from births may have already faded sufficiently to become undetectable. In contrast, we estimated that most CA were easily visible between April and June, and were correctly identified 97% (91– 100%) of the time. In addition to seals that had recently given birth, our esti- mates indicate that between April and June, CA can also be found in 9% (0– 26%) of seals that had not given birth. Our model was not informative on the carrying capacity of the popula- tion, indicating that density-depen- dent effects were not detectable at the present population size. Hence, the 225 Fig. 4. Estimated (a) population size, (b) birth rate, (c) population growth rate, and (d) age structure for ringed seals in the Bothnian Bay. The rightmost seg- ments show the expected asymptotic values for an unexploited population with and without density-dependent effects Mar Ecol Prog Ser 764: 213–236, 2025226 posterior distribution of the carrying capacity corre- sponded to our prior assumptions based on historical estimates of the population size (Supplement 2). Assuming density dependence primarily affects fe - cundity, birth rates may eventually decline to as low as 0.24 (0.17–0.34) (Fig. 4b). It is worth noting that this latter result is independent of the estimated car- rying capacity (Caswell 2001). Improvements in reproductive rates have implied a substantial change in the age structure of the popula- tion (Fig. 4d). Our estimates suggest that the propor- tion of pups in the population may have increased from 11% (5–15%) in 1988 to 18% (16–21%) in 2023. During the same period, we estimated a decline in the proportion of adults from 67% (54–84%) to 50% (43–55%). Assuming density dependence primarily affects fecundity, the age structure at carrying capac- ity can be expected to consist of 9% (6–11%) pups, 18% (12–29%) sub-adults, and 74% (61–82%) adults. We did not find evidence for a skewed sex ratio which, driven by our prior assumptions, was reflected in similar mortality rates between the sexes in the absence of hunting (Supplement 2). The probability that pups survive all mortality sources other than hunting during their first year was estimated to be 0.63 (0.42–0.87), which increased to 0.86 (0.77–0.95) at age 1 and to 0.95 (0.91–0.97) by maturity (Fig. 5a). However, the large negative posterior correlation between juvenile and adult survival probabilities sug- gested that the model had limited capacity to esti- mate age-specific mortality rates (Fig. S11 in Supple- ment 1). Refitting the model with different subsets of the data confirmed that survival probabilities were primarily informed by pre-2012 aerial survey and the reproduction data, both of which lack information on age-specific mortality (Fig. S5 in Supplement 1). We found significant juvenile bias in bycatch from small-scale fisheries, with pups nearly 8 (4–16) times more likely to be bycaught than 1 yr olds (Fig. 5b). Male pups were also about 40% (1–88%) more likely to be bycaught than female pups. We estimated that Swedish hunting during the spring was represen- tative of population demography (Fig. 5c). In con- trast, the fall hunt was heavily aimed at adults of both sexes, with a slight bias towards males (Fig. 5d). We estimated that pups were the most vulnerable age group to hunting in Finland (Fig. 5e). Sub-adults were also generally underrepresented in the Finnish harvest. We estimated that about 60% (48–74%) of sub- adult and adult seals and 35% (12–60%) of pups may be visible on ice during aerial surveys that coincide with extensive ice cover. Historical ice conditions in the Bothnian Bay suggest that approximately 51% (39–65%) of the total population may be visible dur- ing aerial surveys carried out in typical ice conditions (Fig. 6b). We found that as ice cover diminishes, the fraction of hauled-out seals may gradually decline to as low as 44% (30–62%). However, this proportion was found to increase dramatically to as much as 91% (70–99%) when the ice cover declined below a critical threshold of about 13 000 km2 (Fig. 6). Although our mechanistic haul-out probability model was relatively complex, all parameters appeared to be well in - formed, largely by the aerial survey data. The excep- tion was the baseline haul-out probability , which was given an informative prior (Supplement 2) and was only weakly informed by data. Nonetheless, posterior estimates were generally robust to prior choice. Only estimates of total population size, and consequently population growth rate under harvesting, showed moderate sensitivity, with estimates varying by less than 10% under sensible prior choices (Table S1 in Supplement 1). An analysis of the impact of hunting on popula- tion growth revealed that at present, hunting 1200 seals per year may be sufficient to cause population decline (Fig. 7a), although the uncertainty around this estimate was high (1200–2600). Achieving a growth rate of 7 %, the benchmark set by the Baltic Marine Environment Protection Commission (HELCOM) for designating good status, might prove challenging with any level of hunting activity (Fig. 7b), especially if more than 380 seals are hunted annually. Posterior predictive simulations suggested that maintaining hunting quotas at their current levels of 350 and 375 seals per year in Sweden and Finland, respectively, may allow for a slight improvement in the population growth rate over the next 10–15 yr (Fig. 7b). In contrast, increasing quotas by 15 licenses per year in each of Sweden and Finland may cause a slight decline in the growth rate, and an increase of 35 licenses per year in each country may significantly slow down population growth, and may even lead to population decline within the next 15 yr. 4. DISCUSSION So far, different sources of long-term monitoring data on Baltic ringed seals have been analyzed sep- arately to assess population growth, reproductive health and other relevant metrics of population status. A major limitation of this approach is its inability to leverage all available information, as the ,s a~t Ersalman et al.: Integrated population model for ringed seal 227 Fig. 5. (a) Probabilities of surviving natural mortality (includ- ing bycatch), and the relative probabilities that seals are (b)  bycaught, (c) hunted in Sweden during the spring, (d) hunted in Sweden during the fall, and (e) hunted in Finland. The dashed lines in (b)–(e) show the relative mortality prob- abilities if all individuals were equally likely to be hunted or bycaught. Calculations of the relative mortality probabilities are presented in Supplement 3 Mar Ecol Prog Ser 764: 213–236, 2025 synergies between different data sources are not exploited (Schaub & Abadi 2011, Zipkin & Saunders 2018). This limitation has become more apparent than ever during the last decade, when unexpected trends and large fluctuations in population counts from aerial surveys made it impossible to obtain reliable estimates of population growth from survey data alone. Growth in closed populations, however, is ultimately a consequence of births and deaths. Thus, data related to reproduction and hunting also contain information on the growth rate. By incorpo- rating all available information into a mechanistic IPM, we were able to address recent challenges in ringed seal monitoring in the Bothnian Bay. Our model showed a good fit to all available data (Sup- plement 1) and was able to estimate a large number of ecologically important parameters. Moreover, fit- ting our model in Stan (Stan Development Team 2023), while requiring some approximations, proved highly efficient, achieving convergence in under 1 h on a personal laptop computer despite the large number of parameters. Earlier analyses of ringed seal population trends in the Bothnian Bay suggested that the population had been growing at a constant rate of approximately 5% per year since 1988 (Sundqvist et al. 2012), although more recent analyses showed that an increasing trend was likely (HELCOM 2023a). We estimated that improvements in reproductive rates may have led to a substantial increase in the growth rate between 1988 228 Fig. 6. (a) Posterior predictive distribution for aerial survey estimates. (b) Expected proportion of seals hauled out in each year. Error bars indicate the 95% posterior credible intervals. (c) Annual variation in the ice-covered area of the Bothnian Bay around the third week of April (blue line) and the expected proportion of seals hauled out during aerial surveys as a function of ice-covered area (red line). The points depict the median ratio of observed aerial survey estimates to the posterior estimates of total population size, and the red shaded region shows the 95% posterior credible interval for the expected proportion of seals hauled-out. Note that the overall proportion of seals hauled out depends on the population age structure, and panels b and c are based on the most recent estimate of the age structure Ersalman et al.: Integrated population model for ringed seal and the re-introduction of hunting in 2015, which accounted for much of the systematic deviation between recent population size estimates and earlier expectations based on historical trends. On the other hand, a small number of unusually large population estimates obtained in recent years were explained surprisingly well by an increase in the fraction of seals hauling out during aerial surveys conducted in poor ice conditions, supporting earlier speculations (HELCOM 2023a). It is not clear why seals would haul out in significantly greater numbers under such circumstances. Sea ice conditions during the surveys likely correlate with air temperature, wind speed, and snow depth, which are known to affect ringed seal haul-out probability (Härkönen & Lunneryd 1992, Hamilton et al. 2018). Snow depth may additionally influence the proportion of seals that are hiding in lairs (Kelly et al. 2010). However, as surveys are conducted in late April, when most lairs have collapsed and seals are at the height of molting, and only on clear, calm days, the impact of these vari- ables on population size estimates is likely limited. Another possibility is that the break-up of sea ice causes adult seals to relinquish territorial behavior typical of winter, allowing younger sub-adults to haul out in greater numbers (Härkönen & Lunneryd 1992, Härkönen et al. 1998, Kelly et al. 2010, Oksanen et al. 2015b). This may additionally result in large congre- gations of seals, potentially contributing to the high variability in survey estimates (Härkönen et al. 1998, Lindén & Mäntyniemi 2011). Since the sub-adult age classes account for about a third of the total population, it seems unlikely that an increase in their visibility alone can account for a nearly 2-fold increase in population size estimates. Likewise, immigration from southern sub-popula- tions, which are collectively believed to be nearly an order of magnitude smaller than the Bothnian Bay population (Sundqvist et al. 2012), also appears insuf- ficient to explain the observed increase in counts. The increase in the proportion of visible seals during low ice cover could, in part, be attributed to an increase in the cost of foraging. During the molting period, ringed seals are likely to derive greater bene- fit from maintaining elevated skin temperatures than from consuming resources (Thometz et al. 2021). Diminishing sea ice will most likely result in in - creased distances between optimal haul-out sites and productive foraging areas, and the trade-offs associ- ated with foraging could compel seals to decrease the frequency with which they venture out to sea. More- over, seals may anticipate that the molting period 229 Fig. 7. (a) Critical harvest level for which the population growth rate is expected to be zero, as a function of total population size. The critical harvest level is calculated by setting the net reproduction rate equal to one. The red error bar shows the esti- mated population size and hunting quota (Finland and Sweden combined) in 2022. (b) Posterior predictions for future popula- tion growth rates under 4 different hunting quota scenarios: (1) quotas maintained at their current level of 350 and 375 ringed seals in Sweden and Finland, respectively, (2) quotas increased by a total of 30 licenses per year (15 in both Sweden and Fin- land), (3) quotas increased by a total of 70 licenses per year (35 in both Sweden and Finland) and (4) quotas reduced by a total of 540 in 2024 (270 in both Sweden and Finland) and kept constant thereafter Mar Ecol Prog Ser 764: 213–236, 2025 could be interrupted prematurely, causing them to spend longer periods of time out of the water to ensure that they attain adequate levels of solar expo- sure before the ice melts completely. While our findings demonstrate a clear effect of ice cover on aerial survey estimates, this conclusion was largely driven by 2 outliers that corresponded to unusually mild winters. Establishing haul-out behav- ior as the causal mechanism demands further investi- gations, including additional data and model compar- isons to evaluate alternative hypotheses. Regardless of the mechanism, the number of seals on ice must be 0 when no sea ice is present. Extreme inter-annual variability in population counts from aerial surveys may therefore be expected following mild winters (Fig. 6c), which could pose additional challenges for future ringed seal monitoring efforts in the Bothnian Bay. As ice conditions in the Baltic Sea continue to deteriorate (Meier et al. 2004, Haapala et al. 2015), understanding the factors that affect ringed seal haul- out behavior will become increasingly important for reliable monitoring. Our study demonstrates that aer- ial surveys can be a valuable source of information to this end, and survey estimates that appear unreliable at first may provide important insights on ringed seal behavior. We therefore emphasize the need for con- tinued monitoring efforts, as well as the need for detailed mechanistic models that go beyond simple analyses of trends. Future IPMs could also incorpo- rate individual-level data collected from telemetry devices with dry/wet sensors, enabling direct estima- tion of haul-out probabilities (London et al. 2024). Statements regarding the total population size of ringed seals require an estimate of the proportion of seals that are hauled out during the surveys. Haul-out behavior is likely to vary by age (Smith 1973, Lydersen & Hammill 1993, Crawford et al. 2012, Oksanen et al. 2015b), but little is known to quantify age-specific dif- ferences. Most studies have focused on sub-adult and adult ringed seals, which suggested that 50–84% of seals may be visible during surveys (Smith 1973, Här- könen & Lunneryd 1992, Born et al. 2002, Kelly et al. 2010). However, pups undergo their first molt and shed their lanugo hair before the molting season of older seals. Thus they spend most of their time in the water by the time they are 5 wk old (Smith 1973, Lydersen & Hammill 1993). Failing to account for their lower visibility during the surveys may lead to an underestimation of the total population size. We found that following typical winters, roughly half of the population may be visible on ice during surveys, which corresponds to the lower end of previous esti- mates, and is similar to what has been proposed by Smith (1973). The number of ringed seals in the Both- nian Bay may therefore be larger than previously expected (Sundqvist et al. 2012). However, our results were influenced by prior assumptions about haul-out probabilities in abundant ice conditions. Detailed studies on the molting behavior of Baltic ringed seals will be crucial for obtaining reliable estimates of total abundance. Little is known about the survival probabilities of ringed seal pups, but previous estimates range from as low as 0.34 in Lake Saimaa, Finland, before active conservation efforts (Kokko et al. 1998) to 0.6–0.7 in the Arctic (Smith 1973, Kelly 1988). A survival prob- ability as high as 0.8 has been suggested for unhar- vested Arctic populations (Smith 1973). For Baltic ringed seals, a pup survival probability of 0.65 has previously been assumed (Sundqvist et al. 2012), which is very similar to our posterior median esti- mate. However, the uncertainty around our esti- mate was high due to weak parameter identifiability (Fig. S11 in Supplement 1). Baltic ringed seal pups are safe from large predators that are common in the Arc- tic such as polar bears Ursus maritimus and Arctic foxes Vulpes lagopus, which might lead to compa- rably higher survival probabilities (Stirling & Smith 2004). On the other hand, higher bycatch mortality and greater chance of early snow and ice melt in the Baltic Sea could compensate for the limited presence of predators. Snow and ice conditions in the Baltic Sea are expected to decline in the future, which will most likely lead to increased pup mortality (Smith & Stir- ling 1975, Meier et al. 2004, Ferguson et al. 2005, Kelly et al. 2010, Sundqvist et al. 2012, Reimer et al. 2019). Although previous estimates of sub-adult survival probabilities are rare, our estimate aligns closely with the 0.81–0.93 range reported in earlier studies (Sundqvist et al. 2012, Koivuniemi et al. 2019). Our posterior median estimate of 0.95 for adult survival probability corresponds to the upper end of previous estimates for ringed seals, which range from 0.88– 0.96 (Durant & Harwood 1986, Kelly 1988, Kokko et al. 1998, Sundqvist et al. 2012, Koivuniemi et al. 2019, Reimer et al. 2019), and is consistent with previous assumptions for Baltic ringed seals (Sundqvist et al. 2012). Similarly high adult survival probabilities have also been estimated for Saimaa ringed seals (Koivu - niemi et al. 2019) and British grey seals Halichoerus grypus (Thomas et al. 2019). However, the high poste- rior correlation between juvenile and adult survival probabilities suggests that these parameters were not individually identifiable (Fig. S11 in Supplement 1). Direct data on survival, such as from mark–recapture 230 Ersalman et al.: Integrated population model for ringed seal studies, will be needed to obtain precise age-specific estimates. Such data can additionally support the estimation of overall abundance and, in turn, haul-out probabilities. We estimated a historical minimum pregnancy rate that was strongly in agreement with some empirical estimates from the late 1970s (Helle 1980b). However, the uncertainty around our estimate was high due to limited data on female reproductive status during the initial years of our study period. Our estimates indi- cate that the current pregnancy rate may be nearly the same as the maximum attainable by a healthy Bothnian Bay population. Thus, the population app - ears to have almost fully recovered from the effects of organochlorine contamination. Assessments of the reproductive health of Baltic ringed seals are cur- rently based on a tentative pregnancy rate threshold of 0.9 that was established by HELCOM based on studies of seal populations elsewhere (HELCOM 2023b). Our results suggest that this threshold may be too high even for a healthy Bothnian Bay population, possibly because the Bothnian Bay is a relatively unproductive environment (Kauhala et al. 2019). A threshold be tween 0.80 and 0.85 may be a more realis- tic target. As the population continues to grow, rising intra-specific competition may cause pregnancy rates to decrease. Body conditions of Baltic ringed seals may already be declining due to poor nutritional status (Kauhala et al. 2019), although it is unclear whether population density is a contributing factor. Our model did not provide information on density- dependent effects on reproductive rates, either be - cause the current population size is substantially below carrying capacity, or because other demo- graphic para meters, such as pup survival, were more strongly affected. Long-term predictions of ringed seal population dynamics will require detailed con- sideration of density-dependent mechanisms, which would greatly benefit from additional demographic data such as long-term mark–recapture studies (e.g. Hiby et al. 2007, Koivuniemi et al. 2019). Understand- ing seasonal patterns of reproductive failure and their links to population density and nutritional stress would also be valuable for both assessing current reproductive health and improving future population projections. The most reliable assessments of reproductive rates will be based on the presence of embryos in female seals sampled in the fall. Unfortunately, the current sample size for this measure remains relatively small, with substantial inter-annual variability in the ob - served pregnancy rate. Assessments based on placen- tal scars may underestimate the pregnancy rate, as our results indicate that some scars that were present during parturition may have already faded by the end of April. Many of these scars are likely to be from early births in February. Additionally, a small fraction of fetuses may be aborted in early pregnancy, and placental scars from these pregnancies may have also faded by spring. Accuracy of pregnancy rate esti- mates from placental scars can be improved either by using the earliest available samples in the spring, or by adjusting the estimates to account for the effect of fading. Assessments based only on CA may be more difficult to interpret since a CA could also be present in seals that had an infertile estrous cycle (Boyd 1984). However, we found that CA may yield very accurate estimates of the pregnancy rate when the pregnancy rate is high. An additional challenge when estimating pregnancy rates is accounting for poten- tial sampling biases. Most assessments, including the present study, assume that reproductive signs in har- vested or bycaught females are representative of the entire female population. This assumption may intro- duce bias if reproductive status affects a female’s like- lihood of being harvested or bycaught. For instance, preferential harvesting of pups can inflate reproduc- tive rate estimates if their mothers are harvested with them. Similarly, if post-partum females forage differ- ently due to reduced energy reserves or molt at differ- ent locations, their susceptibility to hunting or by - catch may differ. Detailed studies on seal and hunter behavior will be essential for addressing potential sampling biases. Our results suggest that since its re-introduction, hunting has had a substantial impact on the pop- ulation growth rate, possibly reducing it by more than 3 percentage points. An unexploited Bothnian Bay population could achieve a maximum growth rate of about 7%, satisfying HELCOM’s current threshold for good status. However, this threshold is unlikely to be met in the presence of even a small amount of hunting, and a growth rate of 4–5% may be a more likely outcome from the current hunting practices (Fig. 7b). It is possible that the quotas in 2022 were close to a critical threshold beyond which population growth could no longer be maintained. However, this thres- hold will increase in the near future provided that the population continues to grow (Fig. 7a). Current an - nual hunting quotas are established at 350 and 375 seals in Sweden and Finland, respectively. Our simu- lation study suggested that while increasing quotas by fewer than 35 licenses per year in each of Sweden and Finland is unlikely to cause population decline within the next 10–15 yr, increases in excess of 15 per 231 Mar Ecol Prog Ser 764: 213–236, 2025 year in each country may further decrease the pop- ulation growth rate (Fig. 7b). Our model assumed that there is sufficient demand for seal hunting such that harvest rates will increase proportionally to hunting quotas. While this assumption will not hold for large quotas, it remains appropriate within a precautionary framework. It should be emphasized that, due to the short time frame of available demographic data and the oppor- tunistic nature of sampling, our model did not take into account likely effects of climate change and other environmental variables, such as prey availabil- ity, on demographic parameters like pup mortality and reproductive rates (Meier et al. 2004, Ferguson et al. 2005, Sundqvist et al. 2012, Reimer et al. 2019). Thus, our simulation results should be viewed as a comparison of the potential impact of different hunt- ing quota decisions, rather than as forecasts of future population dynamics. As climate change is expected to lead to further declines in snow and ice cover in the Baltic Sea (Meier et al. 2004, Haapala et al. 2015), understanding its effects on ringed seal demography is essential for making longer-term predictions. Future IPMs could explicitly link ringed seal survival and reproduction to environmental variables such as snow and ice conditions to predict population re - sponses to various climate change scenarios (e.g. Sundqvist et al. 2012, Reimer et al. 2019). However, estimating parameters of such models will likely require direct data on survival probabilities, such as from mark–recapture studies. Our estimates suggest that the demographic com- position of Swedish harvests may differ significantly between the spring and the fall. We found that hunt- ing was largely aimed at adults during the fall, pos- sibly because of the greater damage they cause to fishing gear and catch. Studies of grey seals have shown that some adults, typically males, may special- ize in raiding fishing gear (Königson et al. 2013). In contrast, the adult bias was completely absent during the spring hunt. This is not particularly surprising considering that adult seals are molting on ice in large numbers during the spring, and seldom venture out at sea (Smith 1973, Härkönen & Lunneryd 1992, Born et al. 2002, Kelly et al. 2010). Younger seals may be much more likely to be foraging in open water dur- ing most of the molting period, and thus have more frequent interactions with fishermen (Smith 1973, Lydersen & Hammill 1993, Crawford et al. 2012, Oksanen et al. 2015b). In fact, we estimated that adult seals were generally more likely to be hunted than sub-adults during the spring in Finland, where hunt- ing primarily takes place on sea ice. Pups were an exception and were overrepresented in Finnish har- vests despite their relatively low presence on sea ice, although some late-born pups are often still with their mothers during the Finnish hunting season. Since hunting in Finland is recreational, hunters may spe- cifically seek out inexperienced pups for their meat and fur (Kingsley & Byers 1998). The response of a population to harvesting is strongly influenced by the age and sex composition of the harvest, with the removal of adult females typi- cally having the greatest impact in long-lived mam- mals like ringed seals (Kokko et al. 1999, Heppell et al. 2000, Reimer et al. 2019). Hence, it is important to ensure that recovered samples are either selected randomly from the harvests or that any sampling biases are accounted for. In Sweden, hunter-reported data on the sex and body length of each seal, along with records of whether or not each harvested seal was recovered as a sample, allowed us to quantify size- and sex-related sampling biases. Although such biases are unlikely in Finland, similar data could help ensure accurate and unbiased estimates of harvest compositions. We were not able to estimate the overall magni- tude of bycatch mortality due to a lack of data. Such data could be obtained through interviews with fishermen (Vanhatalo et al. 2014, Tubbs & Berggren 2024). However, consistent with findings from many other seal populations, we found that pups were significantly more at risk of getting bycaught in small fisheries than older seals (Sipilä et al. 1990, Bäcklin et al. 2011, Niemi et al. 2013, Vanhatalo et al. 2014, Jounela et al. 2019, 2024). As pups tend to favor shallow waters for foraging, and are generally curious and inexperienced, it is probable that they frequently engage with coastal fisheries and become caught in fishing gear (Kelly et al. 2010, Niemi et al. 2013, Cronin et al. 2014). Their relatively small body sizes may also make them more likely to enter smaller fishing gear and make escaping more diffi- cult once they are caught (Cronin et al. 2014). The juxtaposition between the substantial juvenile bias in bycatch and the pronounced adult bias in pro- tective hunting by fishermen may reflect the fact that young, inexperienced seals are inclined to - wards exploration, whereas experienced adults pri- oritize exploitation (Sjöberg & Ball 2000). On the other hand, larger seals may be more likely to de - tach from fishing nets, and fishermen often report the difficulty of lifting out larger seals from the water (Cronin et al. 2014). Older seals may therefore be underrepresented in the samples compared to the actual bycatch. 232 Ersalman et al.: Integrated population model for ringed seal 5. CONCLUSIONS Amid the dynamic and uncertain conditions brought on by climate change, varying reproductive rates, and the re-introduction of seal hunting, our Bayesian IPM succeeded in providing a comprehensive assessment of the Baltic ringed seal population in the Bothnian Bay — a task that has not been possible for over a dec- ade. In addition to estimating population size and growth, we inferred key demographic parameters including survival probabilities, reproductive rates and the relative vulnerabilities of different demo- graphic groups to hunting and bycatch. Moreover, our model revealed possible changes in ringed seal haul-out behavior in response to changing sea ice patterns. The mechanistic nature of our model additionally enabled near-term predictions of pop- ulation response to changes in hunting quotas, in - forming management decisions. Wildlife populations across the globe are increas- ingly exposed to novel conditions that fundamentally alter their dynamics. The recent difficulties in mon- itoring and managing ringed seals in the Bothnian Bay may foreshadow similar challenges elsewhere. Our study demonstrates the value of mechanistic IPMs for monitoring populations in uncertain and rapidly changing environments, testing ecological hypotheses regarding mechanisms of change, and supporting science-based management decisions. IPMs such as ours could be developed into digital twins of their target populations (de Koning et al. 2023, Trantas et al. 2023). Embedding these models and Bayesian inference software within a user- friendly interface could substantially streamline re - search and monitoring efforts, as well as hasten man- agement responses. We believe that the modeling approach presented here will pave the way towards the embrace of IPMs as digital twins of wildlife pop- ulations, which could prove to be a critical compo- nent of the adaptive management toolkit in a rapidly changing world. Given the accelerating pace of anthropogenic change, we anticipate increasing adop- tion of IPMs in studies of wild animal populations. Data availability. Code and data are available on Zenodo at https://doi.org/10.5281/zenodo.14243458. Acknowledgements. The present work is based on the MSc thesis of M.E. The work received funding from the Helsinki Institute of Life Science (HiLIFE) (M.E.), Research Council of Finland (grant 317255), and Jane & Aatos Erkko Founda- tion (J.V.). In addition, J.V. acknowledges funding from the European Union (ERC Consolidator Grant BEFPRE- DICT, 101087409). The monitoring of ringed seals in the Bothnian Bay was conducted by the Swedish Museum of Natural History and funded by the Swedish Environmental Protection Agency and the Swedish Agency for Marine and Water Management. The Finnish monitoring of seals was funded by the Ministry of Agriculture and Forestry. We thank Yessenia Rojas, Jannikke Räikkönen, Petri Timonen, and Charlotta Moraeus for help in age determinations, and Eva Kisdi for support in building the mathematical models. Finally, we are grateful to the 2 anonymous reviewers for their valuable in sights and constructive feedback, which have greatly strengthened this paper. LITERATURE CITED Abadi F, Gimenez O, Arlettaz R, Schaub M (2010) An assess- ment of integrated population models: bias, accuracy, and violation of the assumption of independence. 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