# Mapping sex-and age-structure reveals lonely males at the front in an expanding brown bear population

Ana Sanz-Pérez, Victor Sazatornil, Santiago Palazón, Cécile Vanpé, Pierre-Yves Quenette, Jérôme Sentilles, Maëlis Kervellec, Cyril Milleret, Jose Vicente López-Bao, Ivan Afonso, et al.

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## To cite this version:

Ana Sanz-Pérez, Victor Sazatornil, Santiago Palazón, Cécile Vanpé, Pierre-Yves Quenette, et al.. Mapping sex-and age-structure reveals lonely males at the front in an expanding brown bear population. Biological Conservation, 2025, 306, pp.111122. 10.1016/j.biocon.2025.111122. hal-05024683

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# Mapping sex- and age-structure reveals lonely males at the front in an expanding brown bear population

Ana Sanz-Pérez<sup>a,b,c,d,e,f</sup>, Victor Sazatornil<sup>b</sup>, Santiago Palazón<sup>e</sup>, Cécile Vanpé<sup>f</sup>, Pierre-Yves Quenette<sup>f</sup>, Jérôme Sentilles<sup>f</sup>, Maëlis Kervellec<sup>g</sup>, Cyril Milleret<sup>h</sup>, Jose Vicente López-Bao<sup>d</sup>, Ivan Afonso Jordana<sup>i</sup>, Ramón Jato<sup>j</sup>, Jordi Solà de la Torre<sup>k</sup>, Rahel Sollmann<sup>a</sup>

## ARTICLE INFO

### Keywords:

- Density

- Distribution

- Population dynamics

- Population projections

- Pyrenees

- Range expansion

- Small population

- OPSCR

## ABSTRACT

Range expansion is a common feature of invasive, reintroduced, and recovering populations. This process is driven by population growth and dispersal, and intrinsic species characteristics and dispersal mechanisms yield contrasting population structures in space. The spatial distribution of sex and age classes is key to understanding and forecasting range expansions, but mapping age and sex categories is methodologically challenging. Here, we develop an age-structured open population spatial capture recapture (OPSCR) model to understand how spatial sex and age structures can shape population dynamics, as well as recovery processes. We use the endangered Pyrenean brown bear population as a case study, analysing non-invasive monitoring data from 2017 to 2021. Results revealed an expansion front dominated by adult (>4 years) and subadult males (2-4 years), while females and juveniles (<2 years) prevailed at the core. This, together with an overall decrease in density towards the expansion front in spite of available habitat, suggest an expansion process constrained by female philopatry. Future projections suggest continued population growth even under demographic stochasticity, and potential for population spread with increased reproduction events at the periphery. Our novel OPSCR model allows for statistically rigorous mapping of the sex and age structure of a population from non-invasive monitoring data. This is an important step towards better understanding and predicting the dynamics of recovering populations worldwide. In the case of large carnivores, it could inform conservation action such as anticipating the adoption of damage prevention measures and raising awareness campaigns to improve co-existence in future expansion areas.

## 1. Introduction

While human activity is reducing the distribution of many species (Díaz et al., 2019), some species – native and invasive – are expanding

their ranges (Bellard et al., 2018; Chapron et al., 2014). Range expansion is driven by population growth and dispersal (Burton et al., 2010); and the dispersal process is often biased to specific life stages, age, and sex (Greenwood, 1980). Age at dispersal drives the spatial structure of

<footnote><sup>a</sup> Department of Ecological Dynamics, Leibniz Institute for Zoo and Wildlife Research, Berlin, Germany</footnote>

<footnote><sup>b</sup> Biodiversity Conservation and Management Program, Centre de Ciència i Tecnologia Forestal de Catalunya (CTFC), Solsona, Spain</footnote>

<footnote><sup>c</sup> Departament de Biologia Evolutiva, Ecologia i Ciències Ambientals. Universitat de Barcelona, Facultat de Biologia, Avinguda Diagonal, 643, 08028 Barcelona, Spain</footnote>

<footnote><sup>d</sup> Biodiversity Research Institute (CSIC - Oviedo University - Principality of Asturias), University of Oviedo, E-33600 Mieres, Spain</footnote>

<footnote><sup>e</sup> Fauna and Flora Service, Department of Climate Action, Food and Rural Agenda, Generalitat de Catalunya. Carrer del Foc, 57, 08038 Barcelona, Spain</footnote>

<footnote><sup>f</sup> Service Conservation and Gestion des Espèces à Enjeux, Direction de la Recherche et de l'Appui Scientifique (DRAS), Office Français de la Biodiversité (OFB), Villeneuve de Rivière, France</footnote>

<footnote><sup>g</sup> CEFE, University of Montpellier, CNRS, EPHE, IRD, Montpellier, France</footnote>

<footnote><sup>h</sup> Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Ås, Norway</footnote>

<footnote><sup>i</sup> Departament de Territori, Paisatge e Gestion Ambientau, Conselh Generau d'Aran, Plaça d'Aran 1-2, 25530 Vielha, Spain</footnote>

<footnote><sup>j</sup> Área de Biodiversidad, Sociedad Aragonesa de Gestión Agroambiental (SARGA - Gobierno de Aragón), 22004 Huesca, Spain</footnote>

<footnote><sup>k</sup> Departament de Medi Ambient i Sostenibilitat, Ministeri de Medi Ambient, Agricultura i Ramaderia, Govern d'Andorra, Andorra</footnote>

<footnote>* Corresponding author at: Department of Ecological Dynamics, Leibniz Institute for Zoo and Wildlife Research, Berlin, Germany.
E-mail address: anasanz.asp@gmail.com (A. Sanz-Pérez).</footnote>
different age categories (Reichert et al., 2016), while sex-biased dispersal – performed mainly by males in most birds and mammals (Greenwood, 1980) – leads to uneven sex ratios at the expansion front (Miller and Inouye, 2013). These factors can, in turn, affect the dynamics of range expansion (Phillips, 2009). For instance, Allee effects (i.e., increased costs of finding a mate at low densities) can intensify at the expansion front under male-biased dispersal, where leading-edge males are less likely to find mates (Travis and Dytham, 2002). The subsequent low levels of reproduction result in old age structures at the periphery, slowing range expansion (Chuang and Peterson, 2016; Miller and Inouye, 2013).

Understanding the spatial distribution of sex and age in expanding populations can provide relevant information for conservation (Bogich et al., 2008; Bubac et al., 2019). For instance, it can help determining the contribution of intrinsic (Lafferty and Tinker, 2014; Miller and Inouye, 2013; e.g., philopatry or dispersal capability; Schloss et al., 2012) or extrinsic factors (landscape connectivity; Fletcher et al., 2018; e.g., habitat suitability; Reichert et al., 2016) to expansion processes. It can also be useful to identify regions of high conservation concern and guide conservation action (e.g., enhance breeding in areas switching to old age structures; Reichert et al., 2016). For species with potential for human-wildlife conflict, such as large carnivores, forecasting the spatially explicit fate and age structure of a population can help anticipating the adoption of damage prevention measures, and raising awareness on human-wildlife co-existence in areas of future range expansion (Eklund et al., 2017; e.g., campaigns to reduce human-bears encounters, to perform hunting or forestry practices compatible with bear presence, or to decrease livestock predation; Linnell et al., 2008).

Although most large carnivores are globally declining (Ripple et al., 2016), some populations are growing and expanding (Boitani et al., 2022; e.g., in Europe; Chapron et al., 2014). This increases the number of human-carnivore interactions (Packer et al., 2013), and certain sex and age classes can be overrepresented among conflict individuals (Elfström et al., 2014). Among large carnivores, the Brown bear (*Ursus arctos*) is a solitary and non-territorial species presenting male-biased dispersal and female philopatry (although some females can disperse; Swenson et al., 1998), which has been suggested as determining features of its spatial population structure (Steyaert et al., 2012; Støen et al., 2005; Swenson et al., 1998). Given the historic declines of bear populations worldwide (Servheen, 1990), bears have been the subject of several reintroduction programs with varying success (Clark, 2009; Clark et al., 2001), some of them resulting in population expansion.

The endangered Pyrenean brown bear constitutes an example of population recovery after reinforcement. Several translocations between 1996 and 2018 (11 bears in total) prevented the population from going extinct in the mid-1990s, when only 5 individuals remained (Camarra and Dubarry, 1997). The population has since grown to ~83 individuals ranging over 5700 km² (minimum number of individuals known alive; Sentilles et al., 2024). Nonetheless, it still constitutes one of the most endangered bear populations in Europe due to its low population size, high inbreeding (Bassi, 2021), and fragmentation in two nuclei (Sentilles et al., 2021). Aside from extrinsic factors such as availability of suitable habitat (Martin et al., 2012) and habitat connectivity (Dumortier, 2022; Kervellec et al., 2023), intrinsic biological traits (e.g., female dispersal; Halotel, 2022) likely shape the expansion of this population. However, the contribution of intrinsic traits to the dynamics and future population expansion remains poorly understood.

Studying spatially explicit population dynamics in large carnivores is challenging, owing to their cryptic behaviour resulting in imperfect detection of individuals over time. Capture-recapture methods provide a robust framework to estimate demographic processes while accounting for imperfect detection (Lebreton et al., 1992). Previous age-structured models have focused on estimating survival by conditioning on an individual's first capture, circumventing the problem of unobserved ages for individuals never captured, but not allowing abundance estimation (Lebreton et al., 1992; Pledger et al., 2003). Hostetter et al. (2021)

developed an open-population age-structured capture-recapture model that addresses this issue. In addition, the recent development of Open Spatial Capture-Recapture models (OPSCR), which explicitly incorporate information on the spatial location and movement of individuals, allow estimating population dynamics in space (Gardner et al., 2018, 2010). However, so far, age-structure has not been integrated into OPSCR.

Here, we develop and apply an age structured OPSCR model to the Pyrenean bear population to quantify how the spatial sex and age structure can shape population dynamics and to reveal ecological factors determining population expansion, opening new pathways for conservation action. We fit the model to non-invasive genetic monitoring data of the Pyrenean bear population collected from 2017 to 2021, and estimated age and sex-specific spatially explicit population dynamics. We predicted 1) a decrease of overall density with increasing distance to the population origin (Jerina and Adamić, 2008; Moqanaki et al., 2023); and 2) a spatial shift in sex and age structure with a higher proportion of juveniles and adult females at the core than at the periphery. Such patterns would suggest an expansion limited by female philopatry. We illustrate the potential of this modelling approach to inform conservation actions, by projecting density and abundance into the future under different scenarios.

## 2. Material and methods

### 2.1. Study area

The study area was in the Pyrenees mountains and covered the transboundary bear population range (~10,622 km²) across northern Spain, southern France, and Andorra (Fig. 1a). The Pyrenees are characterized by large massifs and valleys with steep slopes and elevation ranging from 500 to 3400 m. The landscape is composed of ~40 % deciduous and coniferous forests (dominated by beech *Fagus sylvatica* and silver fir *Abies alba*), interspersed with open shrublands (*Rhododendron ferrugineum*, *Vaccinium myrtillus*), alpine pastures above 1800 m, and pine forests (*Pinus uncinate*, *Pinus sylvestris*) in the south (Martin et al., 2012). Road density averages 3.8 km/km² and is mostly concentrated in the valleys (Kervellec et al., 2023). Human activities such as forestry, extensive farming practices (mostly sheep), and recreational activities shape the landscape.

### 2.2. Data collection and individual identification

We used non-invasive individual detection data collected from 2017 to 2021 within the long-term monitoring program of the population (Sentilles et al., 2022). We used detection data obtained from two types of traps (Vanpé et al., 2022): hair snags baited with beech tar, aimed at the genetic identification of individuals, and the same baited hair snags combined with camera traps, also allowing detection of females with cubs or juveniles (Kervellec et al., 2023). Traps were visited monthly from May to November (7 sampling occasions), except for the traps in areas with reproductive females in France that were visited twice per month in May, June, and September. Given the highly isolated character of the population, its low mortality and the ecology of the species (i.e., recruitment occurring during hibernation, before the sampling period), the population was considered closed from May to November.

Hair samples were used to identify individual genotypes. Samples were analysed at the ANTAGENE laboratory (France) and the UAB University (Spain), using 13 microsatellite markers (Vanpé et al., 2022). Individuals detected since the beginning of population recovery in 1996 have been exhaustively monitored and identified since birth, which allowed us to know the pedigree of the population, and the exact age and sex of all detected individuals. Bears were classified into three age categories: juveniles (individuals until 2 years of age), subadults (3 and 4 years), and adults (> 4 years) (Chapron et al., 2003; Vanpé et al., 2022). Cubs until three months of age remain in their natal dens, so they are not
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Estimated age structure of the Brown bear population studied during 2017–2021 at the core and periphery of its distribution range in the Pyrenees (Fig. 1a, top left). Fig. 1b (top right) shows the age structure, represented by the proportion of individuals of each sex and age category throughout the study period. For each age category, we show the spatial arrangement of individuals using the density (n° of bears / 25 km²) in year 2021 as an example (Fig. 1c, bottom left; see Figure S2, SI 3, for all years), and the evolution of density per sex across time at the core and periphery of the distribution range (Fig. 1d, bottom right). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

represented in our sample (Planella et al., 2019), and data from the first months of life after leaving the den was very limited. Therefore, our youngest age category includes both mobile cubs and juveniles.

## 2.3. OPSCR model

SCR models provide spatially explicit density estimates by estimating the number and location of individual activity centres (ACs, a latent variable) from spatial individual detection data (Efford, 2004; Royle et al., 2014). The number and locations of ACs are estimated by

combining a spatial point process model, which describes the distribution of ACs, and a detection process model, which uses individual detections to estimate the detection probability conditional on the distance to the individual AC (Milleret et al., 2020; Royle et al., 2014). SCR assumes that ACs are located within a state space S encompassing the sampling grid and a surrounding buffer area, which needs to be large enough to include all individuals that could have been exposed to sampling. We buffered the most extreme coordinates of the grid by 25 km to define S (~ 3.5 times male σ; see Detection component; Kervellec et al., 2023), which we discretized to a 5 × 5 km grid (~ 0.5 times female
σ). Open-population SCR models integrate the information of multiple surveys over time, also called primary occasions (i.e., years in our study), and allow modelling demographic parameters (e.g., survival and recruitment) and movement of individuals between primary occasions (Bischof et al., 2020; Gardner et al., 2018, 2010). Our OPSCR model integrates three different components (Figure S1, SI 2): 1) Demography; 2) Density and movement; and 3) Detection

### 2.3.1. Demography: Age-structured model

To build an age-structured OPSCR model, we combined OPSCR with the approach of Hostetter et al. (2021). Their non-spatial Jolly-Seber model uses known age at first capture to inform the alive state $z_{it}$ of individuals i in all previous primary occasions t. For example, an individual first detected as a 2-year-old is considered alive and part of the population in the previous year. With this model formulation, individuals cannot be first recruited as a > 1-year old. Therefore, the model assumes no recruitment through immigration (only through local birth), which is a reasonable assumption for our isolated study population. The model uses data augmentation with a superpopulation formulation (Royle and Dorazio, 2008), where the superpopulation includes all animals (M) that are part of the population at any point of the study period. Each individual i is part of the superpopulation with probability ψ:

$$w_i \sim \text{Bernoulli}(\psi) \qquad (1)$$

where $w_i=1$ if the individual is part of the superpopulation and $w_i = 0$ otherwise. Individuals enter the superpopulation each year according to a multinomial process:

$$\mathbf{m} \sim \text{Multinomial}(\beta, M) \qquad (2)$$

where m is the number of individuals entering the superpopulation each year with year-specific recruitment probabilities β. Recruitment probabilities are reformulated as conditional probabilities η (i.e., individual probability of recruitment conditional on not being recruited yet):

$$\eta_1 = \beta_1 \qquad (3)$$

$$\eta_{t>1} = \beta_t / \left( 1 - \sum_{l=1}^{t-1} \beta_l \right), \quad t = 2, 3, \dots, T \qquad (4)$$

This formulation ensures that all individuals in the superpopulation but not yet recruited at time T-1 will be recruited at time T.

At t = 1, individual age, $x_{i1}$ (defined as the numeric age of individual i in year 1) is a categorical random variable, with probabilities π (corresponding to the age distribution of the population in year 1). We expand π to include a category for individuals not yet alive at t = 1 (for which we define $x_{i1} = 0$). We describe age unconditional on being alive as:

$$(x_{i1} + 1) \sim \text{Categorical}(\pi'_{1:(A+1)}) \qquad (5)$$

where the purpose of indexing ($x_{i1} + 1$) is that age 0 corresponds to the first age category, and A is the maximum possible age in year 1. Considering that $\pi'_{1}$ corresponds to the probability of not being recruited in year 1 ($\pi'_{1} = 1 - \eta_{1}$; see Eq. 3), we can describe the starting age distribution as:

$$\pi'_{1:(A+1)} = ((1 - \eta_1)(\eta_1 \pi_{1:A})) \qquad (6)$$

Our age distribution π consisted of five age classes (one class per year of age, except the last class that included all individuals ≥5 years old).

The alive state of individual i in year 1 ($z_{i1}$) is subsequently assigned as a deterministic function of age, where:

$$z_{i1} = 1 \text{ if } x_{i1} > 0 \qquad (7)$$

$$z_{i1} = 0 \text{ if } x_{i1} = 0$$

After year 1, aging occurs annually according to:

$$x_{it} = (x_{it-1} + 1) \left( 1 - \prod_{l=1}^{t} (1 - z_{il}) \right) \qquad (8)$$

where the second term of the equation ensures that individuals remain at age 0 while they are not recruited.

The state process of subsequent years is determined by individuals surviving if they are alive or being recruited if they have not previously entered the population:

$$z_{it} \sim \text{Bernoulli} \left( \phi_{c|t} z_{it-1} + \eta_t \prod_{l=1}^{t-1} (1 - z_{il}) \right) \qquad (9)$$

Here, the second term ensures that individuals not yet recruited enter with a recruitment probability $\eta_t$ and $\phi$ represents the survival probability of individuals already present. We estimated $\phi$ for the three age categories c (juveniles: age 1 and 2, subadults: age 3 and 4, adults: age 5 and up).

### 2.3.2. Density and movement

We modelled the distribution of individual ACs by using an inhomogeneous binomial point process (Borchers and Efford, 2008; Zhang et al., 2023), which allows the density of ACs to vary according to a spatial intensity function (Supporting Information: SI 2). We defined the intensity function as a linear function of the distance to origin (DO). The definition of the origin was based on the location of remaining individuals in 1995 and reproductive translocated females (SI 1). This resulted in four polygon areas defined as the origin. We then calculated the distance from each 5 × 5 km grid cell of the state space to the nearest polygon border. The location of individual ACs in the first year is modelled as a function of DO. Because female bears are known to be philopatric, whereas males are more likely to disperse (Swenson et al., 1998), we allowed the effect of DO to vary by sex. Because the spatial behaviour of the mother is tightly linked to that of its cubs and juvenile individuals (Martin et al., 2008), we restricted juveniles of both sexes to have the same DO effects as females. Movement of individual ACs between years was modelled as a first-order Markov process (Gardner et al., 2018) where the location at t followed a bivariate normal distribution centred on the location at t − 1. To maintain the effect of DO on bear distribution for t > 1, the probability density of ACit was also conditional on the habitat intensity (Bischof et al., 2022, 2020; Zhang et al., 2023). See SI 2 for further details.

### 2.3.3. Detection

Detection data y consists of encounter histories that are specific for each individual i, trap j, study year t (primary occasion), and secondary sampling occasion k. Conditional on being alive ($z_{it} = 1$), detections are modelled as

$$y_{ijkt} \sim \text{Bernoulli}(p_{ijkt}) \qquad (10)$$

where p is the probability of detection. We used a half-normal detection function to describe a decrease in p as distance from the AC increases (Royle and Converse, 2014):

$$p_{ijkt} = p_{0_{ijkt}} e^{-\frac{d_{ijkt}^2}{2\sigma^2}} \qquad (11)$$

Here, d is the Euclidean distance from the trap j to ACit and σ represents the scale parameter of the detection function. We estimated sex-specific σ because males are known to have larger home ranges than females (Dahle and Swenson, 2003). We modelled the unknown sex of augmented individuals as a Bernoulli random variable (sex$_i \sim \text{Bernoulli}(\Omega)$), where Ω represents the proportion of males. Because the movement of the mother is tightly linked to that of its cubs and juvenile individuals (Martin et al., 2008), we restricted juveniles of
both sexes to have the same σ as females.

We estimated the baseline detection probability ($p_{0_{jk}}$; detection probability when the individual AC is at the trap location) separately for each of the three age categories. We modelled variation in $p_{0_{jk}}$ as a function of covariates known to explain spatio-temporal heterogeneity in bear detection in the same population (Kervellec et al., 2023). See SI 2 for further details.

## 2.4. Model implementation

We implemented the model in a Bayesian framework using Markov chain Monte Carlo (MCMC) simulation with NIMBLE (de Valpine et al., 2023). We fitted the model in R (v4.1.3; R Core Team, 2021), and used the R package “nimbleSCR” (v0.2.0; Bischof et al., 2022). We ran three chains of 50,000 iterations thinned by 10 and a 1000-iteration burn-in period. We tested for chain convergence by visual inspection of trace plots and using the Gelman–Rubin statistic (values <1.1; Gelman et al., 2013). We used standard vague priors (Beta or Dirichlet with all-1 parameters for probabilities, Normal (0,10) for covariate coefficients). We summarized posterior distributions of structural parameters by using their mean and 95 % BCI (Bayesian Credible Interval). We used the Bayesian posteriors to derive quantities of interest (see next section) and reported their mean/median and associated uncertainty. Links to data, scripts and model code are provided in the Data availability statement.

## 2.5. Derived quantities

### 2.5.1. Density and abundance estimation

We evaluated spatiotemporal patterns in the Pyrenean bear population by estimating annual density and abundance from 2017 to 2021. The state-space S includes areas that are theoretically suitable for bears, but in practice outside the current distribution range. To avoid over-estimating total abundance, we reported abundance estimates within the current distribution range, which was defined by a buffer of 8500 m (~ average home range radius; Kervellec et al., 2023) around the sampling array. Even though the intensive monitoring of the population points towards the absence of bears outside the distribution range, the ACs of three observed individuals known to be alive in the sampling period fell outside this area (Figure S2, SI 2), so we buffered their AC across years by the same width and included the resulting polygon in the distribution range.

To address our questions of whether sex and age categories are distributed differently in space and the link to population expansion, ideally, the model should have contained sex, age and year-specific effects of DO as well as sex and age-specific interannual movement parameters. Owing to the model complexity and the data sparseness for some age categories, this was not feasible. As such, we cannot formally explore the contribution of the different processes (e.g., survival, reproduction, movement) to population expansion. Instead, we mapped realized sex and age specific annual densities by summing the number of ACs of alive individuals in each habitat grid cell and visually examined these maps. We obtained total and sex-age-specific annual abundance estimates by summing the density values of all grid cells in the distribution range.

### 2.5.2. Demographic structure at core and periphery

To contrast sex and age population structure at the core versus the periphery (i.e., expansion front), we created a buffer around the pre-defined population origin (Fig. 1) with a width equivalent to the female average dispersal distance in this population (~10,000 m; Sanz-Pérez and Sazatornil, 2021). The resulting core of the population included both the population origin and the central stronghold of the current population (~3969 km²). The periphery constituted the current distribution range outside the core of the population (~6654 km²). We calculated age-sex-specific density at both the core and periphery. The

sex-age structure was derived as the density of each sex and age category alive in proportion to the total density present in each zone ($N_{sex.cat.zone}/N_{zone}$).

## 2.6. Future projections

To project population trajectory, we performed posterior predictions from the fitted OPSCR model. Following Bischof et al. (2020), we used a set of posterior samples (i.e., 5000 randomly selected iterations) and generated predictions from these samples based on the fitted OPSCR model for future years with no data, thus fully propagating uncertainty. We restricted our projections to five years (2022–2026) to avoid excessive uncertainty posed by longer time series. Because the super-population formulation of our OPSCR model provided conditional recruitment probabilities (Eq. 4), we reparametrized the recruitment process in the projection model as

$$R_t = \gamma_{t-1} * \rho$$

Here $R_t$ is the number of recruits in year t, $\gamma_{t-1}$ is the number of adult females at t − 1 and $\rho$ is the per-capita recruitment rate. We derived $\rho$ from the OPSCR model output by dividing estimates of $R_t$ by estimates of adult female population size at t − 1 and averaged its values across all t > 1. We used the projection model for two types of future projections:

### 2.6.1. Demographic projection

We first considered a scenario with no change in the current demographic parameters (Scenario 0). To mimic stochasticity in survival, we then simulated the loss of adult females, which are often the limiting factor of bear population growth (Wiegand et al., 2004, 1998). We created scenarios removing between 5 and 20 % of the females in the year 2021.

### 2.6.2. Spatial projection

Density was negatively affected by the distance to the origin of the population, suggesting that population expansion is affected by its historical distribution (Table S2, SI 3; Moqanaki et al., 2023). Future population expansion could differ depending on whether this effect remains constant or relaxes across time (e.g., in the case of emergent reproductive cores outside the origin). We considered a scenario where the effect of distance to origin (DO) remains constant, and another scenario where the effect decreases by 10 % each year. The decreasing effect of DO was chosen arbitrarily to show the potential of the model in predicting the spatial fate of age-structured populations.

## 3. Results

Between 2017 and 2021, we identified 61 individuals from the 680 genetic samples that allowed successful individual identification. On average, annual data contained 13 samples of juveniles (sd = 9.5), 10 of subadults (sd = 5.7), and 112 of adults (sd = 55.7). The number of samples increased from 105 in year 2017 to 216 in year 2021 (Table S1, SI 3).

### 3.1. Population dynamics and density

Adult bears (> 4 years old) presented the highest survival estimates (Mean [95 % BCI] = 0.96 [0.89 - 0.99]), followed by juveniles (≤ 2 years old; 0.90 [0.72 - 0.99]), then subadults (0.86 [0.71 - 0.97]; Table S2, SI 3). Average per-capita recruitment per female was 0.71 (95 % BCI = 0.4 - 1.19). The annual age structure in the population remained fairly constant over time, with, on average, 32 % juveniles, 22 % subadults and 46 % adults (Figure S1, SI 3; Fig. 1d). The sex ratio of the population was skewed, with a male proportion of 0.34 (95 % BCI = 0.32 - 0.34). Bear abundance increased over time, from 53 individuals (95 % BCI = 45 - 64) in 2017 to 80 individuals (95 % BCI = 64 - 99) in 2021 (Fig. 2a, 3). Bear density was negatively affected by distance to origin, with males
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Evolution of density (bears / 25 km²) of the Pyrenean Brown bear population during 2017–2021, including all individuals analysed according to the OPSCR data model (Fig. 2a, top maps). The bottom maps (Fig. 2b) show the spatial projection of the population during 2022–2026 under a scenario where the effect of the Distance to Origin density covariate remains constant (~ DO: Mean = -0.371 across years; Table S2, SI 3), and an scenario were its effect decreases across time (↓ DO: Mean decreases by 10 % every projected year from 2022 to 2026). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Abundance estimates obtained using an OPSCR model on the Pyrenean Brown bear population during the period 2017–2021 (brown violins). The future projection of the population under a scenario of no change in demographic parameters (Sc0, dark green violins), and under stochastic events of different intensities expressed as proportional loss of females in the year 2021 (Sc1–4, see legend for violin colours), are shown for the period 2022–2026. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

showing a marginally weaker effect than females ($\beta.DO_{female} = -0.37$ [−0.57 – (−0.17)]; $\beta.DO_{male} = -0.32$ [−0.62 – (−0.01)]; Table S2, SI 3; Fig. 2a). The movement parameter between study years $\tau$ was 8.23 km [95 % BCI = 6.63 – 10.23] (Table S2, SI 3). See SI 3 for results on the Detection component.

## 3.2. Age-sex structure at core and periphery

Juveniles were principally located at the core of the population

(Fig. 1c) and showed a higher density therein for both sexes (Fig. 1d). However, the age structure (density of sex-age class relative to total density in each zone) showed the same proportion of juveniles at both the core and periphery (Fig. 1b), which was due to the high density of females at the core (Fig. 1d). Subadults presented the lowest density estimates (Fig. 1c, d). The spatial distribution of subadults and adults differed between sexes: males were present at a higher proportion at the periphery, and females at the core (Fig. 1b). Male adult density remained similar and low at both the core and periphery (Fig. 1d), but
the proportion of males compared to the rest of the population was higher in the periphery (Fig. 1b). This sex-skewed pattern at the core and periphery was similar when considering all age categories of the population (Fig. 1b, d).

### 3.3. Future projections

Projections with constant demographic parameters (Scenario 0) showed an increase in population size up to an average 146 individuals in 2026, with a high level of uncertainty (sd = 41.61; Fig. 3). The increasing loss of females (from 5 to 20 %) slowed down population growth but did not lead to a decline (Fig. 3). The probability of extinction after five projected years (calculated as the proportion of posterior projections that reached 0) remained 0 in all scenarios (Fig. 3). The spatial projection of the population from 2022 to 2026 resulted in a progressively increasing density at the core of the population for the scenario of constant effect of DO, while the scenario of a decreasing effect of DO across time resulted in a more even increase of density across the bear range (Fig. 2b).

## 4. Discussion

Our novel age-structured OPSCR model quantified for the first time spatially explicit age-sex structure at the population level using non-invasive monitoring data, while accounting for various sources of sampling bias. The expansion front of the Pyrenean bear population was mainly driven by adult and subadult males, while females and juveniles remained at the core. Overall bear density was highest in the area where the population originated and decreased with distance from this area, and the effect of the origin on density was only marginally weaker for males than females. These results meet our prediction on the overall and sex-age specific distribution of brown bears in space. They also confirm previous studies on the structure of expanding bear populations largely based on harvest data (Slovenia/Italy: Jerina and Adamić, 2008; e.g., Scandinavia: Swenson et al., 1998), which is usually limited to adults, biased towards males (Bischof et al., 2008), and not available for fully protected populations.

In spite of its continued growth and the large amount of available suitable habitat (Martin et al., 2012), the Pyrenean bear seems to be expanding slowly. The observed spatial sex-age-structure, combined with an overall decrease in density with increasing distance to the population origin, is likely contributing to its slow expansion (see also Moqanaki et al., 2023). These results point towards female philopatry – an intrinsic biological trait – as one of the ultimate mechanisms limiting brown bear population expansion (Jerina and Adamić, 2008; Støen et al., 2005), a pattern that is comparable to other small bear populations (e.g., Palomero et al., 2021).

Still, female brown bears do disperse (i.e., 35 % in the Pyrenees: Halotel, 2022; Karamanlidis et al., 2021; Støen et al., 2006), even before carrying capacity has been reached (pre-saturation dispersal; Swenson et al., 1998). A visual assessment of female AC locations over our five study years showed movement patterns mostly restricted to the core (SI 4). Low dispersal distances in females (Halotel, 2022) restricted to the core likely contribute to limited reproduction events at the periphery, highlighting the importance of female long-dispersal events for the expansion of this population. Thus, further research identifying landscape factors that inhibit female dispersal could aid in developing habitat management actions. Aside from intrinsic biological features, the influence of extrinsic factors modulating population expansion such as habitat connectivity (Kervellec et al., 2023), human tolerance towards sharing the landscape (Herrero et al., 2021), or human-related mortality (i.e., after encounters with hunters, poaching or retaliatory killing; Boitani et al., 2015; Carter et al., 2017), deserves further investigation.

Reproduction and survival were high during the study period. With an average of 0.70 juveniles raised annually per adult female across

study years, the Pyrenees population surpassed many other bear populations worldwide (i.e., ranging from 0.23 in Deosai National Park, Pakistan, to 0.96 in the Scandinavian population; Steyaert et al., 2012). Survival estimates were high and comparable among age classes. Adult survival estimates were similar to those previously found in this (Chapron et al., 2009; Vanpé et al., 2022) and other bear populations (Garshelis et al., 2005; McLellan et al., 2021). The study of Vanpé et al. (2022) based on a longer time frame yielded higher subadult survival estimates (Mean ± sd = 0.95 ± 0.028), so survival of this age class might be decreasing; however, differences may also stem from their non-spatial modelling framework. Our estimates of juvenile survival were higher than in previous studies of the same (Vanpé et al., 2022) and other populations (e.g., McLellan et al., 2021). This could be related to the fact that individuals up to two years old were assigned to the juvenile age class, owing to sample size limitations. Further, the non-invasive data are likely biased towards older juveniles: once cubs are detectable, they are moving with their mother and have already survived the most vulnerable period when leaving their den (Planella et al., 2019). Thus, our estimates should not be applied to early cub survival. High juvenile survival might also be explained by the low adult male proportion at the core, which may reduce the likelihood of infanticide, the main mortality cause for cubs (Planella et al., 2019).

Abundance estimates reflected an increase in population size, supporting previous population assessments (Vanpé et al., 2022). A major mechanism behind fluctuations in population size are changes in age structure, by influencing population growth rates (Hoy et al., 2020). The Pyrenean bear age structure was characterized by a high proportion of juveniles across years. The increasing population size, young age structure, and overall high survival and recruitment are typical from growing populations (e.g., Templeton et al., 2022). Finally, we estimated a female-biased sex ratio, which was previously suggested for this population (Vanpé et al., 2022), but does not agree with other bear populations showing an even sex ratio (Bellemain et al., 2005). We may be overestimating the proportion of females in the population. Namely, we defined a single distribution range to calculate bear abundance for both sexes (by counting ACs within that range). Because females in this population remain more concentrated in the core, their current range may be more limited than that of males. By counting ACs of females outside of their actual current range, we may be overestimating total female abundance.

The high complexity of the model and spareness of the data imposed further limitations. We were unable to add other relevant covariates on density or to make parameters specific to age-sex classes (e.g., inter-annual movement) or year (e.g., effect of DO). Spatially explicit survival and reproduction also likely contribute to the observed distribution of individuals, but were not considered in our model. Because of that, we were limited to mapping realized densities to evaluate differences in spatio-temporal distribution of the different sex-age classes. This approach has been criticised as it is focused on detected individuals, dependent on sampling intensity (Durbach et al., 2024), and can lead to unrealistic distribution patterns (Murphy et al., 2017). We believe that this approach is nonetheless valid for the present population, as its extensive and intensive monitoring leaves few individuals undetected and little if any area within the distribution range unsampled. This may not hold, however, in other applications.

Under current demographic conditions, our model projections showed a steady population growth till 2026. The extreme upper limits of the 95 % BCI for 2026 (Fig. 3) should not be misconstrued as actual possible future population sizes; rather, they constitute a methodological artefact resulting from increased uncertainty as predictions are made further into the future (see also Bischof et al., 2020), using a model that contains no abundance-limiting mechanisms such as density dependence. Future population stability did not seem affected by even a 20 % female loss, and the probability of extinction over 5 years remained zero in all scenarios. Current population resilience to stochastic events indicates an improvement in population viability compared to previous
assessments, and confirms the success of the translocation program (Chapron et al., 2003). Both projections have limitations, for example, they do not consider habitat connectivity or inbreeding (Bassi, 2021; e. g., Benson et al., 2016). Moreover, the model has no mechanism to limit juvenile recruitment (spatially and temporally) to the presence of adult females (Chandler et al., 2018; Milleret et al., 2022).

Our approach constitutes a powerful tool to inform managers on population viability and possible outcomes of population management. Our simulation of the impact of losing reproductive females can easily be adjusted to evaluate the effect of additional translocations into a population or other management actions. Beyond future projections, mapping the spatially explicit sex and age structure of a population is in itself of high value to inform conservation action. For instance, the concentration of reproductive females and their offspring near the historic core highlights the continued importance of these areas for this population, and suggests that conservation measures in these areas (e.g., limit human access to certain sensitive zones during specific periods such as den exit) would be beneficial to ensure future population performance. The spatial sex-age distribution of the Pyrenean bear population further showed areas adjacent to the population core presenting low female density and relatively high subadult and adult male density (Figure S4, SI 3). As these can be interpreted as potential expansion areas of the reproductive core, they are important areas to allocate efforts to reduce human-bear conflicts, such as performing campaigns to avoid human-bear encounters, or increasing prevention measures for livestock preparation. Finally, the observed spatial population structure suggests that enhancing reproduction at the periphery could aid its spatial expansion. Thus, additional female translocations – if implemented – should be focused on peripheral areas with suitable habitat and males (i.e., as the ones suggested in Figure S4, SI 3). Combined with strategies mitigating human-bear conflict, these actions could help this endangered bear population recolonize more of its former range.

### CRediT authorship contribution statement

**Ana Sanz-Pérez:** Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation, Conceptualization. **Victor Sazatornil:** Writing – review & editing, Project administration, Investigation, Funding acquisition, Data curation. **Santiago Palazón:** Writing – review & editing, Investigation, Funding acquisition. **Cécile Vanpê:** Writing – review & editing, Investigation, Funding acquisition. **Pierre-Yves Quenette:** Writing – review & editing, Investigation, Funding acquisition. **Jérôme Sentilles:** Writing – review & editing, Investigation, Data curation. **Maëlis Kervellec:** Writing – review & editing, Methodology, Investigation, Data curation. **Cyril Milleret:** Writing – review & editing, Validation, Methodology, Investigation, Formal analysis. **Jose Vicente López-Bao:** Writing – review & editing, Investigation, Conceptualization. **Ivan Afonso Jordana:** Writing – review & editing, Investigation, Funding acquisition. **Jordi Solà de la Torre:** Writing – review & editing, Investigation, Funding acquisition. **Rahel Sollmann:** Writing – review & editing, Visualization, Validation, Supervision, Software, Project administration, Methodology, Investigation, Formal analysis, Conceptualization.

### Declaration of competing interest

This statement is to certify that:

- The work is all original research carried out by the authors. All authors agree with the contents of the manuscript and its submission to the journal.

- No part of the research has been published in any form elsewhere, unless it is fully acknowledged in the manuscript.

- Authors should disclose how the research featured in the manuscript relates to any other manuscript of a similar nature that they have published, in press, submitted or will soon submit to Biological

Conservation or elsewhere.

- The manuscript is not being considered for publication elsewhere while it is being considered for publication in this journal.

- Any research in the paper not carried out by the authors is fully acknowledged in the manuscript.

- All sources of funding are acknowledged in the manuscript, and authors have declared any direct financial benefits that could result from publication.

- All appropriate ethics and other approvals were obtained for the research. Where appropriate, authors should state that their research protocols have been approved by an authorized animal care or ethics committee, and include a reference to the code of practice adopted for the reported experimentation or methodology. The Editor will take account of animal welfare issues and reserves the right not to publish, especially if the research involves protocols that are inconsistent with commonly accepted norms of animal research.

### Acknowledgements

We acknowledge the insights provided by Olivier Gimenez and Julien Steinmetz. We gratefully acknowledge all brown bear field co-workers from the Brown Bear Network (ROB) in France and from Spanish and Andorran teams. Financial and logistical supports for this study were provided by the Office Français de la Biodiversité (OFB) in France. Genetic analyses were performed by the ANTAGENE Company (France) and the Servei Veterinari de Genètica Molecular, Universitat Autònoma de Barcelona (Spain). A.S.P. was funded by a Margarita Salas research fellowship from Next Generation UE awarded by Universitat de Barcelona. J.V.L.B was supported by the Spanish Ministry of Economy, Industry and Competitiveness (CGL2017-87528-R AEI/FEDER EU), and by a GRUPIN research grant from the Regional Government of Asturias (IDI/2021/000075). Financial and logistical supports for this study were provided by the Office Français de la Biodiversité (OFB) in France. The Departament de Recerca i Universitats from Generalitat de Catalunya (2021-SGR 00302) has supported this article.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.biocon.2025.111122.

### Data availability

Data and novel code to reproduce the analysis are provided in the following GitHub repository: https://github.com/anasanz/opscr_bearPyr.git.

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