Modelling the mating system of polar bears: a mechanistic approach to the Allee effect

Land-based foraging by polar bears reveals sexual conflict outside mating season

According to sexual selection theory, the sexes are faced with opposing evolutionary goals. Male fitness benefits from access to females, whereas female fitness is constrained by food resources and safety for themselves and their offspring. Particularly in large solitary carnivores, such as polar bears (Ursus maritimus), these divergent goals can potentially lead to conflict between the sexes. Outside the mating season, when polar bears are on the move across vast distances, the consequences of such conflict can become apparent when individuals arrive at the same food source. To investigate interrelationships between the sexes, we observed successive polar bears visiting a bird breeding colony to feed on clutches of eggs. We found that males succeeded females more frequently and more closely than expected by chance. Moreover, when males were closer to conspecifics, they walked faster, spent less time in the colony and ingested less food. In contrast, female foraging performance was not associated with proximity to other bears. Irrespective of proximity, females generally spent short periods in the colony and ingested fewer clutches than males. Our results suggest that in polar bears, there is a trade-off between the benefits of food intake and the opportunities (in males) and risks (in females) posed by encountering conspecifics.

Tipping points emerge from weak mutualism in metacommunities

The coexistence of obligate mutualists is often precariously close to tipping points where small environmental changes can drive catastrophic shifts in species composition. For example, microbial ecosystems can collapse by the decline of a strain that provides an essential resource on which other strains cross-feed. Here, we show that tipping points, ecosystem collapse, bistability and hysteresis arise even with very weak (non-obligate) mutualism provided the population is spatially structured. Based on numeric solutions of a metacommunity model and mean-field analyses, we demonstrate that weak mutualism lowers the minimal dispersal rate necessary to avoid stochastic extinction, while species need to overcome a mean threshold density to survive in this low dispersal rate regime. Our results allow us to make numerous predictions for mutualistic metacommunities regarding tipping points, hysteresis effects, and recovery from external perturbations, and let us draw general conclusions for ecosystems even with random, not necessarily mutualistic, interactions and systems with density-dependent dispersal rather than direct mutualistic interactions.

Simulating the dynamics of dispersal and dispersal ability in fragmented populations with mate-finding Allee effects

We consider the spatial propagation and genetic evolution of model populations comprising multiple subpopulations, each distinguished by its own characteristic dispersal rate. Mate finding is modeled in accord with the assumption that reproduction is based on random encounters between pairs of individuals, so that the frequency of interbreeding between two subpopulations is proportional to the product of local population densities of each. The resulting nonlinear growth term produces an Allee effect, whereby reproduction rates are lower in sparsely populated areas; the distribution of dispersal rates that evolves is then highly dependent upon the population's initial spatial distribution. In a series of numerical test cases, we consider how these dynamics affect lattice-like arrangements of population fragments, and investigate how a population's initial fragmentation determines the dispersal rates that evolve as a habitat is colonized. First, we consider a case where initial population fragments coincide with habitat islands, within which death rates differ from those that apply outside; the presence of inhospitable exterior regions exaggerates Allee effect-driven reductions in dispersal ability. We then examine how greater distances separating adjacent population fragments lead to more severe reductions in dispersal ability. For populations of a fixed initial magnitude, fragmentation into smaller, denser patches leads not only to greater losses of dispersal ability, but also helps ensure the population's long-term persistence, emphasizing the trade-offs between the benefits and risks of rapid dispersal under Allee effects. Next, simulations of well-established populations disrupted by localized depopulation events illustrate how mate-finding Allee effects and spatial heterogeneity can drive a population's dispersal ability to evolve either downward or upward depending on conditions, highlighting a qualitative distinction between population fragmentation and habitat heterogeneity. A final test case compares populations that are fragmented across multiple scales, demonstrating how differences in the relative scales of micro- and macro-level fragmentation can lead to qualitatively different evolutionary outcomes.

Glacial ice supports a distinct and undocumented polar bear subpopulation persisting in late 21st-century sea-ice conditions

Polar bears are susceptible to climate warming because of their dependence on sea ice, which is declining rapidly. We present the first evidence for a genetically distinct and functionally isolated group of polar bears in Southeast Greenland. These bears occupy sea-ice conditions resembling those projected for the High Arctic in the late 21st century, with an annual ice-free period that is >100 days longer than the estimated fasting threshold for the species. Whereas polar bears in most of the Arctic depend on annual sea ice to catch seals, Southeast Greenland bears have a year-round hunting platform in the form of freshwater glacial mélange. This suggests that marine-terminating glaciers, although of limited availability, may serve as previously unrecognized climate refugia. Conservation of Southeast Greenland polar bears, which meet criteria for recognition as the world's 20th polar bear subpopulation, is necessary to preserve the genetic diversity and evolutionary potential of the species.

Polar Bear Harvest Patterns Across the Circumpolar Arctic

Wildlife harvest remains a conservation concern for many species and assessing patterns of harvest can provide insights on sustainability and inform management. Polar bears (Ursus maritimus) are harvested over a large part of their range by local people. The species has a history of unsustainable harvest that was largely rectified by an international agreement that required science-based management. The objective of our study was to examine the temporal patterns in the number of polar bears harvested, harvest sex ratios, and harvest rates from 1970 to 2018. We analyzed data from 39,049 harvested polar bears (annual mean 797 bears) collected from 1970 to 2018. Harvest varied across populations and times that reflect varying management objectives, episodic events, and changes based on new population estimates. More males than females were harvested with an overall M:F sex ratio of 1.84. Harvest varied by jurisdiction with 68.0% of bears harvested in Canada, 18.0% in Greenland, 11.8% in the USA, and 2.2% in Norway. Harvest rate was often near the 4.5% target rate. Where data allowed harvest rate estimation, the target rate was exceeded in 11 of 13 populations with 1–5 populations per year above the target since 1978. Harvest rates at times were up to 15.9% of the estimated population size suggesting rare episodes of severe over-harvest. Harvest rate was unrelated to a proxy for ecosystem productivity (area of continental shelf within each population) but was correlated with prey diversity. In the last 5–10 years, monitored populations all had harvest rates near sustainable limits, suggesting improvements in management. Polar bear harvest management has reduced the threat it once posed to the species. However, infrequent estimates of abundance, new management objectives, and climate change have raised new concerns about the effects of harvest.

Dispersal-induced resilience to stochastic environmental fluctuations in populations with Allee effect

Many species are unsustainable at small population densities (Allee effect); i.e., below the so-called Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to extinction. Here, we show how, in spatially extended habitats, dispersal can lead to a sustainable population in a region, provided the amplitude of environmental fluctuations is below an extinction threshold. We have identified two types of sustainable populations: high-density and low-density populations (through a mean-field approximation, valid in the limit of large dispersal length). Our results show that patches where population is high, low, or extinct coexist when the population is close to global extinction (even for homogeneous habitats). The extinction threshold is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations. The extinction threshold increases proportionally to the square root of the dispersal rate and decreases with the Allee threshold. The low-population-density solution can allow understanding of difficulties in recovery after harvesting. This theoretical framework provides a unique approach to address other factors, such as habitat fragmentation or harvesting, impacting population resilience to environmental fluctuations.

Demographic risk assessment for a harvested species threatened by climate change: polar bears in the Chukchi Sea

Climate change threatens global biodiversity. Many species vulnerable to climate change are important to humans for nutritional, cultural, and economic reasons. Polar bears Ursus maritimus are threatened by sea-ice loss and represent a subsistence resource for Indigenous people. We applied a novel population modeling-management framework that is based on species life history and accounts for habitat loss to evaluate subsistence harvest for the Chukchi Sea (CS) polar bear subpopulation. Harvest strategies followed a state-dependent approach under which new data were used to update the harvest on a predetermined management interval. We found that a harvest strategy with a starting total harvest rate of 2.7% (˜85 bears/yr at current abundance), a 2:1 male-to-female ratio, and a 10-yr management interval would likely maintain subpopulation abundance above maximum net productivity level for the next 35 yr (approximately three polar bear generations), our primary criterion for sustainability. Plausible bounds on starting total harvest rate were 1.7-3.9%, where the range reflects uncertainty due to sampling variation, environmental variation, model selection, and differing levels of risk tolerance. The risk of undesired demographic outcomes (e.g., overharvest) was positively related to harvest rate, management interval, and projected declines in environmental carrying capacity; and negatively related to precision in population data. Results reflect several lines of evidence that the CS subpopulation has been productive in recent years, although it is uncertain how long this will last as sea-ice loss continues. Our methods provide a template for balancing trade-offs among protection, use, research investment, and other factors. Demographic risk assessment and state-dependent management will become increasingly important for harvested species, like polar bears, that exhibit spatiotemporal variation in their response to climate change.

Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I

Abstract

Approaches to modeling population dynamics using discrete-time models are described in this two-part review. The development of the scientific ideas of discrete time models, from the Malthus model to modern population models that take into account many factors affecting the structure and dynamics, is presented. The most important and interesting results of recurrent equation application to biological system analysis obtained by the authors are given. In the first part of this review, the population dynamic effects that result from density-dependent regulation of population, the age and sex structures, and the influence of external factors are considered.

Ecological and evolutionary consequences of predator-prey role reversal: Allee effect and catastrophic predator extinction

In many terrestrial, marine, and freshwater predator-prey communities, young predators can be vulnerable to attacks by large prey. Frequent prey counter-attacks may hinder the persistence of predators. Despite the commonness of such role reversals in nature, they have rarely been addressed in evolutionary modelling. To understand how role reversals affect ecological and evolutionary dynamics of a predator-prey community, we derived an ecological model from individual-level processes using ordinary differential equations. The model reveals complex ecological dynamics, with possible bistability between alternative coexistence states and an Allee effect for the predators. We find that when prey counter-attacks are frequent, cannibalism is necessary for predator persistence. Using numerical analysis, we also find that a sudden ecological shift from coexistence to predator extinction can occur through several catastrophic bifurcations, including 'saddle-node', 'homoclinic', and 'subcritical Hopf'. The analysis of single-species evolution reveals that predator selection towards increasing or decreasing cannibalism triggers a catastrophic shift towards an extinction state of the predators. Such an evolutionary extinction of the predators may also be caused by prey selection towards increasing foraging activity because it facilitates encounters with vulnerable, young predators. The analysis of predator-prey coevolution further demonstrates that predator's catastrophic extinction becomes an even more likely outcome than in single-species evolution. Our results suggest that when young predators are vulnerable to prey attacks, a sudden extinction of the predators may be more common than currently understood.

Divergent density feedback control of migratory predator recovery following sex-biased perturbations

Uncertainty in risks posed by emerging stressors such as synthetic hormones impedes conservation efforts for threatened vertebrate populations. Synthetic hormones often induce sex-biased perturbations in exposed animals by disrupting gonad development and early life-history stage transitions, potentially diminishing per capita reproductive output of depleted populations and, in turn, being manifest as Allee effects. We use a spatially explicit biophysical model to evaluate how sex-biased perturbation in life-history traits of individuals (maternal investment in egg production and male-skewed sex allocation in offspring) modulates density feedback control of year-class strength and recovery trajectories of a long-lived, migratory fish-shovelnose sturgeon (Scaphirhynchus platorynchus)-under spatially and temporally dynamic synthetic androgen exposure and habitat conditions. Simulations show that reduced efficiency of maternal investment in gonad development prolonged maturation time, increased the probability of skipped spawning, and, in turn, shrunk spawner abundance, weakening year-class strength. However, positive density feedback disappeared (no Allee effect) once the exposure ceased. By contrast, responses to the demographic perturbation manifested as strong positive density feedback; an abrupt shift in year-class strength and spawner abundance followed after more than two decades owing to persistent negative population growth (a strong Allee effect), reaching an alternative state without any sign of recovery. When combined with the energetic perturbation, positive density feedback of the demographic perturbation was dampened as extended maturation time reduced the frequency of producing male-biased offspring, allowing the population to maintain positive growth rate (a weak Allee effect) and gradually recover. The emergent patterns in long-term population projections illustrate that sex-biased perturbation in life-history traits can interactively regulate the strength of density feedback in depleted populations such as Scaphirhynchus sturgeon to further diminish reproductive capacity and abundance, posing increasingly greater conservation challenges in chemically altered riverscapes.

Modeling optimal responses and fitness consequences in a changing Arctic

Animals must balance a series of costs and benefits while trying to maximize their fitness. For example, an individual may need to choose how much energy to allocate to reproduction versus growth, or how much time to spend on vigilance versus foraging. Their decisions depend on complex interactions between environmental conditions, behavioral plasticity, reproductive biology, and energetic demands. As animals respond to novel environmental conditions caused by climate change, the optimal decisions may shift. Stochastic dynamic programming provides a flexible modeling framework with which to explore these trade-offs, but this method has not yet been used to study possible changes in optimal trade-offs caused by climate change. We created a stochastic dynamic programming model capturing trade-off decisions required by an individual adult female polar bear (Ursus maritimus) as well as the fitness consequences of her decisions. We predicted optimal foraging decisions throughout her lifetime as well as the energetic thresholds below which it is optimal for her to abandon a reproductive attempt. To explore the effects of climate change, we shortened the spring feeding period by up to 3 weeks, which led to predictions of riskier foraging behavior and higher reproductive thresholds. The resulting changes in fitness may be interpreted as a best-case scenario, where bears adapt instantaneously and optimally to new environmental conditions. If the spring feeding period was reduced by 1 week, her expected fitness declined by 15%, and if reduced by 3 weeks, expected fitness declined by 68%. This demonstrates an effective way to explore a species' optimal response to a changing landscape of costs and benefits and highlights the fact that small annual effects can result in large cumulative changes in expected lifetime fitness.

Mate choice strategies in a spatially-explicit model environment

Decisions about the choice of a mate can greatly impact both individual fitness and selection processes. We developed a novel agent-based model to investigate two common mate choice rules that may be used by female gray treefrogs (Hyla versicolor). In this model environment, female agents using the minimum-threshold strategy found higher quality mates and traveled shorter distances on average, compared with female agents using the best-of-n strategy. Females using the minimum-threshold strategy, however, incur significant lost opportunity costs, depending on the male population quality average. The best-of-n strategy leads to significant female:female competition that limits their ability to find high quality mates. Thus, when the sex ratio is 0.8, best-of-5 and best-of-2 strategies yield mates of nearly identical quality. Although the distance traveled by females in the mating task varied depending on male spatial distribution in the environment, this did not interact with female choice for the best-of-n or minimum-threshold strategies. By incorporating empirical data from the frogs in this temporally- and spatially-explicit model, we thus show the emergence of novel interactions of common decision-making rules with realistic environmental variables.

Allee effect in polar bears: a potential consequence of polychlorinated biphenyl contamination

Polar bears (Ursus maritimus) from East Greenland and Svalbard exhibited very high concentrations of polychlorinated biphenyls (PCBs) in the 1980s and 1990s. In Svalbard, slow population growth during that period was suspected to be linked to PCB contamination. In this case study, we explored how PCBs could have impacted polar bear population growth and/or male reproductive success in Svalbard during the mid-1990s by reducing the fertility of contaminated males. A dose-response relationship linking the effects of PCBs to male polar bear fertility was extrapolated from studies of the effects of PCBs on sperm quality in rodents. Based on this relationship, an individual-based model of bear interactions during the breeding season predicted fertilization success under alternative assumptions regarding male-male competition for females. Contamination reduced pregnancy rates by decreasing the availability of fertile males, thus triggering a mate-finding Allee effect, particularly when male-male competition for females was limited or when infertile males were able to compete with fertile males for females. Comparisons of our model predictions on age-dependent reproductive success of males with published empirical observations revealed that the low representation of 10-14-year-old males among breeding males documented in Svalbard in mid-1990s could have resulted from PCB contamination. We conclude that contamination-related male infertility may lead to a reduction in population growth via an Allee effect. The magnitude of the effect is largely dependent on the population-specific mating system. In eco-toxicological risk assessments, appropriate consideration should therefore be given to negative effects of contaminants on male fertility and male mating behaviour.

Demographic and traditional knowledge perspectives on the current status of Canadian polar bear subpopulations

Subpopulation growth rates and the probability of decline at current harvest levels were determined for 13 subpopulations of polar bears (Ursus maritimus) that are within or shared with Canada based on mark-recapture estimates of population numbers and vital rates, and harvest statistics using population viability analyses (PVA). Aboriginal traditional ecological knowledge (TEK) on subpopulation trend agreed with the seven stable/increasing results and one of the declining results, but disagreed with PVA status of five other declining subpopulations. The decline in the Baffin Bay subpopulation appeared to be due to over-reporting of harvested numbers from outside Canada. The remaining four disputed subpopulations (Southern Beaufort Sea, Northern Beaufort Sea, Southern Hudson Bay, and Western Hudson Bay) were all incompletely mark-recapture (M-R) sampled, which may have biased their survival and subpopulation estimates. Three of the four incompletely sampled subpopulations were PVA identified as nonviable (i.e., declining even with zero harvest mortality). TEK disagreement was nonrandom with respect to M-R sampling protocols. Cluster analysis also grouped subpopulations with ambiguous demographic and harvest rate estimates separately from those with apparently reliable demographic estimates based on PVA probability of decline and unharvested subpopulation growth rate criteria. We suggest that the correspondence between TEK and scientific results can be used to improve the reliability of information on natural systems and thus improve resource management. Considering both TEK and scientific information, we suggest that the current status of Canadian polar bear subpopulations in 2013 was 12 stable/increasing and one declining (Kane Basin). We do not find support for the perspective that polar bears within or shared with Canada are currently in any sort of climate crisis. We suggest that monitoring the impacts of climate change (including sea ice decline) on polar bear subpopulations should be continued and enhanced and that adaptive management practices are warranted.

Sex and friendship in a multilevel society: behavioural patterns and associations between female and male Guinea baboons

One key question in social evolution is the identification of factors that promote the formation and maintenance of stable bonds between females and males beyond the mating context. Baboons lend themselves to examine this question, as they vary in social organisation and male-female association patterns. We report the results from the first systematic observations of individually identified wild female Guinea baboons. Guinea baboons live in a multilevel society with female-biased dispersal. Although several males could be found within 5 m of females, each female chiefly associated with one "primary" male at the 2 m distance. Social interactions occurred predominantly with the primary male, and female reproductive state had little influence on interaction patterns. The number of females per primary male varied from 1 to 4. During the 17-month study period, half of the females transferred between different males one or multiple times. A subset of females maintained weaker affiliative nonsexual relationships with other "secondary" males. Units composed of primary males with females, and occasional secondary males, apparently form the core of the Guinea baboon society. The social organisation and mating patterns of Guinea and hamadryas baboons may have a common evolutionary origin, despite notable differences in relationship quality. Specifically, Guinea baboon females appear to have greater leverage in their association patterns than hamadryas baboon females. Although we cannot yet explain the lack of overt male control over females, results generally support the notion that phylogenetic descent may play an important role in shaping social systems.

Estimating Allee dynamics before they can be observed: polar bears as a case study

Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.

Females roam while males patrol: divergence in breeding season movements of pack-ice polar bears (Ursus maritimus)

Intraspecific differences in movement behaviour reflect different tactics used by individuals or sexes to favour strategies that maximize fitness. We report movement data collected from n = 23 adult male polar bears with novel ear-attached transmitters in two separate pack ice subpopulations over five breeding seasons. We compared movements with n = 26 concurrently tagged adult females, and analysed velocities, movement tortuosity, range sizes and habitat selection with respect to sex, reproductive status and body mass. There were no differences in 4-day displacements or sea ice habitat selection for sex or population. By contrast, adult females in all years and both populations had significantly more linear movements and significantly larger breeding range sizes than males. We hypothesized that differences were related to encounter rates, and used observed movement metrics to parametrize a simulation model of male-male and male-female encounter. The simulation showed that the more tortuous movement of males leads to significantly longer times to male-male encounter, while having little impact on male-female encounter. By contrast, linear movements of females are consistent with a prioritized search for sparsely distributed prey. These results suggest a possible mechanism for explaining the smaller breeding range sizes of some solitary male carnivores compared to females.

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for ℛ(0)≫1.

The mating system of polar bears: a genetic approach

Parentage analysis data for 583 individuals genotyped at 27 microsatellite loci were used to study the mating system of polar bears ( Ursus maritimus Phipps, 1774) in the Barents Sea area. We discriminated statistically between full and half-siblings identified through only one common parent. We document for the first time multiple paternity in polar bears. We demonstrated for both sexes low fidelity to mating partners over time. We did not detect any significant difference between the age distribution of adult males at capture and the age distribution of males siring cubs. This might indicate that the male’s age and size are less indicative of the reproductive success than previously thought. This is further supported by a rather long mean litter interval of 3.9 years for males siring several litters. The mating system of polar bears in the Barents Sea appears to be promiscuous, usually with a single successful father siring full siblings within a year, but with consecutive litters of a mother being fathered by different males. We discuss how population density, landscape characteristics, and adult sex ratio might influence the mating system of polar bears. This is of particular importance for management decisions such as, e.g., implementing sex ratios in hunting quotas.

The Allee effect in mechanistic models based on inter-individual interaction processes

Recently, Eskola and Geritz (Bull. Math. Biol. 69:329-346, 2007) showed that several discrete-time population models can be derived mechanistically within a single ecological framework by varying the within-season patterns of reproduction and inter-individual aggression. However, these models do not have the Allee effect. In this paper, we modify the original modelling framework by adding different mate finding processes, and thus derive mechanistically several population models with the Allee effect.

The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations

Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri- or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease-induced extinction is thus possible for density-dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond R(0) = 1. This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.