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

ABSTRACT: Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an unpredictable habitat and harvest-depleted male populations result in infrequent mating encounters. We develop a mechanistic model for the polar bear mating system that predicts the proportion of fertilized females at the end of the mating season given population density and operational sex ratio. The model is parametrized using pairing data from Lancaster Sound, Canada, and describes the observed pairing dynamics well. Female mating success is shown to be a nonlinear function of the operational sex ratio, so that a sudden and rapid reproductive collapse could occur if males are severely depleted. The operational sex ratio where an Allee effect is expected is dependent on population density. We focus on the prediction of Allee effects in polar bears but our approach is also applicable to other species.

SUBMITTER: Molnar PK

PROVIDER: S-EPMC2596188 | biostudies-literature | 2008 Jan

REPOSITORIES: biostudies-literature

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

Molnár Péter K PK Derocher Andrew E AE Lewis Mark A MA Taylor Mitchell K MK

Proceedings. Biological sciences 20080101 1631

Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an ...[more]

PMID: 18029307

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Project description: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.

Project description:The conservation of many wildlife species requires understanding the demographic effects of climate change, including interactions between climate change and harvest, which can provide cultural, nutritional or economic value to humans.We present a demographic model that is based on the polar bear Ursus maritimus life cycle and includes density-dependent relationships linking vital rates to environmental carrying capacity (K). Using this model, we develop a state-dependent management framework to calculate a harvest level that (i) maintains a population above its maximum net productivity level (MNPL; the population size that produces the greatest net increment in abundance) relative to a changing K, and (ii) has a limited negative effect on population persistence.Our density-dependent relationships suggest that MNPL for polar bears occurs at approximately 0·69 (95% CI = 0·63-0·74) of K. Population growth rate at MNPL was approximately 0·82 (95% CI = 0·79-0·84) of the maximum intrinsic growth rate, suggesting relatively strong compensation for human-caused mortality.Our findings indicate that it is possible to minimize the demographic risks of harvest under climate change, including the risk that harvest will accelerate population declines driven by loss of the polar bear's sea-ice habitat. This requires that (i) the harvest rate - which could be 0 in some situations - accounts for a population's intrinsic growth rate, (ii) the harvest rate accounts for the quality of population data (e.g. lower harvest when uncertainty is large), and (iii) the harvest level is obtained by multiplying the harvest rate by an updated estimate of population size. Environmental variability, the sex and age of removed animals and risk tolerance can also affect the harvest rate. Synthesis and applications. We present a coupled modelling and management approach for wildlife that accounts for climate change and can be used to balance trade-offs among multiple conservation goals. In our example application to polar bears experiencing sea-ice loss, the goals are to maintain population viability while providing continued opportunities for subsistence harvest. Our approach may be relevant to other species for which near-term management is focused on human factors that directly influence population dynamics within the broader context of climate-induced habitat degradation.

Dataset Information

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

Publications

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

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