Abstract
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.
Highlights
For many animals and plants, the per capita population growth rate is positively correlated with population size or density when populations are small or sparse [1]
Our models suggest that the component Allee effect of reduced fertilization probability under low population densities outlined in [15] leads to a strong demographic Allee effect in low-density polar bear populations (Fig. 2)
The a priori estimation of Allee Dynamics Allee effects have garnered much attention in ecology and conservation biology, and numerous theoretical models have been developed for exploring their causes and consequences
Summary
For many animals and plants, the per capita population growth rate is positively correlated with population size or density when populations are small or sparse [1]. The strength of an Allee effect influences the probability of extinction at low densities [1], making it crucial to determine accurate estimates of low-density growth rates for population management strategies. Knowledge of these growth rates can, for example, help define eradication targets for pests and invasive species, or minimum conservation and reintroduction targets for conservation management [1,3,10,11,12]. Allee effects need to be accounted for in the harvest of exploited populations to avoid overly optimistic assessments of population resilience; neglecting an Allee effect, or accounting for it but with inaccurate low-density growth rate estimates, could inadvertently lead to the reduction of populations to sizes from which recovery is difficult [1,4]
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