Mean time to extinction of a metapopulation with an Allee effect

Abstract

The incorporation of Allee effects into a simple metapopulation extinction model reveals a large non-linear reduction in mean time to extinction with small changes in an Allee limit. The extent of this reduction is dependent on the level of migration in the metapopulation. With small amounts of migration, small changes in the Allee limit result in large changes in the mean time to extinction. With higher levels of migration, the mean time to extinction is not as sensitive to changes in the Allee limit, becoming more similar to the single population case. The metapopulation modeled here is a set of nine patches, driven to extinction by environmental stochasticity. A generalized Allee effect is incorporated by a modification of the standard logistic model. The sensitivity of the mean time to extinction to small changes in the Allee limit is especially relevant to population viability analysis, which uses estimates of extinction times for management decisions.

Single-species Models of the Allee Effect: Extinction Boundaries, Sex Ratios and Mate Encounters

“…This has been demonstrated for the rate of spread of invading populations (Lewis & Kareiva, 1993;Kot et al, 1996;Veit & Lewis, 1996;Berec et al, 2001;Wang et al, 2002), optimal distance of dispersal (South & Kenward, 2001), invasion pinning (Keitt et al, 2001), persistence and size heterogeneity of metapopulations (Gruntfest et al, 1997;Amarasekare, 1998a;Gyllenberg et al, 1999;Brassil, 2001), and stability of competing populations (Wang et al, 1999).…”

“…This fact is not crucial in the basic single-species model but its role in more complicated settings has never been discussed properly. On the other hand, model (6) has already been used in competition, predation and metapopulation models by Courchamp et al (2000) and Brassil (2001). We therefore propose to consider model (6) with C40 which fixes both objections and in fact yields a more flexible model with variable extinction rates.…”

“…Although important per se, we do not consider here metapopulation studies which describe the Allee effect within local patches using one-dimensional heuristic models and only combine them with between-patch migration (Amarasekare, 1998a;Gyllenberg et al, 1999;Brassil, 2001;Gruntfest et al, 1997;Courchamp et al, 2000). We are thus left with only a few models which treat the sexes separately and are characterized by a variable adult sex ratio ð¼ proportion of males in the population) in contrast with a fixed primary sex ratio (¼ proportion of males in the offspring).…”

Model reduction for slow–fast stochastic systems with metastable behaviour

“…Refs. [34][35][36]. These are predominantly cases in which there simultaneously exists a positive and a zero abun- …”

Impact of non-linearities in density dependence beyond the range of the data on predicting population extinction risk

“…Allee effects (Allee, Emerson, Park, Park, & Schmidt, 1949), non-linearities in the density dependence function at low population densities, can have profound impacts on both the probabilities of extinction and on persistence times (Dennis, 1989(Dennis, , 2002. Ignorance of an Allee effect can affect the estimation of model parameters such as growth rate and consequently result in misestimating the population viability (Brassil, 2001). In contrast, our purpose in this note is to demonstrate that unobserved nonlinearities in population growth rate at high population densities may also have important influences on the extinction dynamics of populations and can greatly affect predictions of population risk.…”