Demographic stochasticity and extinction in populations with Allee effect

TL;DR

This paper investigates how demographic stochasticity influences extinction times in populations experiencing Allee effects, using stochastic birth-death models and analytical approximations, with comparisons to numerical simulations.

Contribution

It introduces exact solutions and validity conditions for extinction times in stochastic models with Allee effects, enhancing understanding beyond mean-field approximations.

Findings

Exact solutions for mean extinction time in special cases.

Validation of WKB approximation for different Allee effect strengths.

Identification of boundary conditions between weak and strong Allee effects.

Abstract

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.