The role of dispersal in interacting patches subject to an Allee effect

TL;DR

This paper investigates how the structure of a network influences the long-term survival or extinction of populations with a strong Allee effect, revealing that dispersal patterns critically affect ecological outcomes.

Contribution

It extends a stochastic multi-patch model to analyze the impact of network geometry on population dynamics under an Allee effect, providing analytical and simulation results.

Findings

Critical Allee threshold depends on network degree and initial distribution.

Long-range dispersal can lead to extinction of alien species.

Results support that dispersal patterns influence invasion success.

Abstract

This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that has been recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to infinity, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, strong long range dispersal drives the population toward extinction.