Extinction risk of a Metapopulation under the Allee Effect

TL;DR

This paper investigates how migration rates and the Allee effect influence the extinction risk of fragmented populations on networks, revealing critical migration thresholds and early-warning signals.

Contribution

It introduces a comprehensive analysis of migration effects on extinction risk under the Allee effect, including the identification of a critical migration rate and early-warning indicators.

Findings

Slow migration increases extinction risk compared to isolated patches.

Fast migration leads to synchrony, reducing extinction risk.

A critical migration rate maximizes extinction risk.

Abstract

We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the population's viability. Slow migration is shown to always increase the population's global extinction risk compared to the isolated case. At fast migration, we demonstrate that synchrony between patches minimizes the population's extinction risk. Moreover, we discover a critical migration rate that maximizes the extinction risk of the population, and identify an early-warning signal when approaching this state. Our theoretical results are confirmed via the highly-efficient weighted ensemble method. Notably, our analysis can also be applied to studying switching in gene regulatory networks with multiple transcriptional states.