The evolutionary stability of partial migration with Allee effects

TL;DR

This paper studies how Allee effects influence the evolutionary stability of partial migration, revealing a bifurcation and identifying a unique evolutionarily stable strategy through game theory.

Contribution

It introduces a novel analysis of partial migration stability considering Allee effects and proves the existence of a unique ESS and IFD in this context.

Findings

Population undergoes bifurcation with increasing migration fraction

Existence of a unique evolutionary stable strategy (ESS)

The ESS coincides with the ideal free distribution (IFD)

Abstract

An Allee effect occurs when the per-capita growth rate increases at low densities. Here, we investigate the evolutionary stability of a partial migration population with migrant population experiencing Allee effects. Partial migration is a unique form of phenotypic diversity wherein migrant and non-migrant individuals coexist together. It is shown that when Allee effect is incorporated, the population undergoes a bifurcation as the fraction of migrating population increases from zero to unity. Using an evolutionary game theoretic approach, we prove the existence of a unique evolutionary stable strategy (ESS). It is also shown that the ESS is the only ideal free distribution (IFD) that arises in the context of partially migrating population.