The evolutionary stability of partial migration with Allee effects

Abstract

An Allee effect is a density-dependent phenomenon in which population growth or individual components of fitness increase as population density increases. Understanding the density-dependent effects is vital to elucidate how populations evolve and to investigate evolutionary stability. Partial migration, where a proportion of a population migrates while other individuals remain resident, is widespread across most migratory lineages. However, the mechanism still needs to be better understood in most taxa, especially those experiencing positive density-dependent effects. Here we investigate the evolutionary stability of a partial migration population with only the migrant population experiencing Allee effects. Using the Evolutionary Game Theoretic (EGT) approach, we prove the existence and uniqueness of an evolutionary stable strategy (ESS). EGT provides a mathematical framework for understanding and modelling Darwinian evolution by natural selection. We also show that the ESS is the only Ideal Free Distribution (IFD) that arises in the context of a partially migrating population in a two-habitat environment.

Keywords:

• Partial migration
• Allee effects
• basic reproduction number
• ideal free distribution
• evolutionary game theory
• evolutionary stable strategy

2000 Mathematics Subject Classification:

• 37

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is funded by a start-up research grant, SERB [SRG/2019/002200], to A. M. We would like to thank Professor Patrick De Leenhere for his valuable suggestions and comments on this work.