Population invasion with bistable dynamics and adaptive evolution: the evolutionary rescue

TL;DR

This paper models population invasion using reaction-diffusion equations incorporating ecological and evolutionary effects, demonstrating that evolutionary adaptation can rescue small populations from extinction and enable their spread.

Contribution

It provides a mathematical proof that evolutionary rescue can occur in a coupled ecological and evolutionary population model with bistable dynamics.

Findings

Small populations can persist and spread due to evolutionary effects.

Evolutionary rescue occurs even when ecological conditions alone would lead to extinction.

The model links ecology and evolution through trait-dependent effects.

Abstract

We consider the system of reaction-diffusion equations proposed in [8] as a population dynamics model. The first equation stands for the population density and models the ecological effects, namely dispersion and growth with a Allee effect (bistable nonlinearity). The second one stands for the Allee threshold, seen as a trait mean, and accounts for evolutionary effects. Precisely, the Allee threshold is submitted to three main effects: dispersion (mirroring ecology), asymmetrical gene flow and selection. The strength of the latter depends on the population density and is thus coupling ecology and evolution. Our main result is to mathematically prove evolutionary rescue: any small initial population, that would become extinct in the sole ecological context, will persist and spread thanks to evolutionary factors.