Individual variability in dispersal and invasion speed

TL;DR

This paper models species dispersal and invasion speed considering two phenotypes with small mutation rates, revealing that increased mutation slows spread and determining phenotype ratios at the invasion front.

Contribution

It introduces a reaction-diffusion model with small mutation rates, proving linear determinacy of spreading speed and analyzing the impact of mutation on invasion dynamics.

Findings

Spreading speed is non-increasing with mutation rate.

Greater phenotypic mixing slows invasion.

Phenotype ratios at the invasion front are characterized as mutation vanishes.

Abstract

We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation rate to a Lotka-Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we prove that under some biologically reasonable condition on parameters the spreading speed of the system is linearly determinate. Using this result we show that the spreading speed is a non-increasing function of the mutation rate and hence that greater mixing between phenotypes leads to slower propagation. Finally, we determine the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation.