Speed and shape of population fronts with density-dependent diffusion

TL;DR

This paper studies how the speed and shape of animal population expansion fronts are affected by density-dependent diffusion, revealing critical thresholds where linear analysis applies or fails, and providing variational methods for accurate predictions.

Contribution

It introduces a variational approach to determine wave speed and shape in reaction-diffusion models with density-dependent diffusion, extending understanding beyond linear analysis.

Findings

Wave speed depends on low-density diffusion strength.

Linear analysis suffices for large low-density diffusion.

Variational methods provide accurate predictions for small or zero low-density diffusion.

Abstract

We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts.