Influence of a mortality trade-off on the spreading rate of cane toads fronts

TL;DR

This paper analyzes a mathematical model of cane toad invasion, focusing on how a mortality trade-off influences the spreading rate, revealing regimes of acceleration and linear spread based on penalization strength.

Contribution

It introduces a novel nonlocal reaction-diffusion-mutation model with unbounded diffusivity and analyzes how mortality trade-offs affect invasion speed regimes.

Findings

Weak penalization leads to accelerated spreading.

Strong penalization results in linear spreading.

Mathematical analysis characterizes regimes based on trade-off strength.

Abstract

In this paper, we study the influence of the mortality trade-off in a nonlocal reaction-diffusion-mutation equation that we introduce to model the invasion of cane toads in Australia. This model is built off of one that has attracted attention recently, in which the population of toads is structured by a phenotypical trait that governs the spatial diffusion. We are concerned with the case when the diffusivity can take unbounded values and the mortality trade-off depends only on the trait variable. Depending on the rate of increase of the penalization term, we obtain the rate of spreading of the population. We identify two regimes, an acceleration regime when the penalization is weak and a linear spreading regime when the penalization is strong. While the development of the model comes from biological principles, the bulk of the article is dedicated to the mathematical analysis of the model, which is very technical.