Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment

TL;DR

This study investigates how a nonlocal dispersal population responds to a shifting environment with shrinking favorable regions, revealing conditions for persistence, extinction, and traveling wave solutions based on habitat shift speed.

Contribution

It introduces a novel analysis of nonlocal dispersal models in shifting habitats, establishing critical speeds for species survival and extinction, and demonstrating existence of traveling waves at habitat shift speeds.

Findings

Species go extinct if habitat shifts faster than a critical speed.

Species persist and spread at the asymptotic speed determined by model parameters.

Existence of traveling waves matching habitat shift speed indicates potential for species persistence.

Abstract

This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the speed of the shifting habitat edge $c>c^*(\infty)$, however if $c<c^*(\infty)$, the species will persist and spread along the shifting habitat at an asymptotic spreading speed $c^*(\infty)$, where $c^*(\infty)$ is determined by the nonlocal dispersal kernel, diffusion rate and the maximum linearized growth rate. Moreover, we demonstrate that for any given speed of the shifting habitat edge, this model admits a nondecreasing traveling wave with the wave speed at which the habitat is shifting, which indicates that the extinction wave phenomenon does happen in such a shifting environment.