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

This paper is concerned with the spatial dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species becomes extinct in the habitat if the speed of the shifting habitat edge c>c*(infinity), while the species persists and spreads along the shifting habitat at an asymptotic speed c*(infinity) if c>c*(infinity), where c*(infinity) 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, the model system 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.