  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.
