  This paper is devoted to the study of persistence and extinction of a species
modeled by nonlocal dispersal evolution equations in moving habitats with
moving speed $c$. It is shown that the species becomes extinct if the moving
speed $c$ is larger than the so called spreading speed $c^*$, where $c^*$ is
determined by the maximum linearized growth rate function. If the moving speed
$c$ is smaller than $c^*$, it is shown that the persistence of the species
depends on the patch size of the habitat, namely, the species persists if the
patch size is greater than some number $L^*$ and in this case, there is a
traveling wave solution with speed $c$, and it becomes extinct if the patch
size is {smaller} than $L^*$.
