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

Persistence and Extinction of Nonlocal Dispersal Evolution Equations in Moving Habitats