A nonlocal evolution equation that models the spatial dispersal will be introduced in this talk. Unlike the classic models which are often based upon reaction-diffusion equations, this nonlocal evolution equation is derived from a variation of a position-jump process. We are interested in the steady states of equation and their stabilities. The second half of my talk is devoted to a competition model based on this nonlocal equation. The competition model is related to two similar species and is intended to describe the roles played by the dispersal rate.