Is a nonlocal diffusion strategy convenient for biological populations in competition?

We study the viability of a nonlocal dispersal strategy in a reaction-diffusion system with a fractional Laplacian operator. We show that there are circumstances-namely, a precise condition on the distribution of the resource-under which the introduction of a new nonlocal dispersal behavior is favored with respect to the local dispersal behavior of the resident population. In particular, we consider the linearization of a biological system that models the interaction of two biological species, one with local and one with nonlocal dispersal, that are competing for the same resource.