Calculus of Variations and Geometric Measure Theory

A. Massaccesi - E. Valdinoci

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

created by massaccesi on 06 Mar 2015
modified on 22 Oct 2018


Published Paper

Inserted: 6 mar 2015
Last Updated: 22 oct 2018

Journal: Journal of Mathematical Biology
Volume: 74
Number: 1-2
Pages: 113-147
Year: 2017
Doi: 10.1007/s00285-016-1019-z


We study the convenience 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 a nonlocal dispersal behavior is favored.

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. We give a simple, concrete example of resources for which the equilibrium with only the local population becomes linearly unstable. In a sense, this example shows that nonlocal strategies can become successful even in an environment in which purely local strategies are dominant at the beginning, provided that the resource is sufficiently sparse.

Indeed, the example considered presents a high variance of the distribution of the dispersal, thus suggesting that the shortage of resources and their unbalanced supply may be some of the basic ingredients that favor nonlocal strategies.