Evolution of anisotropic diffusion in two-dimensional heterogeneous environments

We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these probabilities as dispersal strategies. We show that the evolutionarily stable strategies are to move in one direction only. Our results predict that it is more beneficial for the species to choose the direction with smaller variation in the resource distribution. This finding seems to be in agreement with the classical results of Hastings (1983) and Dockery et al. (1998) for the evolution of slow dispersal, i.e. random diffusion is selected against in spatially heterogeneous environments. These conclusions also suggest that broader dispersal strategies should be considered regarding the movement in heterogeneous habitats.