  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 Hasting [15] and Dockery et al. [11]
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.
