  Dispersal is an important strategy that allows organisms to locate and
exploit favorable habitats. The question arises: given competition in a
spatially heterogeneous landscape, what is the optimal rate of dispersal?
Continuous population models predict that a species with a lower dispersal rate
always drives a competing species to extinction in the presence of spatial
variation of resources. However, the introduction of intrinsic demographic
stochasticity can reverse this conclusion. We present a simple model in which
competition between the exploitation of resources and stochastic fluctuations
leads to victory by either the faster or slower of two species depending on the
environmental parameters. A simplified limiting case of the model, analyzed by
closing the moment and correlation hierarchy, quantitatively predicts which
species will win in the complete model under given parameters of spatial
variation and average carrying capacity.
