Dispersal is an important strategy employed by populations to locate and exploit favorable habitats. The question arises: given 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 demographic fluctuations can reverse this conclusion. Competition between the exploitation of resources and fluctuations leads to victory by either the faster or slower of two species depending on the environmental parameters. A simplified model, analyzed by closing the moment and correlation hierarchy, quantitatively predicts which species will win under given parameters of spatial variation and average carrying capacity. This work was done with Leonard M. Sander and Charles R Doering, and extends the work of Kessler and LMS (arXiv:0907.4386v1 [q-bio.PE]).
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