  Dispersal of species to find a more favorable habitat is important in
population dynamics. Dispersal rates evolve in response to the relative success
of different dispersal strategies. In a simplified deterministic treatment (J.
Dockery, V. Hutson, K. Mischaikow, et al., J. Math. Bio. 37, 61 (1998)) of two
species which differ only in their dispersal rates the slow species always
dominates. We demonstrate that fluctuations can change this conclusion and can
lead to dominance by the fast species or to coexistence, depending on
parameters. We discuss two different effects of fluctuations, and show that our
results are consistent with more complex treatments that find that selected
dispersal rates are not monotonic with the cost of migration.
