Doctor of Philosophy, The Ohio State University, 2007, Mathematics

We study the evolution of conditional dispersal using a Lotka-Volterra reaction-diffusion-advection model for two competing species in a nonhomogeneous, temporally constant environment. We assume that the two species are identical except for their dispersal strategies. Both species employ random diffusion combined with advection upward along resource gradients. We use a perturbation argument to understand the evolution of these rates. When the advection rates are small relative to the diffusion rates, we find that stronger advection is preferred. However, when the advection rates are large relative to the diffusion rates, we find that weaker advection is preferred. We also studied the case where the two species have differing strategies, one with a very strong biased movement relative to diffusion, and the other with a more balanced approach. If the advection rate of the latter is small, the two species can coexist. But if its advection rate increases sufficiently, the second species drives the first to extinction. So we see in these results a preference against overly strong advection and in favor of a more balanced strategy, suggesting the existence of an optimal intermediate rate.

Committee: Yuan Lou (Advisor) Subjects: Biology, Ecology; Mathematics