Doctor of Philosophy, The Ohio State University, 2011, Mathematics

We utilize reaction-diffusion-advection equations in an adaptive dynamic framework to study the evolution of dispersal of two competing species. The species are assumed to be identical except for their dispersal strategies which consist of random movement (diffusion) and biased movement (advection) upward along resource gradients. We focus on how spatial heterogeneity in the habitat influences selection. A key facet of this relationship is that diffusion creates a mismatch between a species population density at steady state and the resource function [9]. This led Cantrell et al. [9] to introduce a conditional strategy which can perfectly match the resource, resulting in the ideal free distribution of the species at equilibrium. This ideal free strategy (IFS) serves as a basis for our study. Not only do we show that it is a global evolutionarily stable strategy, but we find conditions under which it is convergent stable, varying random dispersal rates, advection rates, or both of these parameters at the same time. For two similar strategies on the "same side" of the IFS we show that when resource function is monotone, the strategy which is closer to the IFS is generally selected. For nonmonotone resource functions, we find that there may exist nonideal free strategies which are locally evolutionarily stable and/or convergent stable [21]. In addition, we find that for certain nonmonotone resource functions, two similarly competing species can coexist, which enables us to also show how three species coexistence is possible.

Committee: Yuan Lou PhD (Advisor); Chiu-Yen Kao PhD (Committee Member); Barbara Keyfitz PhD (Committee Member) Subjects: Mathematics