Date of Award

Spring 1-1-2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Samuel M. Flaxman

Second Advisor

James D. Meiss

Third Advisor

Juan G. Restrepo

Fourth Advisor

David M. Bortz

Fifth Advisor

Brett A. Melbourne

Abstract

Integrating evolution and ecology into mathematical models allows one to study the role of natural selection in ecological interactions. At suitable spatial scales, landscapes are not homogeneous and species interact across spatially variable environments. Thus to better understand organism distributions, it is essential that we know what cues organisms actually use to direct movement. We begin our inquiry by introducing a general model of single-species habitat selection that includes two sources of information, information on fitness and information on resources. In searching for evolutionarily stable strategies of information use, we discover that organisms constrained by perceptual limits may use an arbitrary combination of these two sources of information, but when realistic evolutionary costs are added, the strategy that maximizes fitness is the one that completely ignores information on fitness.

We analyze the model, which is an extension of previous two-patch models with population dynamics, and give sufficient conditions for the existence of an asymptotically stable equilibrium. We prove the global evolutionary stability of several of the information-use strategies, and we show that the addition of costs causes the equilibrium distribution to deviate from the ideal free (or, "equal fitness across patches") distribution.

Finally, we explore how the evolution of random dispersal of prey, when population dynamics without movement are chaotic, changes with the introduction of a predator. We find that the predator can promote or prevent coexistence of two prey types with different strategies. The outcome depends on the predator mortality rate which has a strong effect on the overall population dynamics of the system.

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