Date of Award

2006

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

David E. Hiebeler

Second Committee Member

André Khalil

Third Committee Member

Sunddar Subramanian

Abstract

Pair approximation equations have been in use as a method to enhance the level of spatial information captured by mathematical models. For several years David Hiebeler, as well as others (Levin, Ellner, Filipe), have been exploring the use of pair approximation as a way to better estimate a system's behavior than previous methods (i.e. mean field approximations). His previous work has involved studying the pair approximations for basic contact processes on homogeneous landscapes, with populations with near and far dispersal, heterogeneous landscapes, and spatially correlated disturbances on the population level. This thesis will explore the combined effect of two of Dr. Hiebeler's previous works: heterogeneous landscapes and spatially correlated population disturbances. The question of the effect of the simultaneous interactions is so far left open. Specifically, this thesis will investigate the effect of having both the landscape (or static) and population level (or dynamic) disturbances on the same spatial scale.

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