Author

Jack L. Hill

Date of Award

12-2014

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

David Hiebeler

Second Committee Member

Andre Khalil

Third Committee Member

Robert Franzosa

Abstract

We study a single-species population model on a landscape with two habitat types, suitable and unsuitable. In our model, the landscape itself is dynamic, with habitat types changing according to a voter cellular automata model. We study the model using two approaches: stochastic computer simulations and ordinary differential equations based on ordinary pair approximations. We find that both the spatial and temporal scales of population dynamics and landscapes affect the success of the population (as measured by equilibrium population density). Unlike previous models of populations on static landscapes, we find that even with global dispersal, the spatial arrangement of habitat types affects equilibrium population density. We also find that population density depends on the birth and death parameters individually, rather than just their ratio as in previous simpler models. Although it is difficult to definitively state exactly what spatial effects cause various outcomes in models of this type, we speculate that the differential turnover rate of habitat types at the edge of suitable patches as compared with sites near the center of a patch, coupled with population clustering when local dispersal is used, play a large role in affecting population dynamics.

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