Date of Award

12-1-2014

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Xiao, Mingqing

Second Advisor

Reeve, John D.

Abstract

In this dissertation, we examine an advection diffusion model for insects inhabiting a spatially heterogeneous environment and moving toward a more favorable environment. We first study the effects of adding a term describing drift or advection toward a favorable environment to diffusion models for population dynamics. The diffusion model is a basic linear two-dimensional diffusion equation describing local dispersal of species. The mathematical advection terms are taken to be Fickian and describe directed movement of the population toward the favorable environment. For this model, the landscape is composed of one homogeneous habitat patch embedded in a spatially heterogeneous environment and the boundary of the habitat inhabited by the population acts as a lethal edge. We also derived the mean occupancy time and the boundary flux of the habitat patch. The diffusion rate and advection parameters of the advection diffusion model are estimated based on mean occupancy time and boundary flux. We then introduce two methods for the identification of these coefficients in the model as well as the capture rate. These two new methods have some advantages over other methods of estimating those parameters, including reduced computational cost and ease of use in the field. We further examine the statistical properties of new methods through simulation, and discuss how mean occupancy time and boundary flux could be estimated in field experiments.

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