Doctoral Dissertations

Holly D. Gaff

Date of Award

8-1999

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Louis J. Gross

Committee Members

Thomas Hallam, Dan Simberloff, Suzanne Lenhart, Mark Kot

Abstract

Two models are developed to explore the dynamics associated with spatial heterogeneity. The first model is the expansion of a single cell, fish population model to a landscape of interacting cells. The second model is a tick-borne disease model using a set of differential equations applied to a series of spatial patches. The spatially-explicit landscape fish population model (ALFISH) is a part of the Across Trophic Level System Simulation (ATLSS) project for the freshwater wetlands of the Everglades and Big Cypress Swamp. ALFISH was applied as part of the ATLSS project to Everglades restoration, one of the largest ecological restoration projects in the world. ALFISH has been improved to include new field information as that information became available. The only variable input into ALFISH is the hydrology. Up to 35% of variation in fish populations observed in field data corresponds to the variations predicted by ALFISH.

The differential equations underlying the tick-borne disease model designed for the lone star tick (Amblyomma americanum) are analytically evaluated for one patch. The results show that under given criteria for the parameters, the system would be locally stable. For further study, the system is then solved numerically. Patches are identified as either grass or wooded and connected by migration. The disease is endemic in both patches unless some type of control is applied. If a control is applied, the disease is reduced to extremely low levels. If two patches, one grass and one wooded, are linked by migration, applying the control to the wooded patch is effective for controlling the disease while applying it in the grass patch is not. A final simulation using a twelve patch system is run to create results to compare with field data. The results show that the model produced qualitatively similar results to the field data which give reductions of 60% in tick density in the areas with control applied.

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