Date of Award

2017

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Bonita Lawrence

Second Advisor

Clayton Brooks

Third Advisor

Basant Karna

Fourth Advisor

James Vance

Abstract

In the ever-changing world of ecology, species survival often depends on approximations and measurements taken by biologists. These approximations help to ensure and predict the future of that given species. Our ecological community of interest involves wolves, elk, and berry producing shrubs within Yellowstone National Park. We use two different systems of ordinary differential equations, each increasing in complexity to model our community. In each model the predator (wolves) and consumers (elk) compete for a common resource, berry producing shrubs. We call this consumption of resources, from more than one trophic level, omnivory. We approximate each system with parameter values from field biologist and wildlife reports. We then use a process called sensitivity analysis to determine how small changes in parameter values affect the solution to each respective system. This process allows us to determine which values biologists should take more care in monitoring to prevent extinction. Both our models offer similar results. The predator (wolf) mortality rate is the most sensitive to small changes. The least sensitive of our parameter values were the carrying capacity of the resource and the handling time of resources by wolves

Subject(s)

Mathematics.

Biologists.

Ecology.

Omnivores.

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