Date of Submission

Spring 2017

Academic Programs and Concentrations

Mathematics; Environmental and Urban Studies

Project Advisor 1

John Cullinan

Project Advisor 2

Elias Dueker

Abstract/Artist's Statement

In this project I am modelling the predator-prey relationship between California sheephead and purple sea urchin populations, respectively, in kelp forests off the coast of southern California. The Lotka-Volterra equations explain predator-prey relationships in their most basic form. These equations incorporate a set of biological assumptions that can be unrepresentative of many ecological systems. I will consider alternate models that incorporate variations of the Lotka-Volterra model which may better represent the biology of the purple sea urchins and California sheephead. Using biological characteristics of both species in kelp forests, I will set possible and likely parameters and solve for unknown parameters. After constructing the models, I will fit each model to the population data. Once I have fit each model to the data, I will compute various error estimations using four possible objective functions and determine the model of best fit.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
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