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
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.