# Simon Maccracken Stump

Harvey Mudd College Mathematics 2005 - 2006

Thesis Proposal: | Recolonization in the Face of Disaster |
---|---|

Annotated Bibliography: | Annotated Bibliography |

Mid-Year Report: | Succession, Invasion, & Coexistence: PDEs & Ecology |

Poster: | Research Poster |

Presentation: | Final Thesis Talk (note: movies do not work. If you want a copy of them, email me and I'll send you the .avi file.) |

Final Report: | Thesis |

Thesis Advisor: | Prof. Jon Jacobsen |

Second Reader: | Prof. Alfonso Castro |

E-Mail Me: | sstump@hmc.edu |

## Succession, Invasion, & Coexistence: PDEs and Ecology

For my thesis, I considered a reaction-diffusion form of the Lotka-Volterra Equation:

u_{t}(x, t) = du_{x}x + u f(x, u, v)

v_{t}(x, t) = dv_{x}x + v g(x, v, u)

where f and g (the growth equations) are represented by

f (u, v) = ru(1 −(u + av)/K(x))

or

f (u, v) = ru(K(x) − u − av).

I chose to focus my attention on two questions:

- If the environment becomes more fragmented, or of r or d change, how does that affect the number of organisms we expect to find in an environment? Does it matter which equation we use?
- If the environment ceases to be temporally stable, how does that change competitive interactions? How do r, d, and the level of environmental heterogeneity affect these things?; Does it matter which equation we use?