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:
ut(x, t) = duxx + u f(x, u, v)
vt(x, t) = dvxx + 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?