Simon Maccracken Stump

Harvey Mudd College Mathematics 2005 - 2006

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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:

  1. 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?
  2. 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?