Ecology 231: Mathematical Methods in Population Biology
3 Units, Offered Fall Quarter
Course Instructor: Alan Hastings, Environmental Science and Policy
1. Course format: The course will cover the basic mathematical methods used in the development and analysis of deterministic mathematical models in population biology. Emphasis will be placed on stability analysis and qualitative behavior of difference and differential equation models, with a brief introduction to the diffusion equation. Problem solving approaches and applications to population biology will be stressed. The role played by computer generated solutions in guiding analytic work will be discussed using basic commercially available dynamical systems packages for personal computers. The course will meet twice weekly for one and one-half hours. Course meetings will be devoted to lectures, problem solving sessions, and demonstrations of the use of simple dynamical systems packages.
2. Prerequisites: Students should have had one year of calculus and an undergraduate course in ecology or population biology, and familiarity with the use of a personal computer (IBM compatible or Macintosh).
3. Text used: Edelstein-Keshet, Leah. 1988. Mathematical Models in Biology. Random House. and Kocak, Huseyin. 1989. Differential and Difference Equations Through Computer Experiments. Springer Verlag. or Hubbard, John H., and Beverly H. West. 1991. MacMath: A Dynamical Systems Software Package for the Macintosh. Springer-Verlag.
4. Mode of grading: Grades will be based on frequent homework assignments and a take home final.
5. Topical outline:
I. Linear Difference Equations
II. Nonlinear Difference Equations
III. Introduction to Continuous Models
IV. Phase Plane Methods and Bifurcations
V. Diffusion Equation