Speaker: Leonard M. Sander, University of Michigan
Title: Fluctuations and Dispersal Rates in Population Dynamics
Abstract: A central question in evolution is to understand the best strategy for dispersal. That is, in an environment which has distributed resources, but where migration has risks, what should you do? --Stay at home (and stay out of trouble), --Or seek your fortune elsewhere? The best strategy will be selected by evolution. A simplified version of this problem considers two competing species that differ only in their dispersal rate, and are treated with deterministic pde's. A rigorous mathematical analysis gives a startling result: it is always best to disperse slowly, and the faster species will be driven to extinction. We show that this conclusion is no longer valid in a stochastic model: the fast species can dominate or there can be coexistence, depending on parameters. That is, fluctuations change the long-time behavior qualitatively. We discuss two different effects of fluctuations, and show that our results are consistent with more complex treatments that find that selected dispersal rates are not monotonic with the cost of migration.
Time: Friday, October 5, 2007, 3:30-4:20 p.m.Place: Science and Technology Building I, Room 242
Refreshments will be served before the talk at 3:00 p.m. in Room 222.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491