Event Type:

Department Colloquium

Date/Time:

Monday, May 9, 2011 - 09:00

Location:

Kidder 350

Guest Speaker:

Institution:

University of the Pacific

Abstract:

This talk will address the adaptive dynamics of predator prey systems modeled by a dynamical system in which the characteristics are allowed to evolve by small random mutations. When only the prey are allowed to evolve, and the size of the mutational change tends to 0, the system does not exhibit prey coexistence and the parameters of the resident prey type converge to the solution of an ODE. When only the predators are allowed to evolve, coexistence of predators occurs. Depending on the parameters being varied we see (i) the number of coexisting predators remains tight and the differences of the parameters from a reference species converge in distribution to a limit, or (ii) the number of coexisting predators tends to infinity and we can study the evolving process of coexisting predator characteristics via connections with killed branching random walks and a toy branching-selection particle system.

Host: