Two Dimensional Lotka-Volterra Models and Superprocesses

  • Date: 04/04/2007

Ed Perkins (University of British Columbia)


University of British Columbia


Neuhauser and Pacala (99) introduced a particle system to model the
dynamics of two competing types on an integer lattice. We study the
model near the parameter values for which there is a cross-over from
preference of one's own type to preference of the other type. The
rescaled system converges to a super-Brownian motion with non-trivial
branching and growth rates. As a corollary, local information about
parameter values for which rare types can survive and both types can
co-exist is obtained. These results had been obtained earlier for
dimensions greater than 2. We extend many of these results to two
dimensions where the mathematics is more delicate, and perhaps the
biology more interesting. This is joint work with Ted Cox (Syracuse

Other Information: 

Probability Seminar 2007