Nicholas Barendregt, Department of Applied Mathematics, University of Colorado Boulder
Heteroclinic Cycling and Extinction in Winnerless Competition Models with Demographic Stochasticity
The winnerless competition formulated by May and Leonard gives a deterministic way to model populations that interact in a rock-paper-scissors style of dominance. However, when applying this and other similar cycling models to actual populations, demographic (counting of copy number) noise can play a large role in the behavior of the model. We formulate three nonequivalent models for a discrete stochastic version of winnerless competition and rigorously study their stationary distributions to show that one or more populations is guaranteed to go extinct. We then numerically show that the timing of these extinction events varies with system size. Finally, we investigate the role of demographic noise in a model for interacting populations of neurons by generalizing winnerless competition.