Particle Systems: Theory for Applications to Biology

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Durrett will continue to apply the theory of stochastic spatial models to problems in biology, specifically studying: (a) abundance distributions generated by the voter model with mutation that are an alternative to the traditional lognormal, (b) hybrid zones and their scaling limits -- motion by mean curvature, (c) a generalization of the biased voter model used by Silvertown to model the competition of grass species, and (d) a nonlinear predator prey model that displays oscillatory behavior. In an interacting particle system, space is represented as a grid of sites each one of which can be in one of a finite set of states and changes its state at a rate that depends on the states of finitely many neighbors. These models have a structure that is well suited to many problems in biology and have recently seen many applications there. Durrett's investigations will continue previous work seeking to understand when the spatial distribution of individuals has an important effect on the outcome of competition and when it can be ignored. Earlier work has already identified a number of situations in which non-spatial approaches give incorrect answers to questions about the persistence or coexistence of competing species.