Voter model perturbations and the evolution of the dispersal distance

Daniel Remenik (April 19, 2012)

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The problem of how often to disperse in a randomly fluctuating environment has long been investigated, primarily using patch models with uniform dispersal. Here, we consider the problem of choice of seed size for plants in a stable environment when there is a trade off between survivability and dispersal range. For this we analyze a stochastic spatial model to study the competition of different dispersal strategies. Most work on such systems has been done by simulation or non-rigorous methods such as pair approximation. I will describe a model based on the general voter model perturbations recently studied by Cox, Durrett, and Perkins (2011) which allows us to rigorously and explicitly compute evolutionarily stable strategies. A main difficulty in this case is to extend the earlier work in three or more dimensions to the more complicated two-dimensional case, which is the natural setting for this problem. This is joint work with Rick Durrett.