Evolution in a spatially structured population subject to rare epidemics.

We study a model that gives rise to spatially inhomogeneous population densities in a system of host individuals subject to rare, randomly distributed disease events. For stationary hosts that disperse offspring over short distances, evolutionary dynamics can lead to persistent populations with a variety of spatial structures. A mean-field analysis is shown to account for the behavior observed in simulations of a one-dimensional system, where the evolutionarily stable state corresponds to the solution of a straightforward optimization problem. In two dimensions, evolution drives the system to a stable critical state that is less well understood.