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Consider a large system of individuals of multiple types, who live in spatially distributed colonies. Let the individuals move randomly around between the colonies (= migration). Assume additionally that the individuals are subject to occasional stochastic non-local reshuffling-resampling events with skewed offspring distribution (= reproduction under constrained amount of resources). What can we say about the ergodic behaviour of such systems? How does it depend on the intensities of the evolutionary forces? Under which circumstances shall we expect in the long run local coexistence of individuals of different types in the colonies? Under which circumstances do mono-type clusters of colonies appear? We suggest a class of stochastic models of such systems (based on the Cannings models from population genetics) and obtain a clear-cut criterion for the clustering vs. local coexistence dichotomy. This is joint work with Frank den Hollander, Andreas Greven, and Sandra Kliem.
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