Symmetry breaking and coarsening in spatially distributed evolutionary processes including sexual reproduction and disruptive selection

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  • 13 April 2000
Abstract
Sexual reproduction presents significant challenges to formal treatment of evolutionary processes. A starting point for systematic treatments of ecological and evolutionary phenomena has been provided by the gene centered view of evolution. The gene centered view can be formalized as a dynamic mean field approximation applied to genes in reproduction / selection dynamics. We show that spatial distributions of organisms with local mating neighborhoods in the presence of disruptive selection give rise to symmetry breaking and spontaneous pattern formation in the genetic composition of local populations. Global dynamics follows conventional coarsening of systems with nonconserved order parameters. The results have significant implications for ecology of genetic diversity and species formation.

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