  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 which assigns effective fitness to each allele instead of
each organism. The gene centered view can be formalized as a dynamic mean field
approximation applied to genes in reproduction / selection dynamics. We show
that the gene centered view breaks down for symmetry breaking and pattern
formation within a population; and show that spatial distributions of organisms
with local mating neighborhoods in the presence of disruptive selection give
rise to such symmetry breaking and 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 the ecology of genetic diversity and species formation.
