We present a theoretical model of evolution of spatially distributed
populations in which organisms mate with and compete against each other
only locally. We show using both analysis and numerical simulation that
the typical dynamics of population density variation is a spontaneous formation
of isolated groups due to competition for resources. The resulting spatial
separation between groups strongly affects the process of genetic invasion
by local reproductive mixing, and spatially inhomogeneous genetic distributions
are possible in the final states. We then consider a specific version of
this model in the presence of disruptive selection, favoring two fittest
types against their genetic intermediates. This case can be simplified
to a system that involves just two nonconserved order parameters: population
density and type difference. Since the coexistence of two fittest types
is unstable in this case, symmetry breaking and coarsening occur in type
difference, implying eventual dominance by one type over another for finite
populations. However, such coarsening patterns may be pinned by the spontaneously
generated spatial separation between isolated groups. The long-term evolution
of genetic composition is found to be sensitive to the ratio of the mating
and competition ranges, and other parameters. Our model may provide a theoretical
basis for consideration of various properties of spatially extended evolutionary
processes, including spontaneous formation of subpopulations and lateral
invasion of different types.