Deborah Beghè, Fabio Caccioli, Luca Dall’Asta

Paper #: 12-07-010

Balancing selection is a special case of frequency-dependent selection that is known to be the major force for the maintenance of biodiversity and polymorphism in natural populations. In finite populations, genetic drift eventually drives the population to fixation to the detriment of biodiversity. The interplay between selection and genetic drift is much richer in spatially-extended populations, where the local density of individuals can be low even in the limit of infinitely large systems. We consider the limit of very low local density of individuals (strong genetic drift) that is well represented by a modified voter model. We show analytically the existence of a non-equilibrium phase transition between a region in which fixation always occurs and a coexistence phase for a one-dimensional system. We also provide a characterization of the dynamical properties of the system, in particular for what concern the coarsening behavior and the existence of traveling waves.