Bose-Einstein distribution, condensation transition, and multiple stationary states in multiloci evolution of diploid populations

The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete with selection processes that tend to reduce genetic variation. Here, we show that the Bose-Einstein distribution describe the multiple stationary states of a diploid population under this multiloci evolutionary dynamics. Moreover, the evolutionary process might undergo an interesting condensation phase transition in the universality class of a Bose-Einstein condensation when a finite fraction of pairs of linked loci is fixed into given allelic states. Below this phase transition the genetic variation within a species is significantly reduced and only maintained by the remaining polymorphic loci.