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

TL;DR

This paper models multiloci diploid evolution using Bose-Einstein distribution, revealing a phase transition that drastically reduces genetic variation by fixing linked loci, akin to Bose-Einstein condensation.

Contribution

It introduces a novel application of Bose-Einstein statistics to describe multiple stationary states in multiloci evolution and identifies a condensation phase transition.

Findings

Bose-Einstein distribution describes stationary states in multiloci evolution.

A phase transition analogous to Bose-Einstein condensation occurs in genetic variation.

Below the transition, genetic diversity is significantly reduced.

Abstract

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 multi-loci 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.