Gaussian closure scheme in the quasi-linkage equilibrium regime of evolving genome populations

Describing the evolution of a population of genomes evolving in a complex fitness landscape is generally very hard. We here introduce an approximate Gaussian closure scheme to characterize analytically the statistics of a genomic population in the so-called quasi-linkage equilibrium (QLE) regime, applicable to generic values of the rates of mutation or recombination and fitness functions. The Gaussian approximation is illustrated on a short-range fitness landscape with two far away and competing maxima. It unveils the existence of a phase transition from a broad to a polarized distribution of genomes as the strength of epistatic couplings is increased, characterized by slow coarsening dynamics of competing allele domains. Results of the closure scheme are corroborated by numerical simulations.