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Describing the evolution of a population of genomes evolving in a complexfitness landscape is generally very hard. We here introduce an approximateGaussian closure scheme to characterize analytically the statistics of agenomic population in the so-called Quasi--Linkage Equilibrium (QLE) regime,applicable to generic values of the rates of mutation or recombination andfitness functions. The Gaussian approximation is illustrated on a short-rangefitness landscape with two far away and competing maxima. It unveils theexistence of a phase transition from a broad to a polarized distribution ofgenomes as the strength of epistatic couplings is increased, characterized byslow coarsening dynamics of competing allele domains. Results of the closurescheme are corroborated by numerical simulations.

Gaussian Closure Scheme in the Quasi-Linkage Equilibrium Regime of Evolving Genome Populations