Volume 132, Number 5, December 2020
|Number of page(s)||7|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||05 January 2021|
Gaussian closure scheme in the quasi-linkage equilibrium regime of evolving genome populations
Laboratoire de Physique de l'Ecole Normale Supérieure, PSL Research & CNRS UM8023, Sorbonne Université 24 rue Lhomond, Paris, France
Received: 15 July 2020
Accepted: 12 November 2020
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.
PACS: 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 87.23.Kg – Dynamics of evolution
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