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.

描述在复杂的适应环境中进化的基因组种群的进化通常非常困难。我们在这里介绍一种近似的高斯封闭方案，以分析地表征所谓的准连锁平衡（QLE）机制中的基因组种群统计数据，适用于突变率，重组率和适应度函数的通用值。高斯近似值在具有两个相距遥远且相互竞争的最大值的短距离健身景观中进行了说明。它揭示了随着上位偶联的强度增加，基因组从宽分布到极化分布的相变的存在，其特征是竞争等位基因域的缓慢变粗动态。封闭方案的结果通过数值模拟得到了证实。