Inferring epistasis from genomic data with comparable mutation and outcrossing rate

We consider a population evolving due to mutation, selection and recombination, where selection includes single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). We further consider the problem of inferring fitness in the evolutionary dynamics from one or several snap-shots of the distribution of genotypes in the population. In the recent literature this has been done by applying the Quasi-Linkage Equilibrium (QLE) regime first obtained by Kimura in the limit of high recombination. Here we show that the approach also works in the interesting regime where the effects of mutations are comparable to or larger than recombination. This leads to a modified main epistatic fitness inference formula where the rates of mutation and recombination occur together. We also derive this formula using by a previously developed Gaussian closure that formally remains valid when recombination is absent. The findings are validated through numerical simulations.