Beyond high mutation highrecombination limit in statisticalgenetics

Abstract: One considers the bi-allelic model in population genetics which describes a population of genomes evolving under the processes of selection, mutation, recombination and drift. A focus is made on the Quasi-Linkage Equilibrium (QLE) phase with recent derivations from Neher and Shraiman, which exists for fast recombinations compared to selection strength and whose dynamics is greatly simplified compared to the general case. Using results in the QLE regime along with Direct Coupling Analysis (DCA) one can infer fitness landscape in a population, in particular epistasis coefficients. Following these ideas, we investigate here in detail a relation between population size, recombination rate and epistasis variance describing where the QLE regime breaks down, from a DCA-inference point of view. In particular, we find that there is no clear variation of the critical recombination rate with population size, but that as expected there is a linear dependence between the standard deviation of total epistasis and that critical recombination rate.