Stochastic Models for the Inference of Life Evolution

Statistical Genetics in and out of Quasi-Linkage Equilibrium

December 6, 2022

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Statistical Genetics in and out of Quasi-Linkage Equilibrium (Extended) Vito Dichio, Hong-Li Zeng, Erik Aurell

This review is about statistical genetics, an interdisciplinary topic between statistical physics and population biology. The focus is on the phase of quasi-linkage equilibrium (QLE). Our goals here are to clarify under which conditions the QLE phase can be expected to hold in population biology and how the stability of the QLE phase is lost. The QLE state, which has many similarities to a thermal equilibrium state in statistical mechanics, was discovered by M Kimura for a two-locus two-allele model, and was extended and generalized to the global genome scale by (Neher and Shraiman, 2011). What we will refer to as the Kimura-Neher-Shraiman (KNS) theory describes a population evolving due to the mutations, recombination, natural selection and possibly genetic drift. A QLE phase exists at sufficiently high recombination rate and/or mutation rates with respect to selection strength. We show how in QLE it is possible to infer the epistatic parameters of the fitness function from the knowledge of the (dynamical) distribution of genotypes in a population. We further consider the breakdown of the QLE regime for high enough selection strength. We review recent results for the selection-mutation and selection-recombination dynamics. Finally, we identify and characterize a new phase which we call the non-random coexistence (NRC) where variability persists in the population without either fixating or disappearing.