Statistical Genetics and Direct Coupling Analysis beyond Quasi-Linkage Equilibrium

Abstract

This work is about statistical genetics, an interdisciplinary topic between Statistical Physics and Population Biology. Our focus is on the phase of Quasi-Linkage Equilibrium (QLE) which has many similarities to equilibrium statistical mechanics, and how the stability of that phase is lost. The QLE phenomenon was discovered by Motoo Kimura and was extended and generalized to the global genome scale by Neher & Shraiman (2011). What we will refer to as the Kimura-Neher-Shraiman (KNS) theory describes a population evolving due to the mutations, recombination, genetic drift, natural selection (pairwise epistatic fitness). The main conclusion of KNS is that QLE phase exists at sufficiently high recombination rate ($r$) with respect to the variability in selection strength (fitness). Combining these results with the techniques of the Direct Coupling Analysis (DCA) we show that in QLE epistatic fitness can be inferred from the knowledge of the (dynamical) distribution of genotypes in a population. Extending upon our earlier work Zeng & Aurell (2020) here we present an extension to high mutation and recombination rate. We further consider evolution of a population at higher selection strength with respect to recombination and mutation parameters ($r$ and $\mu$). We identify a new bi-stable phase which we call the Non-Random Coexistence (NRC) phase where genomic mutations persist in the population without either fixating or disappearing. We also identify an intermediate region in the parameter space where a finite population jumps stochastically between QLE-like state and NRC-like behaviour. The existence of NRC-phase demonstrates that even if statistical genetics at high recombination closely mirrors equilibrium statistical physics, a more apt analogy is non-equilibrium statistical physics with broken detailed balance, where self-sustained dynamical phenomena are ubiquitous