  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.
