A Gaussian Ansatz for Gene Chains, Advances Beyond the Quasi-Linkage Equilibrium

by Mr Vito Dichio (U Trieste, Italy)

Thursday 6 Aug 2020, 13:00 → 14:00 Europe/Stockholm

AlbaNova Main Building

Population genetics has long benefited from tools and ideas borrowed from statistical physics. A seminal study in this area is the recent work of R.A. Neher and B.I. Shraiman: genomic sequences are Ising spin chains and the evolutionary process is encoded in a master equation for the probability distribution P(g) of the genotypes that takes into account selection, mutations, recombination. In such a framework, they study the particular case of the Kimura's Quasi-Linkage Equilibrium, where selection is weak and recombination is prominent, and write a simple formula that relates parameters of P(g) to parameters of the evolutionary dynamics, paving the way for the inference of fitness from raw data. We present a new theory based on a Gaussian Ansatz for P(g) that extends and outperforms the Kimura-Neher-Shraiman theory in the case where selection is still weak but the mutational contribution is comparable or larger than the recombination effect. We validate our theoretical results through numerical simulations.

The talk is partly based on [arXiv:2006.16735].