Ancestral lines under recombination

TL;DR

This paper reviews recent advances in solving the deterministic recombination equation in population genetics by applying ancestral processes from stochastic models, resulting in a clear solution through ancestral partitioning.

Contribution

It introduces ancestral partitioning processes into deterministic models, providing a transparent solution to the long-standing recombination equation challenge.

Findings

Derived explicit solutions for the recombination equation

Connected stochastic ancestral processes with deterministic models

Enhanced understanding of ancestral lineages in population genetics

Abstract

Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of \emph{stochastic} models of population genetics, into the deterministic setting. With the help of an ancestral partitioning process, which is obtained by letting population size tend to infinity (without rescaling parameters or time) in an ancestral recombination graph, we obtain the solution to the recombination equation in a transparent form.