Asymptotic sampling distributions made easy: loose linkage in the ancestral recombination graph

TL;DR

This paper extends a probabilistic approach to analyze the distribution of genetic samples under high recombination rates across multiple loci, simplifying complex calculations and generalizing classical results in population genetics.

Contribution

It generalizes a probabilistic coupling method from two loci to multilocus settings, providing a new, more intuitive way to understand asymptotic sampling distributions.

Findings

Generalizes the coupling approach to multiple loci

Simplifies derivation of asymptotic distributions

Extends classical results to multilocus models

Abstract

Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is strong compared to resampling are often based on the approximate solution of certain recursions, which is technically hard and offers little conceptual insight. This work generalises an elegant probabilistic argument, based on the coupling of ancestral processes but so far only available in the case of two sites, to the multilocus setting. This offers an alternative route to, and slightly generalises, a classical result of Bhaskar and Song.