Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci

TL;DR

This paper develops a universal asymptotic framework to derive closed-form approximations of the multi-locus sampling distribution under the coalescent with recombination, extending previous two-locus results to an arbitrary number of loci.

Contribution

It introduces a combinatorial approach to obtain the first terms of an asymptotic expansion for the multi-locus sampling distribution, applicable to various mutation models.

Findings

Derived closed-form expressions for the first terms of the asymptotic expansion.

Expressions are universal across finite- and infinite-alleles mutation models.

Extended the asymptotic framework from two loci to multiple loci.

Abstract

Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.