Closed-Form Asymptotic Sampling Distributions under the Coalescent with Recombination for an Arbitrary Number of Loci

Abstract

Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case oftwoloci, a new framework based on an asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, anarbitrarynumber 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.