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 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.

17 pages, 2 figures

References in corpus (2)

• Padé approximants and exact two-locus sampling distributions
• An asymptotic sampling formula for the coalescent with Recombination

Cited by in corpus (6)

• Approximate sampling formulae for general finite-alleles models of mutation
• Tractable diffusion and coalescent processes for weakly correlated loci
• Chromosome Painting: how recombination mixes ancestral colors
• Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection
• Solving the migration-recombination equation from a genealogical point of view
• Solving the selection-recombination equation: Ancestral lines under selection and recombination