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

*(English)*Zbl 1241.92054Summary: 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 an 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.

##### MSC:

92D15 | Problems related to evolution |

65C50 | Other computational problems in probability (MSC2010) |

62E20 | Asymptotic distribution theory in statistics |

92D10 | Genetics and epigenetics |

##### Keywords:

asymptotic expansions##### References:

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