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

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  04 January 2016

Anand Bhaskar  and
Yun S. Song
Anand Bhaskar*
Affiliation:
University of California, Berkeley
Yun S. Song*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Computer Science Division, University of California, Berkeley, CA 94720, USA.
∗∗ Postal address: Computer Science Division and Department of Statistics, University of California, Berkeley, CA 94720, USA. Email address: yss@stat.berkeley.edu
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Abstract

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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.

Keywords

Coalescent theoryrecombinationasymptotic expansionsampling distribution

MSC classification

Primary: 92D15: Problems related to evolution
Secondary: 65C50: Other computational problems in probability 92D10: Genetics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 2 , June 2012 , pp. 391 - 407
Copyright
© Applied Probability Trust 

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