## Advances in Applied Probability

- Adv. in Appl. Probab.
- Volume 44, Number 2 (2012), 391-407.

### 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 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.

#### Article information

**Source**

Adv. in Appl. Probab. Volume 44, Number 2 (2012), 391-407.

**Dates**

First available in Project Euclid: 16 June 2012

**Permanent link to this document**

http://projecteuclid.org/euclid.aap/1339878717

**Digital Object Identifier**

doi:10.1239/aap/1339878717

**Mathematical Reviews number (MathSciNet)**

MR2977401

**Zentralblatt MATH identifier**

06055127

**Subjects**

Primary: 92D15: Problems related to evolution

Secondary: 65C50: Other computational problems in probability 92D10: Genetics {For genetic algebras, see 17D92}

**Keywords**

Coalescent theory recombination asymptotic expansion sampling distribution

#### Citation

Bhaskar, Anand; Song, Yun S. Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci. Adv. in Appl. Probab. 44 (2012), no. 2, 391--407. doi:10.1239/aap/1339878717. http://projecteuclid.org/euclid.aap/1339878717.