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Closed-form two-locus sampling distributions : accuracy and universality

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Jenkins, Paul and Song, Yun S (2009) Closed-form two-locus sampling distributions : accuracy and universality. Genetics, Vol.183 (No.3). pp. 1087-1103. doi:10.1534/genetics.109.107995

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Official URL: http://dx.doi.org/10.1534/genetics.109.107995

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Abstract

Sampling distributions play an important role in population genetics analyses, but closed-form sampling formulas are generally intractable to obtain. In the presence of recombination, there is no known closed-form sampling formula that holds for an arbitrary recombination rate. However, we recently showed that it is possible to obtain useful closed-form sampling formulas when the population-scaled recombination rate ρ is large. Specifically, in the case of the two-locus infinite-alleles model, we considered an asymptotic expansion of the sampling formula in inverse powers of ρ and obtained closed-form expressions for the first few terms in the expansion. In this article, we generalize this result to an arbitrary finite-alleles mutation model and show that, up to the first few terms in the expansion that we are able to compute analytically, the functional form of the asymptotic sampling formula is common to all mutation models. We carry out an extensive study of the accuracy of the asymptotic formula for the two-locus parent-independent mutation model and discuss in detail a concrete application in the context of the composite-likelihood method. Furthermore, using our asymptotic sampling formula, we establish a simple sufficient condition for a given two-locus sample configuration to have a finite maximum-likelihood estimate (MLE) of ρ. This condition is the first analytic result on the classification of the MLE of ρ and is instantaneous to check in practice, provided that one-locus probabilities are known.

Item Type: Journal Article
Divisions: Faculty of Science > Statistics
Journal or Publication Title: Genetics
Publisher: Genetics Society of America
ISSN: 0016-6731
Official Date: 2009
Dates:
DateEvent
2009Published
Volume: Vol.183
Number: No.3
Page Range: pp. 1087-1103
DOI: 10.1534/genetics.109.107995
Status: Peer Reviewed
Publication Status: Published

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