On the two-locus sampling distribution
type: Item
instance of: scholarly article
title: On the two-locus sampling distribution
zbMATH Open document ID: 0729.92012
DOI: 10.1007/BF00168175
published in: Journal of Mathematical Biology
publication date: 1990-01-01T00:00:00Z
review text: This paper is concerned with the distribution of gametic types in a random sample of size n of a two-locus stationary diffusion model with infinitely many neutral alleles. Two methods are used to study the Ewens sampling formula [\textit{W. J. Ewens}, Theor. Population Biology 3, 87-112 (1972; Zbl 0245.92009)]. The first is due to \textit{G. B. Golding} [Genetics 108, 257-274 (1984)] and includes additional probabilities in systems of linear equations satisfied by the probabilities required. This method allows some members of the sample to be specified at one locus only; it is used for numerical computations. The second method considers the joint distribution of the sample configuration and the number of recombination events, since the time of the most recent ancestor. This new method due to the authors is used to derive a two-locus version of an urn model of \textit{F. M. Hoppe} [J. Math. Biol. 20, 91-94 (1984; Zbl 0547.92009)]. Simulation of the two-locus sampling distribution is possible, when the recombination parameter is not too large. The authors point out that a number of their results may also be derived using genealogical processes analogous to the coalescent. Detailed proofs are collected in a 10 page appendix.
reviewed by: J. Gani
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 4207821
zbMATH Keywords: measure-valued diffusion
zbMATH Keywords: complete linkage
zbMATH Keywords: independent loci
zbMATH Keywords: distribution of gametic types
zbMATH Keywords: two-locus stationary diffusion model
zbMATH Keywords: infinitely many neutral alleles
zbMATH Keywords: Ewens sampling formula
zbMATH Keywords: joint distribution of the sample configuration
zbMATH Keywords: number of recombination events
zbMATH Keywords: two-locus version of an urn model
zbMATH Keywords: genealogical processes
Wikidata QID: Q113910145
author: Stewart N. Ethier
author: Robert Griffiths
MaRDI profile type: Publication
cites work: The infinitely-many-sites model as a measure-valued diffusion
cites work: The neutral two-locus model as a measure-valued diffusion
cites work: The sampling theory of selectively neutral alleles
cites work: Neutral two-locus multiple allele models with recombination
cites work: Q4035827
cites work: Pólya-like urns and the Ewens' sampling formula
cites work: The use of sample genealogies for studying a selectively neutral m-loci model with recombination
full work available at URL: https://doi.org/10.1007/bf00168175
OpenAlex ID: W1999314404
description: scientific article; zbMATH DE number 4207821