Allelic frequencies given the sample's common ancestral type
type: Item
instance of: scholarly article
title: Allelic frequencies given the sample's common ancestral type
zbMATH Open document ID: 0657.92007
DOI: 10.1016/0040-5809(88)90009-3
author: B. Beder
published in: Theoretical Population Biology
publication date: 1988-01-01T00:00:00Z
review text: The author considers a population of fixed size N of haploid genes in which K distinct allelic types are possible; it is assumed that the evolution of the population follows a Moran model. Then, looking backward in time, any random sample of n genes eventually has a single common ancestral gene. The probability generating function for the number of times that in a random sample of size n there was a mutation along an individual's genealogical line since the sample's common ancestor is calculated, and from this function the expected proportion of genes in a random sample which are of a particular allelic type, given the allelic type of the sample's common ancestor is derived. It is shown that the same result can be obtained using Kingman's coalescent model. These results are used in the cases of the 2-allele model, the infinitely many alleles model, and the K-alleles model with constant mutation. In the last part, a model with an infinite number of allelic types and stepwise mutation is considered.
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 4074861
zbMATH Keywords: haploid genes
zbMATH Keywords: Moran model
zbMATH Keywords: probability generating function
zbMATH Keywords: Kingman's coalescent model
zbMATH Keywords: 2-allele model
zbMATH Keywords: infinitely many alleles model
zbMATH Keywords: K- alleles model
zbMATH Keywords: stepwise mutation
reviewed by: Monique Bertrand
MaRDI profile type: Publication
full work available at URL: 0040-5809(88)90009-3
OpenAlex ID: W2005824258
Wikidata QID: Q43487304
cites work: POSITIVE DEFINITE SEQUENCES AND CANONICAL CORRELATION COEFFICIENTS1
cites work: Q3671491
cites work: The coalescent
cites work: Wandering distributions and the electrophoretic profile
cites work: Mutant substitutions at linked nucleotide sites
description: scientific article; zbMATH DE number 4074861