The population genealogy of the infinitely-many neutral alleles model
type: Item
instance of: scholarly article
title: The population genealogy of the infinitely-many neutral alleles model
zbMATH Open document ID: 0636.92008
DOI: 10.1007/BF00277163
author: Peter Donnelly
author: Simon Tavaré
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: The author introduces a process \(M_ t\) analogous to Kingman's coalescent to describe the genealogy of populations evolving according to the infinitely-many neutral alleles model. The process \(M_ t\) is defined by \({\mathfrak M}_{D_ t}\), \({\mathfrak M}_ t\) is a Markov chain on \(N_{\infty}\times \Delta\), \[ N_{\infty}=\{0,1,2,3,...\infty \},\quad \Delta =\{(x_ 1,x_ 2,...): 0\leq x_ i\leq 1,\quad \sum x_ i=1\}, \] and \(D_ t\) is an independent death process on \(N_{\infty}\), \(D_ 0=\infty\). Using this process K-allele models are considered. Its marginal distribution is explicitly calculated.
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60J20
zbMATH DE Number: 4037660
zbMATH Keywords: Kingman's coalescent
zbMATH Keywords: genealogy of populations
zbMATH Keywords: infinitely-many neutral alleles model
zbMATH Keywords: K-allele models
zbMATH Keywords: marginal distribution
Wikidata QID: Q52609572
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00277163
OpenAlex ID: W2070433710
description: scientific article; zbMATH DE number 4037660