A classification of coalescent processes for haploid exchangeable population models
type: Item
instance of: scholarly article
title: A classification of coalescent processes for haploid exchangeable population models
zbMATH Open document ID: 1013.92029
author: Martin Möhle
author: S. Sagitov
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: This paper is concerned with haploid population models in which the population size \(N\) is fixed, and the generations are non-overlapping. For any specific \(r\)-th generation, it is assumed that the family sizes \[ \nu_1^{(r)},\dots,\nu_i^{(r)}, \dots,\nu_N^{(r)}, \] of the offspring of the individuals \(i = 1,\dots,N\), alive in this generation, are exchangeable random variables. After appropriate scaling of the ancestral process, the authors establish a weak convergence criterion for these family sizes as \(N\to \infty\). This allows a full classification of the coalescent generators for exchangeable reproduction. Apart from the statement of the relevant theorem and its lengthy proof, the paper devotes a section to the particular population model whose time-scaled ancestral process converges to that of the Wright-Fisher model. The authors conclude with a discussion of their results, and provide a useful historical perspective of coalescent processes.
reviewed by: J. Gani
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1906029
zbMATH Keywords: ancestral processes
zbMATH Keywords: coalescent
zbMATH Keywords: exchangeability
zbMATH Keywords: generator
zbMATH Keywords: neutrality
zbMATH Keywords: population genetics
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1015345761
OpenAlex ID: W1897267496
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DOI: 10.1214/AOP/1015345761
description: scientific article; zbMATH DE number 1906029