The Wright-Fisher model with temporally varying selection and population size
type: Item
instance of: scholarly article
title: The Wright-Fisher model with temporally varying selection and population size
zbMATH Open document ID: 0566.92011
DOI: 10.1007/BF00276544
author: Peter Donnelly
author: Neville Weber
published in: Journal of Mathematical Biology
publication date: 1985-01-01T00:00:00Z
review text: This paper is concerned with the Wright-Fisher model in genetics, for which the population size \(M_ n\) of generation n is allowed to be random, and the selective advantage \(\sigma_ n\) of one of the alleles may also vary with the generation. The authors study the question of whether ultimate genetic polymorphism is possible in the population. In the general case, subject to certain conditions on \(M_ n\) and \(\sigma_ n\), only partial results are obtained. When, however, \(M_ n\) and \(\sigma_ n\) are not density dependent, it is possible to derive complete results. One such, for example, is that fixation occurs with probability 1 if and only if \(\sum^{\infty}_{0}(M_ n^{-1}+\sigma_ n)=\infty\) a.s. The paper ends with the discussion of bounds for the fixation probability in the case where \(\sigma_ n=\sigma\) is a constant.
reviewed by: J. Gani
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 3904389
zbMATH Keywords: ultimate homozygosity
zbMATH Keywords: coupling techniques
zbMATH Keywords: random population size
zbMATH Keywords: Wright-Fisher model
zbMATH Keywords: selective advantage
zbMATH Keywords: ultimate genetic polymorphism
zbMATH Keywords: bounds for the fixation probability
MaRDI profile type: Publication
Wikidata QID: Q113909060
full work available at URL: https://doi.org/10.1007/bf00276544
OpenAlex ID: W1972803944
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description: scientific article; zbMATH DE number 3904389