The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations
type: Item
instance of: scholarly article
title: The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations
zbMATH Open document ID: 0967.92014
author: Kevin J. Dawson
published in: Theoretical Population Biology
publication date: 2001-08-30T00:00:00Z
review text: A classical model of Kimura and Maruyama [see, e.g., \textit{T. Maruyama} and \textit{M. Kimura}, Proc. Natl. Acad. Sci., U.S.A. 72, 1602-1604 (1975)] is investigated, in which infinitesimally rare deleterious alleles segregate at an infinite number of unlinked loci. It has been long known that under multiplicative selection a population that initially is in linkage equilibrium (i.e., the allele frequencies are stochastically independent across loci) remains in linkage equilibrium. However, in practice, linkage equilibrium will often be distorted. In this article, the author provides an exact and explicit solution for the dynamics of this model with arbitrary initial conditions. He achieves this by describing the frequency distribution of types in terms of the factorial cumulant generating function and the factorial cumulants. The latter are most useful in describing departures from the Poisson distribution. Thus, he obtains an explicit representation for the decay of the linkage disequilibria. Furthermore, he applies this method to determine the joint dynamics of a modifier of the mutation rate together with deleterious alleles, whose mutation rate he is altering, and derives a simple invasion criterion for such a modifier.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 1271888
zbMATH Keywords: infinitesimally rare alleles
zbMATH Keywords: factorial cumulants
zbMATH Keywords: deleterious mutations
Wikidata QID: Q77928374
reviewed by: Reinhard Bürger
MaRDI profile type: Publication
full work available at URL: tpbi.1998.1375
OpenAlex ID: W1981743818
cites work: Q3883956
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DOI: 10.1006/TPBI.1998.1375
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description: scientific article; zbMATH DE number 1271888