Dynamics of the classical genetic model for the evolution of dominance
type: Item
instance of: scholarly article
title: Dynamics of the classical genetic model for the evolution of dominance
zbMATH Open document ID: 0535.92017
DOI: 10.1016/0025-5564(83)90096-2
author: Reinhard Bürger
published in: Mathematical Biosciences
publication date: 1983-01-01T00:00:00Z
review text: In 1928 \textit{R. A. Fisher} [Am. Nat. 62, 115-126] published his theory of the evolution of dominance. His explanation of the phenomenon of dominance was that it is the result of the selection of modifier genes which cause the fitness of the heterozygote to approach that of the wild type homozygote in order to protect the phenotype from the influence of deleterious recurrent mutations of the primary genes. In the present paper, the author uses a generalized method of Lyapunov functions to study the dynamics of the classical genetic model for the evolution of dominance. The model is treated as a two locus two allele system of a primary and a modifying locus with selection, mutation, and recombination. Its behavior can be described either by a system of four differential equations or by a system of four difference equations. Under very general conditions global asymptotic stability is proved for mutation-selection balance at the primary locus. Under certain circumstances, extremely low frequency of the modifier and primary allele at the beginning of the evolution can allow the primary allele to become extinct.
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 3850886
zbMATH Keywords: evolution of dominance
zbMATH Keywords: selection of modifier genes
zbMATH Keywords: generalized method of Lyapunov functions
zbMATH Keywords: two locus two allele system
zbMATH Keywords: mutation
zbMATH Keywords: recombination
zbMATH Keywords: differential equations
zbMATH Keywords: difference equations
zbMATH Keywords: global asymptotic stability
reviewed by: J. Keesling
MaRDI profile type: Publication
full work available at URL: 0025-5564(83)90096-2
OpenAlex ID: W2076971811
cites work: Nonlinear analysis of some models for the evolution of dominance
cites work: Q5659379
cites work: Q3856478
cites work: Towards a theory of the evolution of modifier genes
cites work: Q5534447
cites work: Q3948194
Recommended article: Nonlinear analysis of some models for the evolution of dominance
Recommended article: The selection mutation equation
Recommended article: Mutation, selection, and recombination in a model of phenotype evolution
Recommended article: Dynamics of the two-locus haploid model
Recommended article: Q3182627
Recommended article: Global analysis of a two-allele mating system
Recommended article: Q2930430
Recommended article: Evolutionary dynamics in frequency-dependent two-phenotype models
Recommended article: Modifiers of mutation rate: A general reduction principle
description: scientific article; zbMATH DE number 3850886