Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population with random mating. II: The case of constant fertilities
type: Item
instance of: scholarly article
title: Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population with random mating. II: The case of constant fertilities
zbMATH Open document ID: 0804.92015
DOI: 10.1007/BF00161200
author: Joseph M. Szucs
published in: Journal of Mathematical Biology
publication date: 1993-09-07T00:00:00Z
review text: The Nagylaki-Crow continuous model describes the evolution of genotype frequencies in a large population with overlapping generations under the assumption of differential fertilities and differential death rates. In particular, it is not based on the assumption that the genotypes are in Hardy-Weinberg proportions. The corresponding system of ODE's is difficult to analyse and even in simple systems complicated dynamical behavior can occur. The author continues his investigations in ibid., No. 4, 317-349 (1993; Zbl 0783.92026) of this model in the case of an autosomal locus with two alleles (and hence three genotypes). Here he assumes that fertilities are additive, positive and constant and that death rates are constant. He proves that global convergence occurs and that there is at most one polymorphic equilibrium or there exists a continuum of equilibria. A classification of the possible cases is provided.
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 410098
zbMATH Keywords: selection
zbMATH Keywords: Nagylaki-Crow continuous model
zbMATH Keywords: evolution of genotype frequencies
zbMATH Keywords: autosomal locus
zbMATH Keywords: two alleles
zbMATH Keywords: three genotypes
zbMATH Keywords: fertilities
zbMATH Keywords: death rates
zbMATH Keywords: global convergence
zbMATH Keywords: polymorphic equilibrium
zbMATH Keywords: continuum of equilibria
reviewed by: Reinhard Bürger
MaRDI profile type: Publication
cites work: Quasimonotone systems and convergence to equilibrium in a population genetic model
cites work: Q3992992
cites work: Continuous selective models
cites work: Q4126113
cites work: Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population
cites work: Q4692840
full work available at URL: https://doi.org/10.1007/bf00161200
OpenAlex ID: W2884763161
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description: scientific article; zbMATH DE number 410098