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
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.
scientific article; zbMATH DE number 410098