Dynamics of the classical genetic model for the evolution of dominance
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.
generalized method of Lyapunov functions
scientific article; zbMATH DE number 3850886