Open AccessTo the analysis of weak two-locus viability selection and quasi linkage equilibrium
Author(s) -
V. P. Pasekov
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524846781-785
Subject(s) - mathematics , singular perturbation , taylor series , linkage disequilibrium , ordinary differential equation , selection (genetic algorithm) , population , locus (genetics) , statistical physics , mathematical analysis , differential equation , physics , allele , computer science , biochemistry , demography , artificial intelligence , sociology , haplotype , gene , chemistry
A model of weak viability selection at two multi-allele loci with standardization of approaches through the use of perturbation theory is examined. The estimate of the quasi-equilibrium value for the linkage disequilibrium coefficient D is analyzed, and results in terms of average effects in quantitative genetics and in terms of the theory of singular perturbations in mathematics are obtained. The approximation of a discrete-time model of a random mating population with non-overlapping generations under weak selection by ordinary differential equations is considered. Weak selection is considered as a perturbation of the model without selection. The resulting model is singularly perturbed; that is, fast (D) and slow (allele frequencies) variables can be distinguished. The first approximation equation for quasi-equilibrium of D is obtained using the first terms of the Taylor series expansion of the model functions. It coincides with the corresponding part of the system of the first approximation of the asymptotic series for solving singularly perturbed equations.