Observations show that evolutionary processes often relate to multilocus epistatic selection. Here we develop further the approach suggested earlier by Zhivotovsky and Gavrilets to admit arbitrary multilocus epistasis. The obtained dynamic equations for allelic frequencies and gametic disequilibria are represented in a simple form. If selection is weak, this result extends Wright’s evolutionary equation to the case of cis-trans effects and sex differences in both recombination rates and genotypic fitnesses. Additionally to Wright’s equations for allelic frequencies, we derive equations for the gametic disequilibrium terms. We also give a general expression for the gametic disequilibria in a quasi-linkage state.

A general multilocus two-allele model for epistatic selection

The selection for a single additively inherited quantitative character is studied using computer models of 3 types: 1) all the individuals had the same viability, and the paratypic deviation does not depend on their genotype; 2) differential viability of genotypes is taken into account with respect to a number of heterozygous loci; 3) differential paratypic deviation is estimated, it is introduced like viability in the model 2. Two types of trancation selection, stabilizing and directed, under the selection coefficient of approximately 0.5 are studied. There are studied dynamics of genotypic (omega2gamma) and phenotypic (omega2phi) variances, the heritability index and it estimates (for the correlation progeny-parent--rho; for the regression progeny-parent--b; for half-sibses--v), and the non-equilibrium of a population for the models. The number of generation was 10; the population number in every generation was 200; the number of loci in the main experiment was 10.h2 values were calculated in the progeny before selection (p1, b1, v1) and after selection (p2, b2, v2). It is shown that stabilizing selection results in the formation of balanced gene complexes; the rate of decreasing omega2phi depends on the genetic length of a chromosome region in which genes, determining the character, are located, and not on the number of genes. The distribution of a character under directed selection depends on the type of the model. p2, b2, and v2 values are the worst. The best is the b1 value. It is concluded that the problem of predicting the selection effect using statistical estimates of heretability is connected with the problem of investigation of population heterogeneity and integrating their genetical structure.

Dynamics of population genetics parameters and their statistical during assessment selection for quantitative characters. I. An additive model. One character

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Dynamics of population genetics parameters and their statistical during assessment selection for quantitative characters. I. An additive model. One character