Effects of identity disequilibrium and linkage on quantitative variation in finite populations

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Abstract
Summary: Identity disequilibrium, ID, is the difference between joint identity by descent and the product of the separate probabilities of identity by descent for two loci. The effects of ID on the additive by additive (a * a) epistatic variance and joint dominance component between populations and in the additive, dominance and a * a variance within populations, including the effects on covariances of relatives within populations, were studied for finite monoecious populations. The effects are formulated in terms of three additive partitions, ηb, ηa and ηd of the total ID, each of which increases from zero to a maximum at some generation dependent upon linkage and population size and decreases thereafter. ηd is about four times the magnitude of the other two but none is of any consequence except for tight linkage and very small populations. For single-generation bottleneck populations only d is not zero. With random mating of expanded populations ηb remains constant and ηa and ηd go to zero at a rate dependent upon linkage, very fast with free recombination. The contributions of joint dominance to the genetic components of variance within and between populations are entirely a function of the η's while those of a * a variance to the components are functions mainly of the coancestry coefficient and only modified by the η's. The contributions of both to the covariances of half-sibs, full-sibs and parent-offspring follow the pattern expected from their contributions to the genetic components of variance within populations except for minor terms which most likely are of little importance.