A building block model for quantitative genetics.
We introduce a quantitative genetic model for multiple alleles which permits the parameterization of the degree, D, of dominance of favorable or unfavorable alleles. We assume gene effects to be random from some distribution and independent of the D's. We then fit the usual least-squares population genetic model of additive and dominance effects in an infinite equilibrium population to determine the five genetic components--additive variance sigma 2 a, dominance variance sigma 2 d, variance of homozygous dominance effects d2, covariance of additive and homozygous dominance effects d1, and the square of the inbreeding depression h--required to treat finite populations and large populations that have been through a bottleneck or in which there is inbreeding. The effects of dominance can be summarized as functions of the average, D, and the variance, sigma 2 D. An important distinction arises between symmetrical and nonsymmetrical distributions of gene effects. With symmetrical distributions d1 = -d2/2 which is always negative, and the contribution of dominance to sigma 2 a is equal to d2/2. With nonsymmetrical distributions there is an additional contribution H to sigma 2 a and -H/2 to d1, the sign of H being determined by D and the skew of the distribution. Some numerical evaluations are presented for the normal and exponential distributions of gene effects, illustrating the effects of the number of alleles and of the variation in allelic frequencies. Random additive by additive (a*a) epistatic effects contribute to sigma 2 a and to the a*a variance, sigma 2/aa, the relative contributions depending on the number of alleles and the variation in allelic frequencies.(ABSTRACT TRUNCATED AT 250 WORDS)
Tachida
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Department of Statistics, North Carolina State University, Raleigh 27695-8203.
Cockerham
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D000483:Alleles; D005799:Genes, Dominant; D008957:Models, Genetic