On the within-sibship variance

Abstract

An approximate formula for the expected within-sibship genotypic variance of a polygenic, diallelic, additive character is obtained for arbitrary recombination between the loci affecting the character. The formula is exact, when there is no recombination, or when the recombination is free. It is also shown that, if the value of (one-half of the parental genotypic variance) is assigned to the within-sibship genotypic variance, as in the model of Cavalli-Sforza and Feldman (1976, Proc. Natl. Acad. Sci. USA 73, 1689-1692), it implies the assumptions of random mating and of the perfect linkage. If, on the other hand, the value of (one-half of the linkage equilibrium genotypic variance) is assigned to the within-sibship variance, as in the model of Rice, Cloninger, and Reich (1978, Amer. J. Hum. Genet. 30, 618-643), it implies the assumptions of random mating and either of the free recombination, or of the linkage equilibrium, if the recombination is not free.