Genotypic Covariances between Inbred Relatives.

VER nearly half a century numerous workers have considered covariances and/or correlations between genotypic values of relatives and have related these population parameters to more basic parameters descriptive of the Mendelian mechanism of inheritance for diploids and the modes of gene action. FISHER (1918) considered random mating populations and developed formulae for the correlations between various types of relatives for autosomal loci for the cases of no epistasis and dual epistasis. This development involved the concepts of average effects of genes and dominance deviations. WRIGHT (1921) considered inbred populations derived from populations with random mating structure under the assumption of completely additive gene action. MALBCOT (1948) generalized the formulae of FISHER (1918) with his definitions of “identity by descent” and “coefficient de parent&” ~ ~ L J ~ O T also gave a probabilistic definition of the “coefficient of inbreeding” which had previously been defined by WRIGHT ( 1921 ) in terms of correlation between uniting gametes. KEMPTHORNE ( 1954, 1955a, 195 7) and COCKERHAM (1 954) extended the formulae of the previous workers to allow for epistatic gene action in random mating (noninbred) populations. The formula, in KEMPTHORNE’S (1957) notation, for the covariance between the genotypic values for two individuals, X and Y, is