SummaryThe formulae for the mean and variance of squared deviations from an optimum are given for the cases of no dominance and of complete dominance, first assuming no environmental complications but later removing this restriction. The variance in each case is analysed into contributions due to (1) additive gene effects, (2) dominance deviations, (3) epistatic deviations, (4) environmental effects and (5) nonadditive joint effects of heredity and environment. In the case of complete dominance, formulae are developed which apply to epistatic relations in general. These lead to formulae for the correlations between parent and offspring and between two offspring.It appears that in a population in which the mean of some measurable character is at the optimum, the parent-offspring and fraternal correlations in adaptive value are approximately the squares of the corresponding correlations with respect to the character itself, whatever environmental complications there may be. Where the mean is not at the optimum, there is less difference between the correlations in adaptive value and the corresponding ones with respect to the character itself.

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