The Problem of Genotype-Environment Correlation in the Estimation of Heritability from Monozygotic and Dizygotic Twins

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Abstract
It is commonly, but incorrectly, assumed that the presence of genotype × environment covariance must necessarily reduce the heritability (h2) as estimated from twin data, when the formula used to obtain h2 makes no assumption about G × E covariance or assumes that it is zero. But, in fact, G × E covariance does not always reduce the genetic variance, and it can be shown under some conditions, an increase in the G × E covariance implies a greater genetic variance. The effect of G × E covariance on h2 as estimated from data on MZ and DZ twins, depends jointly upon the degree of assortative mating and the degree of environmental correlation between MZ twins and between DZ twins. A method, based on the solution of a pair of simultaneous quadratic equations, is proposed for estimating the range of h2 from twin data under varying assumed values for assortative mating, the environmental correlations between MZ and DZ twins, and the G × E covariance. The solution of three simultaneous equations permits direct estimation of the genetic variance, environmental variance, and G × E covariance, under varying reasonable assumed values for assortative mating and the MZ and DZ environmental correlations. Examples of the method are based on intelligence tests scores of MZ and DZ twins.