A new element in the left-hand side of Fig. 28.7 is the triangle with an effect of the moderator (physical activity) on the mean of the observed levels of BMI. This indicates that the effect of physical activity was regressed from the BMI level and that the ACE decomposition was performed on the residual BMI. In this way twin researchers try to deal with the possibility that the genes that influence BMI may also influence physical activity. This ties in directly with the second omission in Eq. (28.11) where we not only assumed the absence of gene-environment interaction but also left out the terms that capture possible gene-environment (A-E, A-C) correlations. As indicated in the introduction, such gene-environment correlation is quite likely to occur, particularly in behavioral traits.
In both active and reactive gene-environment correlation the non-random aspects of the environment are a consequence of the genetic effects on the behavior of the individual and should be considered to reflect an extended pheno-type (Dawkins, 1982). In this case the heritabil-ity of the phenotype meaningfully incorporates the effects of gene-environment correlation. For instance, the genes that cause individual differences in the drive to be physically active may also influence BMI because low levels of physical activity may cause high levels of BMI. In this case estimating heritability of the residual BMI, i.e., after regressing out (partly genetic) individual differences in physical activity may not be correct. In contrast, when parents transmit the genes for high BMI to their offspring together with low encouragement to engage in physical activity, it makes more sense to take this passive gene-environment correlation into account before attempting a genetic decomposition of the variance in BMI, because such geneenvironment correlation may bias estimation of heritability and mask gene-environment interaction (Purcell, 2002).
To detect the gene-environment in the presence of potential gene-environment correlation, twin researchers first compute the genetic correlation between the moderating environmental variable and the trait of interest. If such a correlation is low or absent, the gene-environment correlation may be set to zero without dire effects on the estimates for the remaining final variance components. Both studies on BMI and physical activity, for instance, did not find a significant genetic correlation between BMI and physical activity in males. In females, however, a low but significant Rg of -0.22 was found. Such gene-environment correlation can be taken into account by regressing the effects of the moderator on the mean as is done in the left-hand side of Fig. 28.7. This removes genetic and environmental effects common to both physical activity and BMI. Similar reasoning applies to the potential E x activity and C x activity interactions.
A second approach is to perform combined test of gene-environment interaction and geneenvironment correlation. This is shown in the right-hand side of Fig. 28.7, where the genetic factors that influence BMI are split up in those that are common to BMI and physical activity (A1) and those that are not in common to these traits (A2). Here A1 is a hypothetical set of pleiotropic genes that lower BMI and increase the drive to exercise regularly. A2 are genes specific to BMI. Importantly physical activity is now allowed to moderate the effects of the genetic and environmental factors it has in common with BMI (a21, c21, e21) and/or the effects of the genetic or environmental factors that are specific to BMI (a22, c22, e22). The test for geneenvironment interaction is simply the test of a model with and ^2 freely estimated versus models that constrain these parameters to be zero.7
By far the best opportunity to test geneenvironment interaction arises when the environment can be experimentally controlled (Falconer, 1952). The same trait is then measured repeatedly in MZ and DZ twins under different environmental conditions. This rules out geneenvironment correlation since all subjects are exposed to all relevant environments. When the genetic correlation between the trait in different environments is found to be less than unity this constitutes robust evidence for geneenvironment interaction. Figure 28.5 already presented an example of this approach where SBP was measured at rest and under stress. The genetic correlation was non-unity (0.87), signaling gene-by-stress interaction. Indeed the emergence of new genetic variance in a stressful environment versus a resting environment is exactly what geneticists mean by geneenvironment interaction, namely that the effects of the individual's genotype on the phenotype are conditional on the environment.
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