3 Genotype $\times$ Environment Interaction

The interaction of genotype and environment (``G $\times$ E'') must always be distinguished carefully from CorGE. Genotype-environment correlation reflects a non-random distribution of environments among different genotypes. ``Good'' genotypes get more or less than their fair share of ``good'' environments. By contrast, G $\times$ E interaction has nothing to do with the distribution of genetic and environmental effects. Instead, it relates to the actual way genes and environment affect the phenotype. G $\times$ E refers to the genetic control of sensitivity to differences in the environment. The old adage ``sauce for the goose is sauce for the gander'' describes a world in which G $\times$ E is absent, because it implies that the same environmental treatment has the same positive or negative effect regardless of the genotype of the individual upon whom it is imposed. An obvious example of G $\times$ E interaction is that of inherited disease resistance. Genetically susceptible individuals will be free of disease as long as the environment does not contain the pathogen. Resistant individuals will be free of the disease even in a pathogenic environment. That is, changing the environment by introducing the pathogen will have quite a different impact on the phenotype of susceptible individuals than on resistant ones. More subtle examples may be the genetic control of sensitivity to the pathogenic effects of tobacco smoke or genetic differences in the effects of sodium intake on blood pressure. The analysis of G $\times$ E in humans is extremely difficult in practice because of the difficulty of securing large enough samples to detect effects that may be small compared with the main effects of genes and environment. Studies of G $\times$ E in experimental organisms (see, e.g., Mather and Jinks, 1982) illustrate a number of issues which are also conceptually important in thinking about G$\times$E in humans. We consider these briefly in turn. The genes responsible for sensitivity to the environment are not always the same as those that control average trait values. For example, one set of genes may control overall liability to depression and a second set, quite distinct in their location and mode of action, may control whether individuals respond more or less to stressful environments. Another way of thinking about the issue is to consider measurements made in different environments as different traits which may or may not be controlled by the same genes. By analogy with our earlier discussion of sex-limitation, we distinguish between ``scalar'' and ``non-scalar'' G $\times$ E interaction. When the same genes are expressed consistently at all levels of a salient environmental variable so that only the amount of genetic variance changes between environments, we have ``scalar genotype $\times$ environment interaction.'' If, instead of, or in addition to, changes in genetic variance, we also find that different genes are expressed in different environments we have ``non-scalar G $\times$ E.'' G $\times$ E interaction may involve environments that can be measured directly or whose effects can be inferred only from the correlations between relatives. Generally, our chances of detecting G $\times$ E are much greater when we can measure the relevant environments, such as diet, stress, or tobacco consumption. The simplest situation, which we shall discuss in Chapter 9, arises when each individual in a twin pair can be scored for the presence or absence of a particular environmental variable such as exposure to severe psychological stress. In this case, twin pairs can be divided into those who are concordant and those discordant for environmental exposure and the data can be tested for different kinds of G $\times$ E using relatively simple methods. One ``measurable'' feature of the environment may be the phenotype of an individual's parent. A problem frequently encountered, however, is the fact that many measurable aspects of the environment, such as smoking and alcohol consumption, themselves have a genetic component so that the problems of mathematical modelling and statistical analysis become formidable. If we are unable to measure the environment directly, our ability to detect and analyze G $\times$ E will depend on the same kinds of data that we use to analyze the main effects of genes and environment, namely the patterns of family resemblance and other, more complex, features of the distribution of trait values in families. Generally, the detection of any interaction between genetic effects and unmeasured aspects of the between-family environment will require adoption data, particularly separated MZ twins. Interaction between genes and the within-family environment will usually be detectable only if the genes controlling sensitivity are correlated with those controlling average expression of the trait (see, e.g., Jinks and Fulker, 1970).