This Applet explores the concept of statistical gene-environment interaction. (Please make certain that you have read the text so that you can distinguish the loose meaning of GE interaction from the strict, statistical sense of the term.)
Instead of giving didactic instructions for the Applet, let us start with a simple example. First, enter three values for the genotypes aa, Aa, and AA. These can be any numbers between -1.0 and 1.0, but values of -1, 0, and 1 are good ones to start with, so enter them now. The next step is to enter a value for each genotype that represents the degree to which the genotype is sensitive to the environment. This number can range between 0.0 (completely insensitive to the environment) to 1.0 (very sensitive to the environment). Enter a value of 0 for each genotype and click on Submit.
A graph will appear above with three horizontal lines. These three lines give the phenotype for a genotype as the environment varies from low to high. Look at the red line (for genotype aa). It is flat (completely horizontal) and the phenotypic value is midway between low and average. The flatness of this line signifies that no matter what the environment for genotype aa, the phenotypic value will always be the same. Genotype aa is completely insensitive to the environment. The lines for genotype Aa (green) and for AA (blue) have a similar flatness-both of these genotypes are insensitive to the environment. However, the phenotypic values for these two genotypes are different-average for Aa (green line), and average to high for AA (blue line).
Keep the values for aa, Aa, and AA at -1, 0 and 1, but change the sensitivity to the environment value to .5 for all three genotypes. Now the lines for the three genotypes are no longer flat. But notice how the slope for all three lines is equal. This implies that each genotype is equally sensitive to the environment.
You will notice a thick vertical line at the end of the lines for each genotype. This line denotes the reaction range (aka norm of reaction) for the genotypes. The reaction range is defined as the range of phenotypes that will be observed for a genotype over all environments. Notice how the reaction range for all three genotypes is the same in the sense that the length of the thick red line equals the length of the thick green line that equals the length of the thick blue line. This indicates that all three genotypes are equally sensitive to the environment. Hence, there is a very important conclusion from this situation-when the slopes of the lines for each genotype are equal (or in different terms, when the reaction ranges are equal), then there is GE interaction in the loose sense but not in the strict, statistical sense.
Now keep the values for the three genotypes at -1, 0, and 1, but change their sensitivities to the environment to .10 (for aa), .5 for (for Aa) and 1 (for AA). Click on submit. What is different from the previous case? Two aspects of the graph are very different. First, the slope of the lines differs. The slope is relatively flat for genotype aa (red line), intermediate for genotype Aa (green line), and steepest for AA (blue line). Second, the reaction range for the three genotypes differs-it is very small for aa, intermediate for Aa and large for AA. This pattern indicates GE interaction in the strict, statistical sense-at least one genotypic slope differs from the others and at least one reaction range differs from the others.
How important is statistical GE interaction for human behavior? The sad fact is that we simply do not have the technology to adequately answer this question. But let us examine the problem for other organisms. Suppose that there were three strains of wheat that were the same except for their sensitivity to water. Genotype aa was water-insensitive; that is, whether there was a drought or monsoon, genotype aa would give the same yield. Genotype Aa was partially sensitive to water-it produced less in drought and more in rainy times. Genotype AA was very sensitive to drought, producing very little in drought but a bumper harvest when there is much rain. We can model this situation in the Applet by letting the values for all three genotypes equal 0, but varying the sensitivity to the environment. So set all three Average Values to 0, but let the Sensitivity to the Environment equal 0 (for aa), .5 (for Aa) and 1 (for AA) and click on Submit. This gives a GE interaction in the strict, statistical sense.
Now it is quite clear that plant breeders have developed special strains of seed that are drought resistance (e.g., genotype aa in the above graph). If plants have such genetic sensitivity to the environment, could we humans not have the same? Perhaps some of us have genotypes that make us "stress resistant" just as plants can have genotypes for drought resistance. Irrespective of the amount of stress in the environment, these types of people turn out the same. May others of us are "stress sensitive." In the presence of environmental stress, these genotypes are likely to develop psychopathology. If this is the case then there is indeed GE interaction in the strict, statistical sense for psychopathology.
This discussion is an interesting topic for speculation and cocktail-party chatter. At present, we lack the technology to measure genotypes and environments to gather empirical data that could answer the question. Hence, a sense of skepticism is advised. One of the most exciting goals of research is to fine-tune the technology of genotypic assessment and environmental measurement so that these questions can indeed be answered.