Genetics, Environment, & The Norm of Reaction [ II ]
"Is the difference between groups genetic?"

    We defined the Norm of Reaction as a curve that relates, for a given genotype, the contribution of  environmental variation to observed phenotypic variation. The norm of reaction curve can be thought of as a mirror that reflects the environmental-effect curve into phenotypic space. We showed how the shape of the curve affects the expression of a single genotype in a single group or population. We now ask, given two alternative genotypes, does the norm of reaction explain observed phenotypic differences between groups?

    Consider two breeds of cattle, corresponding to genotypes A & B, evaluated for milk-fat production in "Good" and "Poor" environments (the group difference), under three forms of the Norm of Reaction curve.

    [Left]  The norm of reaction for each genotype is flat line, and the two lines are offset. Among cattle raised in either a nutrient-poor free-range environment ("Poor" curve on the y-axis) or a nutrient-rich feed-lot environment ("Good" curve), those with genotype A always produce higher milk-fat (narrow red curve on x-axis) than do those with genotype B (narrow blue curve). The range of phenotypes for each breed is quite small and largely independent of the environment. A conventional Heritability study of milk-fat production made in either environment will conclude that genes have a strong influence on milk-fat production (high heritability). This corresponds to a pattern in which the difference between breeds is "genetic", in the sense that it is determined by and predictable from genotype, independent of environment.

    [Middle] The norm of reaction for each genotypes is a sloped line, and the two lines are offset with constant slope. Improvement of the environment from "Poor" to "Good" results in a significant increase in milk-fat quantity in both breeds. In either environment, the performance of genotype A always exceeds that of genotype B. However, the performance of genotype B in the "Good" environment exceeds that of genotype A in the "Poor" environment. Milk-fat production still has high heritability, but has a strong environmental component. Expectations of the performance (phenotype) of either breed must take environment into consideration.

    [Right] The norm of reaction for each genotype is a complex curve, and the curves have different shapes. The two curves are essentially flat and parallel in the "Poor" environment, and heritability is high as in the first example. When the same two breeds are raised in the "Good" environment, both show a marked improvement in average milk-fat production, as in the second example. However, cattle with genotype B now on average produce richer milk  than those with genotype A (mean of the blue curve shifted to the right of the red curve), the reverse of the previous situation. As the norm of reaction becomes steeper, both breeds also show a wider range of milk fat production (broad blue and red curves), depending on the exact environmental conditions. A study of heritability in the "Good" environment will conclude that the difference in genotypes has relatively low influence on milk-fat production (low heritability), which is mostly a consequence of environmental variation.

    Thus the relative importance of "Genetics" and "Environment" cannot be expressed as a unitary Heritability coefficient, which may vary greatly depending on the environment in which the genes are expressed. The conventional quantitative genetic study of heritability measured for a single population within a single environment cannot accurately estimate the Norm of Reaction between groups and environments, and may not predict phenotypic response in a different environment.