Evolutionary Developmental Biology (2): Variational Properties - Geometric Morphometrics for Biologists - page 347

PHENOTY PIC PLASTICITY: QUANTIFYING NORMS OF R EACTION

The central concept in studies of phenotypic plasticity is the norm of reaction
( Wolterek, 1909; Schmalhausen, 1949 ), which is the array of phenotypes produced by a
given genotype reared in different environments. To determine the norm of reaction of a
genotype we might, for example, split the offspring of highly inbred rats into two groups,
feeding one the standard laboratory diet and the other a protein deficient diet. After letting
these two groups grow to adulthood, we could then weigh them and measure their skulls
to determine if body weight and/or skull size is responsive to protein deficiency.
The norm of reactions for weight and skull size could then be represented by plotting the
independent variable (diet in this case) on the x -axis and the phenotypic variable on
the y -axis ( Figure 12.1 ). Figure 12.1A shows a case in which the treatment has no effect

the phenotype is invariant across the two environments. This is what we would see if
protein deficiency had no impact on the weight or skeletal size. Figure 12.1B shows the
alternative the phenotype does differ across the two environments. This is what we

would see if protein deficiency has an impact on weight or skeletal size. In the statistical
analysis of plasticity, the null hypothesis is that the treatment has no effect, a hypothesis
tested by Analysis of Variance (ANOVA, see Chapter 8, and for more complex designs,
see General Linear Models, Chapter 9).
Extending the analysis to two or more genotypes is reasonably straightforward because
we simply add a factor (genotype) to the statistical model and test the interaction term,
genotype

environment. Several of the possible norms of reaction are shown in
Figure 12.2 . One shows that the phenotypes of the two genotypes differ, but both are
invariant across the range of environments ( Figure 12.2A ). In this case, only genotype has
a significant effect on phenotype. The second possibility is that both genotypes exhibit
plasticity, to the same degree and in the same direction, making their norms of reaction
parallel ( Figure 12.2B ). In this case, the statistical analysis would reveal that both genotype
and environment have significant effects but the interaction term would not be significant
because the impact of the environment does not depend on genotype. A third possibility
is that one genotype exhibits plasticity but the other one does not ( Figure 12.2C ). In this

3

FIGURE 12.1 Norms of reaction for a single genotype reared in two environments. The environmental factor
is plotted on the x -axis, the phenotype on the y -axis. (A) The phenotype does not differ across the two environ-
ments. (B) The phenotype differs across the two environments.