Biology Reference
In-Depth Information
the calculation should equal the dimensionality of the data. Fortunately, this procedure
does not actually need to be done by hand.
Using any one of the measures of FA, it is possible to test hypotheses that predict ele-
vated or reduced FA. The hypothesis that two or more populations differ in average FA
can be tested just like the hypothesis that two or more populations differ in variance. One
test that is particularly insensitive to deviations from normality is Levene's test (
Levene,
1960
), often used to test for differences in variance. What Levene's test compares is the
average deviation of points from the mean of the sample. To carry out this test, which can
be done in Excel, calculate the level of overall FA for each individual and subtract that
from the mean (or median) value, and use the absolute value of that deviation in the test.
If FA is high, the mean value of that deviation will be large. Then use a
t-
test or ANOVA
to compare the mean values.
ANALYZING THE RELATIONSHIP BETWEEN PLASTICITY,
CA
NALIZATION AND DEVELOPMENTAL STABILI
TY
Numerous studies have examined the relationship between plasticity, canalization and
developmental stability (e.g.
Scheiner et al., 1991; Debat et al., 2000; Hoffmann and Woods,
2001; Dworkin, 2005a,b; Santos et al., 2005; Willmore et al., 2005; Breuker et al., 2006;
Hollander et al., 2006; Breno et al., 2011; Klingenberg et al., 2012
). One goal of many stud-
ies is to test the hypothesis that there is a “general buffering capacity”. What “general”
means can differ between studies, but the usual aim is to test the hypothesis that the same
mechanism(s) buffer variation arising from different sources. One possibility is that
mechanisms that buffer phenotypes against the perturbations also canalize them against
environmental perturbations, whether the environmental perturbations are macro- or
microenvironmental or even developmental noise. Sometimes the question is framed more
narrowly, such as whether mechanisms that enable phenotypes to respond to macroenvir-
onmental variation make them more sensitive to developmental noise (e.g.
Scheiner et al.,
1991
).
The hypothesis that the same mechanisms buffer more than one sort of perturbation
can be tested in two ways. The first is to estimate the correlation between a measure of
variance (genetic vs environmental or macro- vs microenvironmental) and/or a measure
of FA. The second is by comparing covariance matrices. This is done by comparing the
covariance matrix for one component of variation (e.g. “Individual”) to another (e.g.
“FA”). Using the first approach, the question is whether individuals who most deviate
from the mean also most deviate from bilateral symmetry, i.e. whether an individual's
deviation from the mean predicts its deviation from bilateral symmetry. In the second
case, the question is whether the buffering mechanisms have the same morphological
effects on variation. Both methods for testing the hypothesis are widely used, and both are
often used in the same study.
The first approach is straightforward to apply. The first step is to calculate each indivi-
dual's deviation from the relevant mean (e.g. the mean shape within an environment). The
second is to calculate its deviation from the other relevant mean, or from bilateral symme-
try. Given these two measures of each individual's deviations, the hypothesis is tested by
