Biology Reference
In-Depth Information
constraints may prove to be short-lived, since theoretical models predict that phenotypic
and genetic (co)variance structures evolve to match patterns of developmental and func-
tional integration (e.g.
Lande, 1980; Cheverud, 1982, 1984; Wagner, 1988; Wagner and
Altenberg, 1996
). This matching is expected to result from differential elimination of pleio-
tropic effects between components of different functional complexes, combined with the
maintenance (or augmentation) of pleiotropic effects within a complex.
Whatever the ultimate goal might be, studies of form
function relationships share a
common analytic task: testing whether differences in one set of variables are associated
with differences in another set of variables measured on the same individuals or taxa. As
we showed in previous chapters, tests of this type can be performed for shape variables
using the same techniques as have been used for other morphometric variables.
Suppose we want to know if there is a difference in jaw shape between tree squirrels in
arid environments and those in more humid environments. We might expect a difference
between the squirrels because different species of trees are found in those environments,
with nuts and leaves and other edible bits that have different properties. We could collect
squirrels from the different environments, digitize their jaws and perform an ANOVA to
test the hypothesis that the shape of their jaws differs between environments. The
test could be quite simple, with only two groups from habitats classified as humid and
arid. A more complex, and perhaps, more realistic analysis might have many groups
from many different habitats. If we have
a priori
grounds for expecting that humidity is
the single controlling factor we could regress jaw shape on some measure of humidity
evaluated in all the habitats from which we collected squirrels. If we regard the environ-
mental influences as multidimensional, perhaps expecting that temperature, precipitation,
elevation and other characteristics all have effects and may not be entirely independent,
we might use MANOVA, or General Linear Modeling to identify the influential factors
and their effects. And, as we discussed above, performing these analyses on interspecific
comparisons requires that we include phylogenetic information to avoid inflated type I
error rates.
For complex questions, or complex covariates of shape, it may be useful to apply tech-
niques that look for patterns in both data sets simultaneously. One such approach is
Partial Least Squares, which we discussed in more detail in Chapter 7. This method
finds the axes of covariation within each data set that maximally covary between sets.
Because PLS focuses attention on one dimension of variation in each data set, it is
often useful to combine this analysis with a technique that provides a broad perspective,
like matrix correlation (e.g.
Monteiro and Nogueira, 2009; Zelditch et al., 2009
). Matrix
correlation compares distances computed from one data set to those computed from the
other. For evolutionary morphology studies, one data set could be shape data, the other
might be ecological traits, geographic distances, time or climate. Matrix correlation can
be a powerful tool in the right context, but it should only be used if there is a valid dis-
tance metric for both data sets (
Harmon and Glor, 2010
). For shape data, the distance
metric is the Procrustes distance, so this method can be used to compare distances in
two sets of shape data (shapes of two parts, or shapes of the same part in juveniles
and adults). Other data sets that might be sensibly compared to shape distances
include physical geographic distances between localities and genetic distances between
populations.
