Biology Reference
In-Depth Information
FIGURE 11.15
Principal components analysis of geometric shape data, pooling the ontogenetic series of
S. gouldingi and S. manueli.
therefore the large ontogenetic increase in scale (and the differences between species in
scale) no longer contributes to PC1. The consequence is self-evident in the plots for the
two rodents
whereas PC1 is a size axis in the analysis based on traditional (size) data,
PC1 separates the two ontogenies in the analysis based on geometric data. In that geomet-
ric analysis, the averaged ontogeny is more nearly aligned with PC2, although oblique to
it. The eigenvalues of these axes cannot tell us which hypothesis is best supported nor
quantify the proportion of the disparity that results from each modification of ontogeny.
After all, PCA is an ordination method, not a statistical test of a hypothesis. In these plots,
we cannot even detect that the two trajectories are at 42.7
to each other. Principal compo-
nents analysis, whether of traditional or geometric data, is a low-dimensional projection of
complex data. The eigenvalues of the PCs tell us how much of the total variation projects
onto each axis, not how much each modification of ontogeny contributes to disparity.
DISSE
CTING THE DEVELOPMENTAL BASIS OF DISPA
RITY
Dissecting the developmental basis of disparity is obviously a complex task when there
are many modifications of ontogeny and many species. Not only do we need to identify
what differs among the ontogenies (and between which species they differ), but also we
need to determine the impact of those modifications on disparity. Numerous studies, using
