Biology Reference
In-Depth Information
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(A)
PC1 - 31%
(B)
FIGURE 6.16
Shape variation in three geographic samples of squirrel jaws analyzed by PCA. (A) Scores on
the first 2 axes (circles
5
western Michigan, squares
5
eastern Michigan,
triangles
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southern states).
(B)
Deformation showing shape change association with increasing scores on PC1.
the shape variables were found by CVA to be more effective discriminators of these
samples than were the PCs.
As we did with the PCs, we multiply the original shape variables by the coefficients of
the CVs and sum them. This produces a series of vectors of relative landmark displace-
ment that illustrates the shape differentiation represented by the CVs. As shown in
Figure 6.18A
, the amount of the shape difference described by CV1 of this data set is
imperceptible. When the deformation is exaggerated to visualize the pattern, it can be seen
that differences in the relative heights of the teeth are the most useful trait for discriminat-
ing among the groups. Relative tooth heights are not an efficient discriminator because the
differences between groups are large, but because the variation within groups is even
smaller than the differences between groups. Consequently, a biologically insignificant fea-
ture is determined to be diagnostically important.
Figure 6.18C
illustrates all of the other
shape differences that are correlated with CV1. These changes, which may be helpful for
diagnosing group members, include a portion of the shape differences that were detected
using PCA. This figure demonstrates another important point to bear in mind when using
