Biology Reference
In-Depth Information
To obtain more precise information about the pattern of shape variation, the 31 sets of
landmark coordinates are converted into shape variables (see Chapter 3 for review), and
these shape variables are subjected to PCA. The 15 landmarks yield 26 shape variables, so
there are 26 PCs, and 26 scores for each specimen (its score on each component). The out-
put from PCA consists of the list of coefficients describing the PCs, the variance of each
component, each component's percentage of the total variance, and the scores of each
specimen on each component.
As shown in Table 6.1 , each PC has progressively less variance. Many of the compo-
nents represent such small proportions of the total variance that it is reasonable to ask
whether they describe anything biologically meaningful. One common rule of thumb is to
interpret only those components that represent more than 5% of the variance. In the squir-
rel jaw example, PCs 1 through 5 meet this criterion. They account for a total of 80.4% of
the variance in the sample, leaving 19.6% undescribed. This may seem like a large propor-
tion of the variance to omit from further analysis, but it is doubtful that any one of the
remaining 21 components describes a meaningful amount of variance.
The similarity in magnitudes of variances described by most components can be seen in
a scree plot, in which the variance, or percentage of the total variance, is plotted against
the ordinal number of the PC ( Figure 6.7 ). In this example, there is a large difference
between the variances of the first two PCs, and much smaller differences between succes-
sive pairs of components. This difference is reflected in the scatter-plot of scores in the
two axes ( Figure 6.8 ); the range of scores is much larger on PC1 than PC2, indicating that
PC1 accounts for a much larger portion of the total variance. If two components have simi-
lar variances (e.g. if the distribution of scores in Figure 6.8 were closer to circular), then
we have grounds to question whether either of them can be attributed to a distinct causal
factor. Thus, an alternative rule of thumb is to find the inflection point on the scree plot
and interpret only those components to the left of the inflection point (where the variance
of each component is distinct from the variance of the following component). The main
FIGURE 6.6 Plot of landmark
coordinates of 31 S. niger jaws after
partial Procrustes superimposition.
The locations of landmark 6 in all 31
specimens are enclosed by an ellipse.
Similar ellipses could be drawn for
each landmark.
6
0.2
2
3
1
7
4
5
0.1
8
0.0
9
15
0.1
14
13
12
0.2
10
11
0.3
0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
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