Biology Reference
In-Depth Information
FIGURE 3.13
Comparison of (A) GPA
and (B) RFTRA superimpositions for data
that lack a Pinocchio effect: real differences
in scapula shape between two squirrels.
The circles denote the two landmarks that
undergo large relative displacements, in
addition to the three most ventral landmarks.
The outline of the scapula is approximated
by lines connecting the landmarks.
circled landmarks). The difference between the superimpositions is subtle; it is most
noticeable at the ventral end, where RFTRA attributes somewhat greater anterior displace-
ments to the more ventral landmarks. The principal advantage of RFTRA and other resistant-
fit methods lies in their ability to address the Pinocchio effect. The principal disadvantage of
these methods will become clearer in the next chapter.
Interpreting the Graphical Results
The graphical representation of results is one of the main reasons why geometric methods
are so useful and popular. Different superimposition methods can yield strikingly different
visual displays from the same data, which can be both disconcerting and useful. It is useful
because seeing different depictions of the same results can help you avoid drawing conclu-
sions that depend on a particular visual display. For example, one method might show large
displacements at some landmarks whereas another superimposition method might show large
displacements at other landmarks. Seeing two or more pictures helps to avoid a common error,
that of interpreting the changes as if they are
at
the landmarks. To illustrate the variety of
pictures that can be obtained by different superimposition methods, we use three (BC, GPA
and RFTRA) to depict the ontogeny of body shape in the piranha
S. gouldingi
(
Figure 3.14
).
Perhaps the most obvious difference among the three panels is the degree to which
post-cranial landmarks are vertically displaced. It might appear that Bookstein shape coor-
dinates either exaggerate the degree to which the post-cranial body is deepened, or else
that the other superimpositions understate it. However, this is not the case; all the other
superimpositions show a relative shortening of the body, which is equivalent to a relative
deepening. Both mean exactly the same thing. Relative body depth is a ratio between
depth and length, so it is just as reasonable to think of it as a decrease in length relative to
depth as to think of it as an increase in depth relative to length. Increasing body depth
increases the ratio by increasing the numerator; decreasing body length also increases the
