Biology Reference
In-Depth Information
Interpreting Changes Depicted by the Thin-Plate Spline
Interpretations should be presented in terms of the total deformation, not by detailing
the separate uniform and non-uniform components (or the more finely subdivided compo-
nents of them). Just as we cannot talk about individual landmarks as if they were sepa-
rately moved, we cannot talk about components of the total deformation as if they were
separate parts of the whole. It is important to remember that the changes depicted are
based on an interpolation function
we do not actually know what occurs between land-
marks, and while the thin-plate spline is a smooth interpolation function, and widely
used, other interpolation functions are also available. If we have sparsely sampled some
regions of the body, we cannot assume that the spline provides a realistic picture of their
changes; there might be many highly localized changes that cannot be detected in the
absence of closely spaced landmarks. All we can say is that our data do not require any
more localized changes.
We cannot show an example of a biological transformation depicted by the thin-plate
spline until we have results to show, so we will borrow examples from later chapters to
discuss the description of shape change using the thin-plate spline. In
Figure 5.7
we depict
the ontogenetic changes in body shape of two species of piranhas: S. gouldingi
(
Figure 5.7A
), which we used earlier in this chapter, and Pygopristis denticulata
(
Figure 5.7B
). In both species, the head (as a whole) grows less rapidly than the middle of
the body, and the eye grows far more slowly than the head. In neither species does the
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(A)
(B)
FIGURE 5.7
Ontogenetic shape change for two species of piranhas: (A) Serrasalmus gouldingi; (B) Pygopristis
denticulata.
