Biology Reference
In-Depth Information
FIGURE 1.9
Semilandmarks on four squirrel mandibles to capture information about the curvature of the jaw,
which reflects both the curvature of the incisor and the length and orientation of muscle insertions in regions
where there are no landmarks.
SHAPE AND SIZE
The rapid progress in geometric morphometrics resulted from a coherent mathematical
theory of shape which, in turn, resulted from a precise definition of the concept. Like the
definition of any word, that of “shape” is entirely a matter of semantics. However, seman-
tics is not trivial. We cannot have a coherent theory about an ambiguous concept and we
cannot have a coherent mathematical theory of shape until shape is unambiguously
defined. The definition of shape is thus the foundation for the mathematical theory of
shape. Whether that theory applies to our biological questions depends on whether it cap-
tures what we mean by shape. Thus, it is important to understand the definition of shape
underlying geometric morphometrics; also, because the meaning of “size” depends on the
meaning of “shape” (and vice versa), we cannot understand one without understanding
the other.
Shape
In geometric morphometrics, shape is defined as “all the geometric information that
remains when location, scale and rotational effects are filtered out from an object”
(
Kendall, 1977
). The earliest work that depends on this definition of shape began the
analysis with the coordinates of points; consequently, the “objects” are sets of those
coordinates
i.e. configurations of landmarks, such as that shown in
Figure 1.4
.Animportant
implication of Kendall's definition is that removing the differences between configurations