Simple Size and Shape Variables: Shape Coordinates - Geometric Morphometrics for Biologists - page 54

FIGURE 3.4 (A) Triangle with the baseline along the anteroposterior body axis and the free point at the
anterior dorsal fin base; (B) the difference between two shapes depicted by a vector extending between C and C 0 .

FIGURE 3.5 Ontogenetic changes in the shape of a piranha, Serrasalmus gouldingi, represented by vectors
depicting the change in location of Bookstein shape coordinates from their position in a young juvenile.

statistical machinery also applies. Another procedure also extends without difficulty
from one to many triangles

the depiction of shape differences by vectors at the free
landmarks. In the case of a single triangle, we can depict a change in shape by a single
vector depicting the displacement of one landmark relative to the baseline ( Figure 3.4 ).
In the case of multiple triangles, we can similarly depict the change in shape by vectors
that show the displacements of points relative to the baseline ( Figure 3.5 ). If this base-
line dependence is not seen as a serious problem, the description can proceed in terms
of the displacements of landmarks relative to each other, relative to the baseline. In
describing the ontogenetic change in shape depicted in Figure 3.5 , we would need to
take the relative lengths of all the vectors into account. The most anterior free point on
the dorsal margin (landmark 2, at the epiphyseal bar) is displaced anteriorly, indicating
that the region between it and the baseline point at the tip of the snout is shortened
relative to the length of the baseline. The point immediately posterior to landmark 2
(landmark 3, at the tip of the supra-occipital process) is also displaced anteriorly,
although most of its displacement is along the dorsoventral body axis. Because the
anteroposterior component of this vector is short relative to that of the more anterior
point, the region between the epiphyseal bar and supra-occipital process is relatively
elongated (relative both to the length of baseline and to the more anterior region just
described). Such descriptions can be useful, even if they depend on the baseline.