Biology Reference
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FIGURE 11.2 In the absence of any data on age, the ontogenetic trajectory of shape and size for a piranha,
Serrasalmus gouldingi. The plot shows the Procrustes distance from the juvenile, indicating the magnitude of
change; the deformation grid illustrates the change in shape.
line reorients and points in another direction between 10 and 20 days, and it reorients
again between 20 and 30 days, and points in yet another direction from that age through
sexual maturity. To represent the ontogeny of this species, we need a curve through a
multidimensional shape space not a shape axis. The ontogenetic trajectory, as represented
in the iconic diagram, will thus be an oversimplification of actual ontogenies, especially
when extended to multivariate data. However, that does not compromise the value of the
concept. Even when it takes more than three dimensions to draw it, the ontogenetic trajec-
tory is nonetheless a function of age, size and shape.
The difficulty of drawing complex trajectories does have important implications for
depicting comparative analyses, a subject we discuss in more detail below. The difficulty
is that it is not easy to visualize even three dimensions. Even to show the relationships
between shape, size and age we eased the task of visualization by flattening the picture,
projecting it onto two pairs of dimensions. We did not try to show the whole ontogeny of
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