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2007; Webster, 2007, 2009; Frederich et al., 2008; Sanfelice and De Freitas, 2008; Piras et al.,
2010; Drake, 2011; Frederich and Vandewalle, 2011
). Relatively few, however, explicitly
compare levels of disparity at different ontogenetic stages. In one case, multiple modifica-
tions of ontogeny increase disparity (
Frederich et al., 2008
). In other cases, combinations of
modifications decrease disparity because disparate young develop along divergent trajecto-
ries towards similar adult morphologies (
Zelditch et al., 2003b; Adams and Nistri, 2010;
Piras et al., 2010; Ivanovic et al., 2011
). To dissect the developmental basis of disparity, we
need comparisons of the ontogenetic trajectories plus measures of disparity.
Testing Hypotheses About the Evolution of Ontogeny
To determine what differs between ontogenetic trajectories we need to conduct a series
of tests. How we progress through these tests depends on the results of each one.
What ontogenetic scaling would look like is shown for a hypothetical case in
Figure 11.17
.
In this case, the two species have the same shape at the outset of development, follow the
same ontogeny of shape but one grows to a larger size, with size and shape maintaining the
same relationship with each other that they had in the ancestral species. Thus, we see that
the coordinates of the juveniles completely overlap (
Figure 11.17A
), the two ontogenies of
shape are the same (
Figure 11.17B
), and the trajectories differ in length (
Figure 11.17C
). As a
result, the coordinates of the descendant's adult morphology lie at a subadult position on the
ancestral ontogeny (
Figure 11.17D
). However, ontogenetic scaling is not the only hypothesis
consistent with these figures; with the exception of
Figure 11.17A
, the diagrams are also con-
sistent with another hypothesis
heterochrony more generally. That is because the two
hypotheses differ in only one respect
the association between size and shape. The hypoth-
esis of ontogenetic scaling predicts that size and shape are associated in their evolutionary
changes whereas the hypothesis of heterochrony predicts that they need not be. As a result,
we might not find that the two species are identical in shape at any given size. The ancestral
shape could be identical to that of the descendant at a different size. We would still find that
the trajectories point in the same direction, and the coordinates for one species would be
found at a subadult position for the other. But, in the case of ontogenetic scaling, the two
species have the same regression equation whereas in the case of heterochrony they do not.
We thus need to distinguish between identical regressions versus overlapping trajectories.
Mitteroecker and colleagues (2005)
suggest two tests to make the distinction between those
two cases. The first involves computing the multivariate regression of shape on size for each
species (separately) and randomly assigning the summed squared residuals from the two
regressions to species, recomputing the regression numerous times. If the two trajectories are
identical, the test statistic for the observed case should not be an outlier in the distribution of
summed squared residuals for the permuted data. So, for N permutations, the hypothesis of
identical trajectories is rejected if (C
,whereC is the number of cases that pro-
duce a smaller test statistic than found for the data. For the case of overlapping trajectories,
the test involves using the residuals normal to the regression, ignoring deviations along the
trajectory (because the expectation is that the same shapes will be at different points along the
trajectories). So this test, which is otherwise the same as the first, uses the summed squared
distances from each shape to its nearest point on the regression curve rather than the summed
1)/(N
1)
,
α
1
1
