Biology Reference
In-Depth Information
differs from the others because there is no division of the front from the back, and there is
a division between molar alveolus and ramus. There are six modules because six conden-
sations give rise to the structures of the adult mandible (the seventh gives rise to the tran-
sitory Meckel's cartilage and the symphyseal region). The six modules are the incisor
alveolus, the molar alveolus, the horizontal ramus (which crosses the boundary between
front and back), and three modules corresponding to the three proximal processes (coro-
noid, condyloid and angular).
To test these four hypotheses of modularity, we use a simultaneous superimposition
method because all the methods can analyze simultaneously superimposed data; Mint can-
not analyze separately superimposed data because that would force the analysis to focus
solely on the between-modular associations, i.e. on whether the covariances between mod-
ules are low enough to justify the conclusion that they are indeed modules. Second,
because the mandible serves a mechanical function, the relative sizes and positions of its
parts are functionally important.
“Minimum Intermodular Covariance Method”
The Front/Back model can be tested by the
RV
coefficient because it contains only two
modules. The
RV
for this hypothesis is a moderately high 0.445 and it is highly statistically
higher than expected by chance. Nevertheless, when tested using a large sample of ran-
dom permutations (restricted to contiguous partitions with the same number of landmarks
as contained in the hypothesized modules), none had a lower value. The distribution of
the
RV
coefficient (
Figure 12.18
) including this one and the 10 000 random alternative par-
titions suggests that the alternatives vary little in
RV
and none of them differ much from
the observed value. This is not surprising because the precise dividing line between the
modules is biologically ambiguous (between which ventral semilandmarks should we
divide the front from the back?). Many alternatives might be consistent with the biological
hypothesis rather than conflict with it.
The remaining models are tested with the multiset
RV
M
coefficient. The
RV
M
for the
Satb2
hypothesis is moderately high 0.327, although lower than the
RV
for the Front/Back
model. It, too, is the lowest in the distribution that includes it and
RV
M
of 10 000 random
alternatives. The third hypothesis,
Satb2
Gsc, yields a lower
RV
M
of 0.290, but it is not
clear whether this lower value indicates a better-fitting model or is an artifact of the larger
number of modules. The
RV
M
of this model is also the lowest in the distribution that
includes it and 10 000 random (contiguous) alternatives. The Condensation hypothesis
yields an
RV
M
of 0.230, which is the lowest of the four, and is also lower than all the
values obtained by 10 000 random permutations.
1
“Minimum Deviance Method”
The rankings of the four models are shown in
Table 12.5
. These agree with the rankings
based on the
RV
and
RV
M
. The best fitting is the Condensation model, which is ranked
first with 100% jackknife support, followed by the
Satb
Gsc model, which is consistently
the second best, followed in turn by the
Satb2
model, which is consistently the third best,
and then by the Front/Back model, which is consistently the worst. The difference
1
