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In Primates, the basicranial group had significantly lower disparity than the random sets of "weak" module landmarks (p = 0.002), while the zygomatic-pterygoid group had a significantly higher disparity than the random sets of "strong" modules (p<0.001).
Lastly, all landmarks were grouped into two bins, based on membership in a "strong" module or a "weak" module, and a Mann-Whitney test was used to test for differences in landmark variances between the two bins.
In Carnivora, the molar group had marginally significantly higher disparity than the random sets of "weak" module landmarks (p = 0.05), while the orbit, zygomatic-pterygoid, and vault groups all had significantly or marginally significantly higher disparity than the random sets of "strong" module landmarks (p<0.001, p<0.001, and p = 0.03, respectively).
A complete cluster should meet the requirements of a weak module.
In PPI networks, there exist complexes which have structure of a strong module, or of a weak module, or a combination of the two.
Inspired by the finding, we consider that the cores correspond to the structure of a strong module [ 26] we introduced above and the attachment corresponds to the structure of a weak module [ 26].
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Thus, all of the significant results for the "weak" modules are consistent with the constraint hypothesis.
Based on these analyses, we subdivided these six modules into "strong" modules (anterior oral-nasal, molar, and basicranial) and "weak" modules (orbit, zygomatic-pterygoid, and vault).
Correspondingly, the low correlations in the "weak" modules should exert little control on the variation of individual traits, allowing high morphological disparity to evolve.
Similarly to Disparity A, the constraint hypothesis would predict that strong modules would have significantly lower disparities than observed in random sets of landmarks from weak modules, and that weak modules would have significantly higher disparities than observed in random sets of landmarks from strong modules.
Analyses were also conducted in which "strong" modules (anterior oral-nasal, molar, and basicranium) were compared to disparities generated from random sets of landmarks pulled only from the "weak" modules (orbit, zygomatic-pterygoid, and vault), and vice versa (Disparity B).
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