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Assessment of modularity in the urodele skull: an exploratory analysis using ossification sequence data.

The potential presence of developmental modules is studied in the urodele skull using several classical statistical methods that have not previously been used in this context. Principal component analysis (PCA) of ossification sequence data on 21 bones in 21 extant urodele species suggests the presence of up to four developmental modules, but examination of statistically significant correlations using phylogenetic independent contrasts (PIC) and correcting for multiple tests using the false discovery rate suggests the presence of only two modules of uneven size and of two bones that may not be part of these modules. Thus, PCA does not appear to be a reliable method to investigate modularity; direct investigation of statistically significant correlations using PIC or other phylogeny-informed methods is recommended. A binomial test of the distribution of significant correlations between characters shows significant heterogeneity, which suggests that modularity is indeed present in the data. A cluster analysis gives inconsistent results that apparently do not reflect developmental modules. The data include a phylogenetic signal, as shown by a permutation-based test with squared change parsimony, but this is detectable only when the whole matrix is analyzed, and a plot of the tree onto developmental space through Evolutionary PCA shows that homoplasy is pervasive. Evolutionary rates between characters vary about 90-fold. Canonical variates analyses suggest that obligatorily neotenic urodeles may be discriminated from other urodeles on the basis of cranial ossification sequence data.