Examining character congruence and compatibility of vertebrate cladistic data: empirical approaches applied comparatively across clades

Previous phylogenetic work using conventional character partition homogeneity tests has often revealed significant incongruence between cranial and postcranial character data. We extend this approach by applying pairwise character compatibility tests across a sample of more than 60 pseudo-independent vertebrate data sets. We contrast ‘fuzzy’ compatibility, boildown bootstrap and clique approaches. In particular, we ind that the Le Quesne probability (LQP) has several desirable properties. The LQP is simply the probability that a randomly permuted character will have incompatibility with other characters in the matrix as low or lower than that of the original character. Within recent analyses of Sauropod taxa we often find that characters related to neural arches often conflict with dental characters in some datasets but it is difficult to generalise; we are still exploring possible causative mechanisms for this. In contrast, other vertebrate groups such as ratites appear to have relatively little character conflict between morphological characters. Pairwise tests of character compatibility work well with binary data and ordered multistate characters, but can only give an indication of ‘potential compatibility’ with unordered multistate characters. Composite ‘higher’ taxa and polymorphic codes are also problematic for existing compatibility software, typically creating artificial incompatibilities. We recommend that composite taxa are decomposed into their constituents in order to remove ambiguity for the purpose of these tests, or else that polymorphic states are treated as missing data.