Investigating stagnation in morphological phylogenetics using consensus data.

Rieppel and Kearney (2002) have recently called attention to the lack of progress in resolving several highprofile disagreements in vertebrate phylogeny that, because of the crucial importance of fossil taxa, depend upon the interpretation of morphological data. Perhaps the best-known example concerns the phylogenetic placement of Testudines (turtles) within Amniota. Most textbooks assert that turtles lie outside a clade including all other extant reptiles because they lack temporal fenestrae in their skull (the presumed plesiomorphic, anapsid condition). However, there has long been dissent based on the possibility that, like all other extant reptiles, turtles are diapsids, and that they have secondarily lost the two fenestrae for which this group is named (e.g., Goodrich, 1916). The controversy stems from the highly divergent morphology of the group and the lack of intermediate forms. The earliest known turtle, Proganochelys quenstedti Baur, 1887, already has many of the features of modern turtles. This makes assessments of homology with potential close relatives difficult and, as evidenced by the literature, open to conflicting interpretations (homology assessments) that cannot all be correct. It might have been hoped or expected that the application of modern numerical phylogenetic techniques would resolve the phylogenetic position of turtles and their extinct relatives. Molecular data provide some support for the diapsid hypothesis (Iwabe et al., 2005, and references therein), but recent numerical phylogenetic studies of morphology have largely recapitulated rather than resolved the controversy (Fig. 1), with osteological data interpreted repeatedly as supporting either anapsid (e.g., Lee, 1997, 2001) or diapsid (e.g., Rieppel and deBraga, 1996; Rieppel and Reisz, 1999) affinities of turtles. Consensus objects (e.g., trees, sequences) are widely used in biology (Day and McMorris, 2003). Here we use data pertaining to the relationships of turtles to illustrate the use of a consensus approach for investigating conflict in morphological phylogenetics. We use this approach to identify and investigate agreements and disagreements between recent osteological data sets employed in the debate over diapsid and anapsid hypotheses and to investigate their importance in the stagnation of the debate on turtle origins. Most systematic biologists have some familiarity with the use of consensus techniques to provide representations of and/or inferences from, for example, sets of trees. Consensus objects can be viewed as representations of the input objects and/or as inferences from the input objects. In general, a consensus method is a mapping of a set of input objects (e.g., trees) onto a set of one or more output objects of the same type (e.g., trees). The mapping corresponds to the application of some consensus rule, the commonest of which (e.g., strict, majority-rule) relate to the extent of agreement among the input objects. Because many objects are complex structures that may agree in some respects while disagreeing in others, construction of consensus objects usually involves the decomposition of complex objects into component parts to which the consensus rule is applied. For example, in constructing a strict component consensus tree, the input trees are decomposed into sets of components (full splits, clades in rooted trees) and unanimous agreement upon individual components (i.e., their presence in every input tree) is the condition for inclusion of a component in the consensus tree. Where the objects are data matrices, the decomposition is into individual entries in each data matrix (i.e., the scoring of a taxon for a character) and it is the corresponding entries in different data matrices (i.e., the alternative scorings of a taxon for a character) that are subjected to a consensus rule. For example, unanimous agreement across the input data matrices is required for a datum to be included in strict consensus data. Where there is disagreement over the scoring of a character for a taxon, then at least one of the alternative scorings is incorrect and the conflict is represented by a missing