Which morphological characters are influential in a Bayesian phylogenetic analysis? Examples from the earliest osteichthyans

There has been much recent debate about which method is best for reconstructing the tree of life from morphological datasets. However, little attention has been paid to which characters, if any, are responsible for topological differences between trees recovered from competing methods on empirical datasets. Indeed, a simple procedure for finding characters supporting conflicting tree topologies is available in a parsimony framework, but an equivalent procedure in a model-based framework is lacking. Here, I introduce such a procedure and apply it to the problem of the ‘psarolepid’ osteichthyans. The ‘psarolepids’, which include the earliest known osteichthyans, are weakly supported as stem osteichthyans under parsimony but strongly supported as sarcopterygians in Bayesian analysis. The Bayesian result is driven by just two characters, both of which relate to the intracranial joint of sarcopterygians. Important characters that support a stem osteichthyan affinity for ‘psarolepids’, such as the absence of tooth enamel, have virtually no effect in a Bayesian framework. This is because of a bias towards characters with relatively complete sampling, a bias that has previously been reported for molecular data. This has important implications for Bayesian analysis of morphological datasets in general, as characters from different body parts commonly have different levels of coding completeness. Methods to critically appraise character support for conflicting phylogenetic hypotheses, such as that used here, should form an important part of phylogenetic analyses.