Bayesian Tests of Topology Hypotheses with an Example from Diving Beetles

We review Bayesian approaches to model testing in general and to the assessment of topological hypotheses in particular. We show that the standard way of setting up Bayes factor tests of the monophyly of a group, or the placement of a sample sequence in a known reference tree, can be misleading. The reason for this is related to the well-known dependency of Bayes factors on model-specific priors. Specifically, when testing tree hypotheses it is important that each hypothesis is associated with an appropriate tree space in the prior. This can be achieved by using appropriately constrained searches or by filtering trees in the posterior sample, but in a more elaborate way than typically implemented. If it is difficult to find the appropriate tree sets to be contrasted, then the posterior model odds may be more informative than the Bayes factor. We illustrate the recommended techniques using an empirical test case addressing the issue of whether two genera of diving beetles (Coleoptera: Dytiscidae), Suphrodytes and Hydroporus, should be synonymized. Our refined Bayes factor tests, in contrast to standard analyses, show that there is strong support for Suphrodytes nesting inside Hydroporus, and the genera are therefore synonymized. [Bayes factor; Coleoptera; Dytiscidae; marginal likelihood; model testing; posterior odds; reversible-jump MCMC; stepping-stone sampling.]