A justification for reporting the majority-rule consensus tree in Bayesian phylogenetics.

Systematists must frequently deal with substantial uncertainty in their phylogenetic estimates. Nonparametric bootstrapping (59) and Markov chain Monte Carlo (MCMC) simulations used for Bayesian phylogenetic inference (65; 64; 60) are two of the most popular computational approaches for assessing support for different parts of a phylogenetic tree. Both of these techniques produce large collections of trees. A majority-rule consensus tree is often used to summarize such a collection of trees. As has been discussed (e.g., in 50, and the ensuing debate), a consensus tree is a summary of a set of trees, and not necessarily an optimal estimator of the phylogeny. Here we present a context in which the majority-rule consensus tree of samples from the posterior probability distribution over trees can be viewed as the optimal tree to report. We explicitly rephrase phylogenetic inference as the problem of “what tree should I publish for this group of taxa, given my data?” The majority-rule consensus tree can be shown to be the optimal tree to report if we view the cost of reporting an estimate of the phylogeny to be a linear function of the number of incorrect clades in the estimate and the number of true clades that are missing from the estimate and we view the reporting of an incorrect grouping as a more serious error than missing a clade. The work of Berry and Gascuel (52) on reporting results from nonparametric bootstrapping overlaps significantly with the results presented here. Berry and Gascuel (52) present arguments from Bayesian decision theory, which is also the theoretical basis of our work. Berry and Gascuel focus on frequentist properties of estimators (type I and type II error rates) and interpret bootstrapping proportions as measures of the probability of a clade being present. In order to apply these decision rules to bootstrapping analyses, they study the correlation between bootstrap proportions for clades and the posterior probability of those clades.