Is there a star tree paradox?

Concerns have been raised that posterior probabilities on phylogenetic trees can be unreliable when the true tree is unresolved or has very short internal branches, because existing methods for Bayesian phylogenetic analysis do not explicitly evaluate unresolved trees. Two recent papers have proposed that evaluating only resolved trees results in a star tree paradox: when the true tree is unresolved or close to it, posterior probabilities were predicted to become increasingly unpredictable as sequence length grows, resulting in inflated confidence in one resolved tree or another and an increasing risk of false-positive inferences. Here we show that this is not the case; existing Bayesian methods do not lead to an inflation of statistical confidence, provided the evolutionary model is correct and uninformative priors are assumed. Posterior probabilities do not become increasingly unpredictable with increasing sequence length, and they exhibit conservative type I error rates, leading to a low rate of false-positive inferences. With infinite data, posterior probabilities give equal support for all resolved trees, and the rate of false inferences falls to zero. We conclude that there is no star tree paradox caused by not sampling unresolved trees.