Bayesian support is larger than bootstrap support in phylogenetic inference: a mathematical argument

Abstract

In phylogenetic inference, the support of an estimated phylogenetic tree topology and its interior branches is usually measured either with non-parametric bootstrap support (BS) values or with Bayesian posterior probabilities (BPPs). Extensive empirical evidence indicates that BPP values are systematically larger than BS when measured on the same data set, but there are no theoretical results supporting such a systematic difference. In the present note, we give a heuristic mathematical argument supporting the empirically observed phenomenon. The argument uses properties of the marginal and profile likelihoods of the normal distribution. The heuristic arguments are supported in a simulation study evaluating different steps in the argument.