The Devil in the Details: Interactions between the Branch-Length Prior and Likelihood Model Affect Node Support and Branch Lengths in the Phylogeny of the Psoraceae

Abstract

In popular use of Bayesian phylogenetics, a default branch-length prior is almost universally applied without knowing how a different prior would have affected the outcome. We performed Bayesian and maximum likelihood (ML) inference of phylogeny based on empirical nucleotide sequence data from a family of lichenized ascomycetes, the Psoraceae, the morphological delimitation of which has been controversial. We specifically assessed the influence of the combination of Bayesian branch-length prior and likelihood model on the properties of the Markov chain Monte Carlo tree sample, including node support, branch lengths, and taxon stability. Data included two regions of the mitochondrial ribosomal RNA gene, the internal transcribed spacer region of the nuclear ribosomal RNA gene, and the protein-coding largest subunit of RNA polymerase II. Data partitioning was performed using Bayes' factors, whereas the best-fitting model of each partition was selected using the Bayesian information criterion (BIC). Given the data and model, short Bayesian branch-length priors generate higher numbers of strongly supported nodes as well as short and topologically similar trees sampled from parts of tree space that are largely unexplored by the ML bootstrap. Long branch-length priors generate fewer strongly supported nodes and longer and more dissimilar trees that are sampled mostly from inside the range of tree space sampled by the ML bootstrap. Priors near the ML distribution of branch lengths generate the best marginal likelihood and the highest frequency of "rogue" (unstable) taxa. The branch-length prior was shown to interact with the likelihood model. Trees inferred under complex partitioned models are more affected by the stretching effect of the branch-length prior. Fewer nodes are strongly supported under a complex model given the same branch-length prior. Irrespective of model, internal branches make up a larger proportion of total tree length under the shortest branch-length priors compared with longer priors. Relative effects on branch lengths caused by the branch-length prior can be problematic to downstream phylogenetic comparative methods making use of the branch lengths. Furthermore, given the same branch-length prior, trees are on average more dissimilar under a simple unpartitioned model compared with a more complex partitioned models. The distribution of ML branch lengths was shown to better fit a gamma or Pareto distribution than an exponential one. Model adequacy tests indicate that the best-fitting model selected by the BIC is insufficient for describing data patterns in 5 of 8 partitions. More general substitution models are required to explain the data in three of these partitions, one of which also requires nonstationarity. The two mitochondrial ribosomal RNA gene partitions need heterotachous models. We found no significant correlations between, on the one hand, the amount of ambiguous data or the smallest branch-length distance to another taxon and, on the other hand, the topological stability of individual taxa. Integrating over several exponentially distributed means under the best-fitting model, node support for the family Psoraceae, including Psora, Protoblastenia, and the Micarea sylvicola group, is approximately 0.96. Support for the genus Psora is distinctly lower, but we found no evidence to contradict the current classification.