Propagating uncertainty about molecular evolution models and prior distributions to phylogenetic trees

Phylogenetic trees constructed from molecular sequence data rely on largely arbitrary assumptions about the substitution model, the distribution of substitution rates across sites, the version of the molecular clock, and, in the case of Bayesian inference, the prior distribution. Those assumptions affect results reported in the form of clade probabilities and error bars on divergence times and substitution rates. Overlooking the uncertainty in the assumptions leads to overly confident conclusions in the form of inflated clade probabilities and short confidence intervals or credible intervals. This paper demonstrates how to propagate that uncertainty by combining the models considered along with all of their assumptions, including their prior distributions. The combined models incorporate much more of the uncertainty than Bayesian model averages since the latter tend to settle on a single model due to the higher-level assumption that one of the models is true. Nucleotide sequence data illustrates the proposed model combination method.