Uncertainty in Phylogenetic Tree Estimates

Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy, and medicine. Although trees are estimated, their uncertainties are generally discarded in statistical models for tree-valued data. Here, we explicitly model the multivariate uncertainty of tree estimates. We consider both the cases where uncertainty information arises extrinsically (through covariate information) and intrinsically (through the tree estimates themselves). The latter case is applicable to any procedure for tree estimation, and thus has broad relevance to the entire field of phylogenetics. The importance of accounting for tree uncertainty in tree space is demonstrated in two case studies. In the first instance, differences between gene trees are small relative to their uncertainties, while in the second, the differences are relatively large. Our main goal is visualization of tree uncertainty, and we demonstrate advantages of our method with respect to reproducibility, speed, and preservation of topological differences compared to visualization based on multidimensional scaling. The proposal highlights that phylogenetic trees are estimated in an extremely high-dimensional space, resulting in uncertainty information that cannot be discarded. Most importantly, it is a method that allows biologists to diagnose whether differences between gene trees are biologically meaningful or due to uncertainty in estimation.