Expectation-Maximization enables phylogenetic dating under a Categorical Rate Model

Dating phylogenetic trees to obtain branch lengths in the unit of time is essential for many downstream applications but has remained challenging. Dating requires inferring mutation rates that can change across the tree. While we can assume to have information about a small subset of nodes from the fossil record or sampling times (for fast-evolving organisms), inferring the ages of the other nodes essentially requires extrapolation and interpolation. Assuming a clock model that defines a distribution over rates, we can formulate dating as a constrained maximum likelihood (ML) estimation problem. While ML dating methods exist, their accuracy degrades in the face of model misspecification where the assumed parametric statistical clock model vastly differs from the true distribution. Notably, existing methods tend to assume rigid, often unimodal rate distributions. A second challenge is that the likelihood function involves an integral over the continuous domain of the rates and often l..., , ,