Maximum likelihood inference of pathogen population size history from a phylogeny

Inference of effective population size from genomic data can provide unique information about demographic history, and when applied to pathogen genetic data can also provide insights into epidemiological dynamics. Non-parametric models for population dynamics combined with molecular clock models which relate genetic data to time have enabled phylodynamic inference based on large sets of time-stamped genetic sequence data. The theory for non-parametric inference of effective population size is well-developed in the Bayesian setting, but here we develop a frequentist approach based on non-parametric latent process models of population size dynamics. We appeal to statistical principles based on out-of-sample prediction accuracy in order to optimize parameters that control shape and smoothness of the population size over time. We demonstrate the flexibility and speed of this approach in a series of simulation experiments and apply the models to genetic data from several pathogen data sets.