A Metric Space of Ranked Tree Shapes and Ranked Genealogies

Genealogical tree modeling is essential for estimating evolutionary parameters in population genetics and phylogenetics. Recent mathematical results concerning ranked genealogies without leaf labels enable new opportunities in the analysis of evolutionary trees. In particular, comparisons between ranked genealogies facilitate the study of evolutionary processes for organisms sampled in multiple time periods. We propose a metric space on ranked genealogies for lineages sampled from both isochronous and time-stamped heterochronous sampling. Our new tree metrics make it possible to conduct statistical analyses of ranked tree shapes and timed ranked tree shapes, or ranked genealogies. Such analyses allow us to assess differences in tree distributions, quantify estimation uncertainty, and summarize tree distributions. We show the utility of our metrics via simulations and an application in infectious diseases.