Rapidly changing speciation and extinction rates can be inferred in spite of non-identifiability

Abstract

The birth-death model is commonly used to infer speciation and extinction rates by fitting the model to extant phylogenetic trees. Recently, it was demonstrated that speciation and extinction rates are not identifiable if the rates are allowed to vary freely over time. The group of birth-death models that are not identifiable from each other is called a congruence class. Every model in a congruence class is equally likely, and there is no statistical evidence that can be used to favor one over the other. This issue has led researchers to question if and what patterns can reliably be inferred, and whether time-variable birth-death models should be fitted at all. We explore the congruence class in the context of several empirical phylogenies as well as hypothetical scenarios and summarize shared patterns in the congruence class. We show that strong directional trends in speciation and extinction rates are ubiquitous among most models within the congruence class, and conclude that inference of strong directional trends is therefore robust. Conversely, estimates of constant rates or gentle slopes are not robust and must be treated with caution. Additionally, most conflict in trends within the congruence class is observed near the present, implying that very recent rate changes should be treated carefully. Interestingly, the space of valid speciation rates is limited in contrast to extinction rates, which are less constrained. These results provide further evidence and insights that speciation rates can be estimated more reliably than extinction rates.