Abstract
The estimation of origination and extinction rates and their temporal variation is central to understanding diversity patterns and the evolutionary history of clades. The fossil record provides the most direct evidence of extinction and biodiversity changes through time and has long been used to infer the dynamics of diversity changes in deep time. The software PyRate implements a Bayesian framework to analyze fossil occurrence data to estimate the rates of preservation, origination and extinction while incorporating several sources of uncertainty. This fully probabilistic approach allows us to explicitly assess the statistical support of alternative macroevolutionary hypotheses and to infer credible intervals around parameter estimates. Here, we present a major update of the software, which implements substantial methodological advancements, including more complex and realistic models of preservation, a reversible jump Markov chain Monte Carlo algorithm to estimate origination and extinction rates and their temporal variation, and a substantial boost in performance. We demonstrate the new functionalities through extensive simulations and with the analysis of a large dataset of Cenozoic marine mammals. We identify several significant shifts in origination and extinction rates of marine mammals, underlying a late Miocene diversity peak and a subsequent 50% diversity decline towards the present. Our analyses indicate that explicit statistical model testing, which is often neglected in fossil-based macroevolutionary analyses, is crucial to obtain accurate and robust results. PyRate provides a flexible, statistically sound analytical framework, which we think can serve as a useful toolkit for many future studies in paleobiology.
