PyRate: a new program to estimate speciation and extinction rates from incomplete fossil data

Despite the advancement of phylogenetic methods to estimate speciation and extinction rates, their power can be limited under variable rates, in particular for clades with high extinction rates and small number of extant species. Fossil data can provide a powerful alternative source of information to investigate diversification processes. Here, we present PyRate, a computer program to estimate speciation and extinction rates and their temporal dynamics from fossil occurrence data. The rates are inferred in a Bayesian framework and are comparable to those estimated from phylogenetic trees. We describe how PyRate can be used to explore different models of diversification. In addition to the diversification rates, it provides estimates of the parameters of the preservation process (fossilization and sampling) and the times of speciation and extinction of each species in the data set. Moreover, we develop a new birth-death model to correlate the variation of speciation/extinction rates with changes of a continuous trait. Finally, we demonstrate the use of Bayes factors for model selection and show how the posterior estimates of a PyRate analysis can be used to generate calibration densities for Bayesian molecular clock analysis. PyRate is an open-source command-line Python program available at http://sourceforge.net/projects/pyrate/.