A Bayesian approach for evaluating the impact of historical events on rates of diversification

Evolutionary biologists often wish to explore the impact of a particular historical event ( e. g., the origin of a novel morphological trait, an episode of biogeographic dispersal, or the onset of an ecological association) on rates of diversification (speciation minus extinction). We describe a Bayesian approach for evaluating the correlation between such events and differential rates of diversification that relies on cross-validation predictive densities. This approach exploits estimates of the marginal posterior probability for the rate of diversification ( in the unaffected part of the tree) and the marginal probability for the timing of the event to generate a predictive distribution of species diversity that would be expected had the event not occurred. The realized species diversity can then be compared to this predictive diversity distribution to assess whether rates of diversification associated with the event are significantly higher or lower than expected. Although simple, this Bayesian approach provides a robust inference framework that accommodates various sources of uncertainty, including error associated with estimates of divergence times, diversification-rate parameters, and event history. Furthermore, the proposed approach is relatively flexible, allowing exploration of various types of events ( including changes in discrete morphological traits, episodes of biogeographic movement, etc.) under both hypothesis-testing and data-exploration inference scenarios. Importantly, the cross-validation predictive densities approach facilitates evaluation of both replicated and unique historical events. We demonstrate this approach with empirical examples concerning the impact of morphological and biogeographic events on rates of diversification in Adoxaceae and Lupinus, respectively.