Understanding the tempo and mode in which species diversify is fundamental in explaining the origin and maintenance of biodiversity. The complex interplay of species' evolving ecologies, biotic interactions, geographic distributions and fluctuating environment determine to different extents their evolutionary history. However, because of mathematical and computational limitations, available inferences unrealistically assume that these interconnected evolutionary processes happen independently and that lineages evolve in isolation, and do not integrate all sources of paleontological and neontological evidence. Consequently, our knowledge about how biotic and abiotic factors regulate species evolution and diversification is still deficient. This project aims to significantly advance our mechanistic understanding on the drivers of past biodiversity dynamics across taxa, space and time, through the development of phylogenetic probabilistic models that unify stochastic processes of diversification, trait and biogeographic evolution, integrating present-day, fossil and paleoenvironmental evidence. We will overcome current model limitations posed by the lack of analytical solutions or prohibiting computational costs in evaluating likelihoods by exploiting new unexplored capabilities offered by Bayesian data augmentation techniques to develop full efficient probabilistic inference. This will be enhanced by building a foundational, modular and extensible open-source software package written in Julia, a modern programming language at the forefront of efficient numerical computing. Applying our new models to empirical data we will be first to directly assess a suite of foundational evolutionary hypotheses about how species diversification, trait and biogeographic evolution influence each other and are determined by biotic (e.g., diversity-dependence, competition) and abiotic factors (e.g., geography, environmental fluctuations) in a robust probabilistic framework.
