"Explaining the tremendous disparity in the number of species among different taxonomic groups and geographic regions is one of the greatest challenges in biodiversity research. This project aims to significantly advance our fundamental understanding of the ecological and evolutionary processes that explain how species richness is distributed on earth and in the tree of life. The first part of the project consists in significantly improving phylogenetic approaches to diversification. This implies developing stochastic lineage-based birth-death models that account for species interactions, stochastic lineage-based birth-death models integrating phylogenetic and fossil information, and stochastic individual-based birth-death-speciation models. The second part of the project consists in implementing these models, as well as other recently developed models, in efficient and user-friendly software packages. Finally, the third part of the project consists in applying these phylogenetic tools to large datasets spanning the tree of life in order to understand how and why speciation and extinction rates vary over evolutionary time, geographical space, and species groups. We will use our new phylogenetic comparative methods to uncover diversity-through-time curves for a wide variety of taxonomic groups, evaluate the relative role of the biotic and the abiotic environment in driving diversification, shed new light on the latitudinal diversity gradient, and consider microbial diversity with a macroevolutionary perspective. The proposed research will provide the scientific community with novel, user-friendly modeling tools for understanding biodiversity, and will yield unprecedented insights into the dynamics and determinants of biodiversity."