The relative importance of ecological and stochastic processes in the diversification of life on earth is largely unresolved. I propose to conduct an exhaustive spatially-explicit individual-based simulation study of biodiversity patterns (both phylogenetic and macroecological) generated over time by stochastic models of speciation and extinction. This project will depart from the prevailing paradigm of studying biotas at equilibrium and will, for the first time, focus on understanding how biodiversity patterns (not just species richness) evolve as biotas diversify and reach their equilibrium. Exploring different scenarios of stochastic diversification will enable me to assess how long different models take to reach their equilibrium and how biodiversity patterns are affected by different stochastic processes (demographic stochasticity, dispersal and speciation). New analytical tools will also be developed in this fellowship to model biodiversity dynamics at realistic spatial scales and made available to other researchers in a user-friendly R package. Taken together, these developments will determine if the prevailing paradigm of predicting regional and global biota at equilibrium is appropriate to understand biodiversity, and to what extent stochastic diversification models are sufficient to explain simultaneously the full range of biodiversity patterns seen in nature. The total evidence methodology developed in this project will prove useful to other researchers wishing to disentangle the role that ecological and stochastic processes have played in the diversification of their taxon of interest. For animal and plant taxa with poor biodiversity data, stochastic models of diversification may provide a good first approximation of how their biodiversity may respond to global environmental change.