Biodiversity varies predictably with environmental energy around the globe, but the underlying mechanisms remain incompletely understood. The evolutionary speed hypothesis predicts that environmental energy shapes variation in speciation rates through temperature- or life history-dependent rates of evolution. To test whether variation in evolutionary speed can explain the relationship between energy and biodiversity in birds, mammals, amphibians, and reptiles, we simulated diversification over 65 million years of geological and climatic change with a spatially explicit eco-evolutionary...