Diversity patterns in terrestrial tetrapod clades are governed by equilibrium dynamics

Large-scale patterns of species richness have been attributed to ecological limits, variation in diversification rates, and differences in evolutionary time, yet the relative importance of these drivers remains debated. Here, we present a unifying framework distinguishing four richness-generating scenarios, defined by contrasting roles of evolutionary time and speciation rates, which yields explicit and testable predictions for how evolutionary time, speciation, and environmental factors influence species richness. We applied this framework by analyzing 129 distinct, nonoverlapping clades spanning amphibians, reptiles, birds, and mammals. For each clade, we integrated historical biogeographic reconstructions, multiple estimates of speciation rates, and GIS-based environmental data. Using structural equation modeling, we quantified the direct and indirect effects of evolutionary time, speciation rates, and environmental conditions (productivity, temperature, and precipitation) on species richness. We further tested whether these effects varied systematically with clade-level traits, including age, physiology, diversity, and geographic extent. Productivity emerged as the dominant predictor of species richness, exerting strong and consistent direct effects that were largely invariant to clade traits. In contrast, speciation rates contributed little to species richness, while the influence of evolutionary time was highly context-dependent and most pronounced in younger clades. Temperature showed consistent direct effects not mediated by productivity, evolutionary time, or speciation rates, whereas precipitation influenced richness primarily via productivity. Together, our results support a productivity-driven equilibrium view of species richness, in which diversity reflects a balance between speciation and extinction regulated by energy availability. Deviations from equilibrium dynamics, particularly in younger clades, highlight the role of evolutionary history on biodiversity gradients.