How ecosystem productivity and species richness are interrelated is one of the most debated subjects in the history of ecology. Decades of intensive study have yet to discern the actual mechanisms behind observed global patterns. Here, by integrating the predictions from multiple theories into a single model and using data from 1,126 grassland plots spanning five continents, we detect the clear signals of numerous underlying mechanisms linking productivity and richness. We find that an integrative model has substantially higher explanatory power than traditional bivariate analyses. In addition, the specific results unveil several surprising findings that conflict with classical models. These include the isolation of a strong and consistent enhancement of productivity by richness, an effect in striking contrast with superficial data patterns. Also revealed is a consistent importance of competition across the full range of productivity values, in direct conflict with some (but not all) proposed models. The promotion of local richness by macroecological gradients in climatic favourability, generally seen as a competing hypothesis, is also found to be important in our analysis. The results demonstrate that an integrative modelling approach leads to a major advance in our ability to discern the underlying processes operating in ecological systems.