Background/Question/Methods Increasing species richness towards the tropics is a pattern observed in nearly all taxonomic groups. Understanding the processes responsible for this latitudinal gradient is a key challenge for community ecology and has been the subject of intense study for well over 200 years. The evolutionary speed hypothesis posits that high tropical diversity is due to temperature dependent metabolism such that biological time ‘ticks' faster in the tropics. The metabolic theory of ecology has worked towards formalizing this hypothesis, but it is still unclear if metabolism underlies biodiversity gradients. If metabolism influences the generation and maintenance of biodiversity, it should be through the interactive effects of metabolism-dependent ecological, evolutionary and ecosystem rates, yet no attempt has been made to understand these interactive effects. Here we expand the breadth of metabolic theory by examining how species richness responds to the individual and combined influences of temperature dependent ecological, evolutionary and ecosystem rates. This is achieved by extending a recent eco-evolutionary model that generates realistic size-structured food webs so that ecological and evolutionary rates are defined by temperature and body size dependent metabolism. Productivity is also assumed temperature-dependent. Results/Conclusions Predicted temperature dependencies of species richness emerge from the model due to dynamic feedbacks among community structure, natural selection and ecosystem productivity. These emergent predictions are broadly consistent with empirical species richness-temperature gradients. Specifically, the model predicts the relationship between log-transformed species richness and inverse temperature to vary from linear to saturating (at high or low temperature) to unimodal to null. The functional form of the predicted relationship depends on which components (ecology, evolution and/or productivity) are assumed to be temperature dependent and on the stage of community assembly. The model shows that non-linear empirical relationships (saturating and unimodal) are predicted by metabolic theory and indicate the simultaneous influence of temperature-dependent ecology, evolution and productivity. More quantitatively, the model predicts a similar range in slopes from linear regressions between log-transformed richness and inverse temperature as has been observed empirically. The qualitative and quantitative correspondence between predictions of our metabolic, eco-evolutionary model and empirical data thus provides strong support for a metabolic basis of biodiversity.