Energetic constraints are fundamental to ecology and evolution, and empirical relationships between species richness and estimates of available energy (i.e. resources) have led some to suggest that richness is energetically constrained. However, the mechanism linking energy with richness is rarely specified and predictions of secondary patterns consistent with energy-constrained richness are lacking. Here, we lay out the necessary and sufficient assumptions of a causal relationship linking energy gradients to richness gradients. We then describe an eco-evolutionary simulation model that combines spatially explicit diversification with trait evolution, resource availability and assemblage-level carrying capacities. Our model identified patterns in richness and phylogenetic structure expected when a spatial gradient in energy availability determines the number of individuals supported in a given area. A comparison to patterns under alternative scenarios, in which fundamental assumptions behind energetic explanations were violated, revealed patterns that are useful for evaluating the importance of energetic constraints in empirical systems. We use a data set on rockfish (genus Sebastes) from the northeastern Pacific to show how empirical data can be coupled with model predictions to evaluate the role of energetic constraints in generating observed richness gradients.