The causes of global variation in species richness have been debated for nearly two centuries with no clear resolution in sight. Competing hypotheses have typically been evaluated with correlative models that do not explicitly incorporate the mechanisms responsible for biotic diversity gradients. Here, we employ a fundamentally different approach that uses spatially explicit Monte Carlo models of the placement of cohesive geographical ranges in an environmentally heterogeneous landscape. These models predict species richness of endemic South American birds (2248 species) measured at a continental scale. We demonstrate that the principal single-factor and composite (species-energy, water-energy and temperature-kinetics) models proposed thus far fail to predict (r(2) < or =.05) the richness of species with small to moderately large geographical ranges (first three range-size quartiles). These species constitute the bulk of the avifauna and are primary targets for conservation. Climate-driven models performed reasonably well only for species with the largest geographical ranges (fourth quartile) when range cohesion was enforced. Our analyses suggest that present models inadequately explain the extraordinary diversity of avian species in the montane tropics, the most species-rich region on Earth. Our findings imply that correlative climatic models substantially underestimate the importance of historical factors and small-scale niche-driven assembly processes in shaping contemporary species-richness patterns.