Spatial patterns of species richness follow climatic and environmental variation, but could reflect random dynamics of species ranges (the mid-domain effect, MDE). Using data on the global distribution of birds, we compared predictions based on energy availability (actual evapotranspiration, AET, the best single correlate of avian richness) with those of range dynamics models. MDE operating within the global terrestrial area provides a poor prediction of richness variation, but if it operates separately within traditional biogeographic realms, it explains more global variation in richness than AET. The best predictions, however, are given by a model of global range dynamics modulated by AET, such that the probability of a range spreading into an area is proportional to its AET. This model also accurately predicts the latitudinal variation in species richness and variation of species richness both within and between realms, thus representing a compelling mechanism for the major trends in global biodiversity.