One of the more vexing issues in ecology is how historical processes affect contemporary patterns of biodiversity. Accordingly, few models have been presented. Two corollary models (centre of origin, time-for-speciation) can be used to make quantitative predictions characterizing the tropical niche conservatism hypothesis and describe diversification as diffusion and subsequent cladogenesis of species away from the place of origin of a higher taxon in the tropics. Predictions derived from such models are: (i) species richness declines toward the periphery of the range of a higher taxon; (ii) taxa are more derived toward the periphery than the centre; (iii) ages of taxa are lower toward the periphery than the centre; and (iv) ages and measures of derivedness are less variable toward the periphery of the range of a higher taxon. I tested these predictions to better understand the formation of one of the most ubiquitous patterns of biodiversity—the latitudinal gradient in species richness. Results indicate well-supported predictions for New World leaf-nosed bats and that diversification has had strong influences on latitudinal gradients of species richness. A better understanding of how evolutionary diversification of taxa contributes to formation of patterns of species richness along environmental gradients is necessary to fully understand spatial variation in biodiversity.