Within the tropics, the species richness of tree communities is strongly and positively associated with precipitation. Previous research has suggested that this macroecological pattern is driven by the negative effect of water‐stress on the physiological processes of most tree species. This implies that the range limits of taxa are defined by their ability to occur under dry conditions, and thus in terms of species distributions predicts a nested pattern of taxa distribution from wet to dry areas. However, this ‘dry‐tolerance’ hypothesis has yet to be adequately tested at large spatial and taxonomic scales. Here, using a dataset of 531 inventory plots of closed canopy forest distributed across the western Neotropics we investigated how precipitation, evaluated both as mean annual precipitation and as the maximum climatological water deficit, influences the distribution of tropical tree species, genera and families. We find that the distributions of tree taxa are indeed nested along precipitation gradients in the western Neotropics. Taxa tolerant to seasonal drought are disproportionally widespread across the precipitation gradient, with most reaching even the wettest climates sampled; however, most taxa analysed are restricted to wet areas. Our results suggest that the ‘dry tolerance' hypothesis has broad applicability in the world's most species‐rich forests. In addition, the large number of species restricted to wetter conditions strongly indicates that an increased frequency of drought could severely threaten biodiversity in this region. Overall, this study establishes a baseline for exploring how tropical forest tree composition may change in response to current and future environmental changes in this region.