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Tropical forest vegetation is shaped by climate and by soil, but understanding how the distributions of individual tree species respond to specific resources has been hindered by high diversity and consequent rarity. To study species over an entire community, we surveyed trees and measured soil chemistry across climatic and geological gradients in central Panama and then used a unique hierarchical model of species occurrence as a function of rainfall and soil chemistry to circumvent analytical difficulties posed by rare species. The results are a quantitative assessment of the responses of 550 tree species to eight environmental factors, providing a measure of the importance of each factor across the entire tree community. Dry-season intensity and soil phosphorus were the strongest predictors, each affecting the distribution of more than half of the species. Although we anticipated clear-cut responses to dry-season intensity, the finding that many species have pronounced associations with either high or low phosphorus reveals a previously unquantified role for this nutrient in limiting tropical tree distributions. The results provide the data necessary for understanding distributional limits of tree species and predicting future changes in forest composition.