Significance We present a conceptual framework for testing theories for the latitudinal gradient of species richness in terms of variation in functional diversity at the alpha, beta, and gamma scales. We compared ecological community theory with large-scale observational data of tree species richness and functional diversity. We found that the patterns of functional trait diversity are not consistent with any one theory of species diversity. These conflicting results indicate that none of the broad classes of biodiversity theory considered here is alone able to explain the latitudinal gradient of species diversity in terms of functional trait space. The processes causing the latitudinal gradient in species richness remain elusive. Ecological theories for the origin of biodiversity gradients, such as competitive exclusion, neutral dynamics, and environmental filtering, make predictions for how functional diversity should vary at the alpha (within local assemblages), beta (among assemblages), and gamma (regional pool) scales. We test these predictions by quantifying hypervolumes constructed from functional traits representing major axes of plant strategy variation (specific leaf area, plant height, and seed mass) in tree assemblages spanning the temperate and tropical New World. Alpha-scale trait volume decreases with absolute latitude and is often lower than sampling expectation, consistent with environmental filtering theory. Beta-scale overlap decays with geographic distance fastest in the temperate zone, again consistent with environmental filtering theory. In contrast, gamma-scale trait space shows a hump-shaped relationship with absolute latitude, consistent with no theory. Furthermore, the overall temperate trait hypervolume was larger than the overall tropical hypervolume, indicating that the temperate zone permits a wider range of trait combinations or that niche packing is stronger in the tropical zone. Although there are limitations in the data, our analyses suggest that multiple processes have shaped trait diversity in trees, reflecting no consistent support for any one theory.