Patterns of species richness and relative abundance at some scales cannot be distinguished from predictions of null models, including zero-sum neutral models of population change and random speciation-extinction models of evolutionary diversification. Both models predict that species richness or population abundance produced by independent iterations of the same processes in different regions should be uncorrelated. We find instead that the number of species and individuals in families of trees in forest plots are strongly correlated across Southeast Asia, Africa, and tropical America. These correlations imply that deterministic processes influenced by evolutionarily conservative family-level traits constrain the number of confamilial tree species and individuals that can be supported in regional species pools and local assemblages in humid tropical forests.