The notion that relationships between community-weighted mean (CWM) traits (i.e. plot-level trait values weighted by species abundances) and environmental conditions reflect selection towards locally optimal phenotypes is challenged by the large amount of interspecific trait variation typically found within ecological communities. Reconciling these contrasting patterns is a key to advancing predictive theories of functional community ecology. We combined data on geographical distributions and three traits (wood density, leaf mass per area and maximum height) of 173 tree species in Puerto Rico. We tested the hypothesis that species are more likely to occur where their trait values are more similar to the local CWM trait values (the ‘CWM-optimality’ hypothesis) by comparing species occurrence patterns (as a proxy for fitness) with the functional composition of forest plots across a precipitation gradient. While 70% of the species supported CWM-optimality for at least one trait, nearly 25% significantly opposed it for at least one trait, thereby contributing to local functional diversity. The majority (85%) of species that opposed CWM-optimality did so only for one trait and few species opposed CWM-optimality in multivariate trait space. Our study suggests that constraints to local functional variation act more strongly on multivariate phenotypes than on univariate traits.