Although niche-based and stochastic processes, including dispersal limitation and demographic stochasticity, can each contribute to community assembly, it is difficult to quantify the relative importance of each process in natural vegetation. Here, we extend Shipley's maxent model (Community Assembly by Trait Selection, CATS) for the prediction of relative abundances to incorporate both trait-based filtering and dispersal limitation from the larger landscape and develop a statistical decomposition of the proportions of the total information content of relative abundances in local communities that are attributable to trait-based filtering, dispersal limitation, and demographic stochasticity. We apply the method to tree communities in a mature, species-rich, tropical forest in French Guiana at 1-, 0.25- and 0.04-ha scales. Trait data consisted of species' means of 17 functional traits measured over both the entire meta-community and separately in each of nine 1-ha plots. Trait means calculated separately for each site always gave better predictions. There was clear evidence of trait-based filtering at all spatial scales. Trait-based filtering was the most important process at the 1-ha scale (34%), whereas demographic stochasticity was the most important at smaller scales (37–53%). Dispersal limitation from the meta-community was less important and approximately constant across scales (9%), and there was also an unresolved association between site-specific traits and meta-community relative abundances. Our method allows one to quantify the relative importance of local niche-based and meta-community processes and demographic stochasticity during community assembly across spatial and temporal scales.