The degree to which turnover in biological communities is structured by deterministic or stochastic factors and the identities of influential deterministic factors are fundamental, yet unresolved, questions in ecology. Answers to these questions are particularly important for projecting the fate of forests with diverse disturbance histories worldwide. To uncover the processes governing turnover we use species-level molecular phylogenies and functional trait data sets for two long-term tropical forest plots with contrasting disturbance histories: one forest is older-growth, and one was recently disturbed. Having both phylogenetic and functional information further allows us to parse out the deterministic influences of different ecological filters. With the use of null models we find that compositional turnover was random with respect to phylogeny on average, but highly nonrandom with respect to measured functional traits. Furthermore, as predicted by a deterministic assembly process, the older-growth and disturbed forests were characterized by less than and greater than expected functional turnover, respectively. These results suggest that the abiotic environment, which changes due to succession in the disturbed forest, strongly governs the temporal dynamics of disturbed and undisturbed tropical forests. Predicting future changes in the composition of disturbed and undisturbed forests may therefore be tractable when using a functional-trait-based approach.