Tree allometric relationships are widely employed to estimate forest biomass and production, and are basic building blocks of dynamic vegetation models. In tropical forests, allometric relationships are often modeled by fitting scale-invariant power functions to pooled data from multiple species, an approach that fails to reflect finite size effects at the smallest and largest sizes, and that ignores interspecific differences in allometry. Here, we analyzed allometric relationships of tree height (9884 individuals) and crown area (2425) with trunk diameter using species-specific morphological and life history data of 162 species from Barro Colorado Island, Panamá. We fit nonlinear, hierarchical models informed by species traits and assessed the performance of three alternative functional forms: the scale-invariant power function, and the saturating Weibull and generalized Michaelis-Menten (gMM) functions. The relationship of tree height with trunk diameter was best fit by a saturating gMM model in which variation in allometric parameters was related to interspecific differences in sapling growth rates, a measure of regeneration light demand. Light-demanding species attained taller heights at comparatively smaller diameters as juveniles and had shorter asymptotic heights at larger diameters as adults. The relationship of crown area with trunk diameter was best fit by a power function model incorporating a weak positive relationship between crown area and species-specific wood density. The use of saturating functional forms and the incorporation of functional traits in tree allometric models is a promising approach to improve estimates of forest biomass and productivity. Our results provide an improved basis for parameterizing tropical tree functional types in vegetation models.