Tree allometric relationships are widely employed for estimating 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 capture changes in scaling during ontogeny and physical limits to maximum tree size and that ignores interspecific differences in allometry. Here, we analyzed allometric relationships of tree height (9884 individuals) and crown area (2425) with trunk diameter for 162 species from the Barro Colorado Nature Monument, Panama. We fit nonlinear, hierarchical models informed by species traits – wood density, mean sapling growth, or sapling mortality – 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 for improving estimates of forest biomass and productivity. Our results provide an improved basis for parameterizing tropical plant functional types in vegetation models.