* Wood density (WD) affects plant biomechanics, drought and decay resistance. As a consequence, WD is an important functional trait related to plant demography and ecosystem processes, which is also used to estimate tree biomass. Radial variation in WD (changes from the centre of the stem to the cambium) affects the strength of the entire stem, but also reflects any changes in wood functional properties that might occur during a tree's lifetime. * To understand how WD and radial WD gradients, which were defined as the slope of the relationship between WD and distance to the centre, are related to demographic traits of species, we investigated WD in 335 tree species from a Panamanian moist forest and 501 species from an Ecuadorian rain forest and radial density gradients in 118 and 186 species, respectively, and compared WD with tree growth, mortality and size. * WD was negatively related to tree growth and mortality. WD tended to increase towards the outside in trees with low initial density and to decrease towards the outside in trees with high initial density. Radial WD gradients were largely unrelated to tree size and demographic traits, but some families had higher or lower WD gradients at a given inner WD. * Inner WD was by far the best predictor of radial WD gradients (r2 = 0·39 for Panama and 0·45 for Ecuador) and this relationship was indistinguishable between the two rain forests. This suggests a broadly uniform function of WD variation, likely responding to mechanical requirements during ontogeny. We discuss the factors potentially driving radial increases or decreases in WD and suggest ways to elucidate the relative importance of tree mechanics, hydraulic safety or decay resistance. * We also discuss that not accounting for radial WD gradients may result in substantial errors in WD of the whole stem and consequently biomass estimates, and recommend sampling density gradients when obtaining density data from tree cores.
