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Aim To evaluate how wood density relates to tree growth rates in simple models and two tropical forests. Location Barro Colorado Island, Panama; and Pasoh Forest Reserve, Malaysia. Time Period 1986-2010. Major Taxa Studied Trees. Methods We derived expected relationships of wood density with diameter growth at a given diameter under a null hypothesis that aboveground biomass growth is independent of wood density, and an alternative hypothesis that biomass growth scales with crown area, which itself increases with wood density. We tested these assumptions and predictions through analyses of interspecific relationships of wood density with height, crown area and diameter growth at constant diameter in two tropical forests. Results Height was unrelated to wood density, whereas crown areas showed a slightly positive relationship to wood density. Thus, the expected exponent of diameter growth with wood density was equal to minus one under the null hypothesis, and equal to the exponent of crown area with wood density minus one under the alternative hypothesis. Empirical relationships of diameter growth and biomass growth with wood density were broadly consistent with the null hypothesis that biomass growth is unrelated to wood density at both sites, except in trees < 13 cm in diameter at Barro Colorado Island, which showed more negative relationships. Main conclusions Although most previous analyses of growth with wood density have examined linear relationships, simple models suggest that both tree diameter growth and tree biomass growth are power functions of wood density. Analyses in two tropical forests showed that aboveground biomass growth was approximately constant with wood density, and thus, that diameter growth was inversely proportional to wood density, for most tree sizes, although confidence intervals on the scaling exponents were broad. More negative relationships of growth with wood density at small sizes might reflect differential environmental filtering, in which higher wood density trees are found in less favourable understorey environments. [ABSTRACT FROM AUTHOR]