On the relationship between mass and diameter distributions in tree communities

It has been suggested that frequency distributions of individual tree masses in natural stands are characterized by power-law distributions with exponents near -3/4, and that therefore tree communities exhibit energetic equivalence among size classes. Because the mass of trees is not measured directly, but estimated from diameter, this supposition is based on the fact that the observed distribution of tree diameters is approximately characterized by a power-law with an exponent approximate to -2. Here we show that diameter distributions of this form are not equivalent to mass distributions with exponents of -3/4, but actually to mass distributions with exponents of -11/8. We discuss the implications of this result for the metabolic theory of ecology and for understanding energetic equivalence and the processes structuring tree communities.