Measurement of body size and abundance in tests of macroecological and food web theory.

1. Mean body mass (W) and mean numerical (N) or biomass (B) abundance are frequently used as variables to describe populations and species in macroecological and food web studies. 2. We investigate how the use of mean W and mean N or B, rather than other measures of W and/or accounting for the properties of all individuals, can affect the outcome of tests of macroecological and food web theory. 3. Theoretical and empirical analyses demonstrate that mean W, W at maximum biomass (W(mb)), W when energy requirements are greatest (W(me)) and the W when a species uses the greatest proportion of the energy available to all species in a W class (W(mpe)) are not consistently related. 4. For a population at equilibrium, relationships between mean W and W(me) depend on the slope b of the relationship between trophic level and W. For marine fishes, data show that b varies widely among species and thus mean W is an unreliable indicator of the role of a species in the food web. 5. Two different approaches, 'cross-species' and 'all individuals' have been used to estimate slopes of abundance-body mass relationships and to test the energetic equivalence hypothesis and related theory. The approaches, based on relationships between (1) log(10) mean W and log(10) mean N or B, and (2) log(10) W and log(10) N or B of all individuals binned into log(10) W classes (size spectra), give different slopes and confidence intervals with the same data. 6. Our results show that the 'all individuals' approach has the potential to provide more powerful tests of the energetic equivalence hypothesis and role of energy availability in determining slopes, but new theory and empirical analysis are needed to explain distributions of species relative abundance at W. 7. Biases introduced when working with mean W in macroecological and food web studies are greatest when species have indeterminate growth, when relationships between W and trophic level are strong and when the range of species'W is narrow.