The scale-dependence of population density–body mass allometry: Statistical artefact or biological mechanism?

The relation between population density and body mass has vexed ecologists for nearly 30 years as a consequence of high variability in the observed slope of the relation: No single generalisation of the relation has been accepted as universally representative. Here, we use a simple computational approach to examine how observational scale (the body mass range considered) determines variation in the density–mass pattern. Our model relies on two assumptions: (1) resources are partitioned in an unbiased manner among species with different masses; (2) the number of individuals that can be supported by a given quantity of resources is related to their metabolic rate (which is a function of their mass raised to the power of a scaling coefficient, b). We show that density (1) scales as a function of body mass raised to the power of −b on average, but (2) the slope of the relation varies considerably at smaller scales of observation (over narrow ranges of body mass) as a consequence of details of species’ ecology associated with resource procurement. Historically, the effect of body mass range on the slope of the density–mass relation has been unfailingly attributed to a statistical effect. Here we show that the effect of body mass range on the slope of the density–mass relation may equally result from a biological mechanism, though we find it impossible to distinguish between the two. We observe that many of the explanations that have been offered to account for the variability in the slope of the relation invoke mechanisms associated with differences in body mass and we therefore suggest that body mass range itself might be the most important explanatory factor. Notably, our results imply that the energetic equivalence rule should not be expected to hold at smaller scales of observation, which suggests that it may not be possible to scale the mass- and temperature-dependence of organism metabolism to predict patterns at higher levels of biological organisation at smaller scales of observation.