A mechanistic explanation of size-density scaling in consumers

Background/Question/Methods

The population abundance of many groups of organisms declines with average individual body mass.  This ‘size-density scaling’ is typically characterized by a power-law relationship, which is linear in log space.  Size-density scaling suggests that general rules govern the abundance of living things, but a mechanistic expression of such rules is lacking.

Abundance is determined by the balance of births and deaths in a population.  Thus, the scaling of abundance must be related to these primary processes, which themselves are dependent on individual body mass.  To provide a mechanistic understanding of size-density scaling, then, we may turn to mechanistic consumer-resource models and evaluate their steady-states in terms of the body mass of the parameters.  Although theoretical work on this has been conducted, a clear depiction of the factors that contribute to size-density scaling has not been produced, either in general or for any specific group.  In this study, we analyze a set of consumer-resource models to identify the body-mass dependent factors that produce size-density scaling.  We also ask whether parameterizing such models can enable successful prediction of the size-density scaling for particular groups.

Results/Conclusions

We solved four different consumer-resource models, from the Lotka-Volterra to the MacArthur-Rosenzweig models, for their steady-states and expressed the parameters in terms of their body mass dependence.  The Lotka-Volterra model provides a core expression for size-density scaling that suggests that prey productivity, predator-prey size ratios, and consumer attack efficiency are the primary factors determining the scaling relationship.  Adding additional complexity to the Lotka-Volterra model produces terms that modify the core Lotka-Volterra expression.

We parameterized all four models for mammalian carnivores preying upon mammals, and compared the quantitative predictions of the size-density scaling with the observed scaling in the literature.  All four predictions provided a very close match to data.  Adding complexity did not alter the predictions, suggesting that, at least for carnivores, only the three core factors are important for determining both the height and slope of the size-density scaling.  Our approach provides a mechanistic explanation of - and quantitative predictions for - one of the broadest patterns in ecology.