Abundance-body-size patterns emerge from food web dynamics

Within communities, species’ abundance approximately scales as an inverse power law with body mass. This relationship is different for species within a single trophic level compared to species across trophic levels, with empirical evidence suggesting a large variation in the power parameter of this relationship for both cases. We used a simple food chain model of population dynamics, with birth/death rate and consumption rate parameters scaling with empirically observed mass dependencies to investigate these relationships. Autotrophic species self limitation was modeled with mass in two different ways to approximate two empirically observed scaling patterns, first consistent with the linear biomass hypothesis and second the energetic equivalence rule. Under the linear biomass hypothesis the abundance-body-mass scaling within each trophic level scaled to the -1 power, whereas the energetic equivalence rule lead to different scalings in different trophic levels. In each case the scaling across trophic levels is a complicated function of model parameters, but can be approximated by a function similar to that produced by an energetic argument from the metabolic theory of ecology. Controlling for the autotrophic species productivity and variation in parameters between simulations we were able to identify sources of variation in the exponent of the power function. Consequently, the population dynamic approach can be used to explain the presence of mass power scaling and some of the variation in exponents predicted by empirical studies.