Using mass scaling of movement cost and resource encounter rate to predict animal body size–Population density relationships

The negative relationship between body mass and population abundance was documented decades ago and forms one of the most fundamental scaling-laws in ecology. However, current theory fails to capture observed variations and the subject continues to raise controversy. Here we unify empirically observed size–abundance relationships with theory, by incorporating allometries in resource encounter rate and metabolic costs of movements. Fractal geometry is used to quantify the underlying resources distributions. Our model predicts that in environments packed with resources, body mass to population abundance relationships is less negative than the commonly assumed −3/4 power law. When resources are more patchily distributed, we predict a more negative exponent. These predictions are consistent with empirical observations. The current research provides an important step towards synthesizing metabolism, resource distribution and the global scaling of animal abundance, explaining why size–abundance relationships vary among feeding guilds and ecosystems.