Demystifying the West, Brown & Enquist model of the allometry of metabolism

The allometry of metabolic rate has long been one of the key relationships in ecology. While its existence is generally agreed on, the exact value of the scaling exponent, and the key mechanisms that determine its value, are still hotly debated. The network model of West, Brown & Enquist (Science 276, 122-126, 1997) predicts a value of (3)/4 but, although appealing, this model has not been generally accepted. Here we reconstruct the model and derive the exponent in a clearer and much more straightforward way that requires weaker assumptions than the original model. Specifically, self-similarity of the network is not required. Our formulation can even be used if one or several assumptions of West et al. (1997) are considered invalid. Moreover, we provide a formula for the proportionality constant (i.e. the intercept of the allometric scaling relation) that shows explicitly where factors as temperature and stoichiometry affect metabolism.