Rivers, blood and transportation networks

Abstract

The long-standing problem of explaining metabolic scaling² in animals, whereby whole-animal metabolic rate B is observed to increase as a function of body mass M approximately as M^3/4, has been recently revisited by Banavar et al.¹ (see also ref. 3, in which allometric scaling rules are derived from fractal geometry). These authors¹ derive and generalize to non-biological systems, including river networks, a three-quarter-power 'allometric' scaling rule, which arises, in their treatment, from an assumption of the efficiency of the resource distribution network. Here I present a simple derivation of 3/4-power scaling based on the geometric requirements of inventorying resources before metabolization, which does not support the notion of allometric scaling suggested by Banavar et al.¹ for rivers, at least not when applied to the problem of fluvial sediment transport. Although some distributary systems 'metabolize' according to the 3/4-power rule, this rule is not golden — each system needs to be investigated on its own merits.