Scaling

Rivers, blood and transportation networks

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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 M3/4, 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.

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References

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    Banavar, J. R., Maritan, A. & Rinaldo, A. Nature 399, 130– 132 (1999).

  2. 2

    Schmidt-Nielsen, K. Scaling: Why is Animal Size so Important? (Cambridge Univ. Press, 1984).

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    West, G. B., Brown, J. H. & Enquist, B. J. Science 284, 1677– 1679 (1999).

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    Ritter, D. F., Kochel, C. R. & Miller, J. R. Process Geomorphology 3rd edn (WCB/McGraw-Hill, Boston, 1995).

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    Rodriguez-Iturbe, I. & Rinaldo, A. Fractal River Basins: Chance and Self-Organization (Cambridge Univ. Press, New York, 1997).

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    Banavar, J. R. et al. Phys. Rev. Lett. 78, 4522– 4525 (1997).

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Correspondence to Peter K. Haff.

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