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A general basis for quarter-power scaling in animals

Banavar, J. R., Moses, M. E., Brown, J. H., Damuth, J., Rinaldo, A., Sibly, R. M. ORCID: and Maritan, A. (2010) A general basis for quarter-power scaling in animals. Proceedings of the National Academy of Sciences of the United States of America, 107 (36). pp. 15816-15820. ISSN 0027-8424

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To link to this item DOI: 10.1073/pnas.1009974107


It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarterpower scaling can arise even when there is no underlying fractality. The canonical “fourth dimension” in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal “service volume” where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

Item Type:Article
Divisions:Life Sciences > School of Biological Sciences > Ecology and Evolutionary Biology
ID Code:25646
Uncontrolled Keywords:allometric; fractal; hierarchical; metabolic rate; network
Publisher:National Academy of Sciences

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