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Systems 2014, 2(2), 89-118; doi:10.3390/systems2020089

A Fractional Probability Calculus View of Allometry

Mathematics and Information Sciences Directorate, Army Research Office, Research Triangle Park, NC 27709, USA
Received: 7 January 2014 / Revised: 2 April 2014 / Accepted: 10 April 2014 / Published: 14 April 2014
(This article belongs to the Special Issue Allometric Scaling)
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The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are only two of the many allometry relations that emerge from empirical studies in the physical, social and life sciences. Herein, we present a theory of allometry that provides a foundation for the allometry relation between a network function and the size that is entailed by the hypothesis that the fluctuations in the two measures are described by a scaling of the joint probability density. The dynamics of such networks are described by the fractional calculus, whose scaling solutions entail the empirically observed allometry relations.
Keywords: allometry; fractional calculus; probability statistics; inverse power laws; Levy statistics allometry; fractional calculus; probability statistics; inverse power laws; Levy statistics
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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West, B.J. A Fractional Probability Calculus View of Allometry. Systems 2014, 2, 89-118.

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