Statistical origin of allometry

¹ Physics Department, Rensselaer Polytechnic Institute - Troy, NY 12180, USA
² Information Science Directorate, Army Research Office - Durham, NC 27709, USA

^a Bruce.J.West@us.army.mil

Received: 11 February 2011
Accepted: 29 March 2011

Abstract

The allometry relationship (AR) between two properties of a living network X and Y is X=aY^b where one or both of the variables is a measure of size and the allometry coefficient a and exponent b are fit to data. Many investigators have focused on determining the proper value of b entailed by an appropriate biological model, whereas others have argued that the allometry coefficient plays the more important role. Herein we use metabolic data to determine a probability density function (pdf) for the allometry coefficient P(a) with constant allometry exponent and a pdf for the allometry exponent Ψ(b) with a constant allometry coefficient. The two distributions are found to imply that the allometry parameters co-vary and an explict functional relation between them is determined. The empirical pdf P(a) is a Pareto distribution and establishes an inconsistency between reductionistic and statistical models of the interspecies AR. This inconsistency is resolved using the probability calculus to establish that the scaling of the pdf is the proper origin of allometry.