Physica A 390 (2011) 1733–1736 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Are allometry and macroevolution related? Bruce J. West a,∗ , Damien West b a Information Science Directorate, Army Research Office, Durham, NC 27709, United States b Physics Department, Rensselaer Polytechnic Institute, Troy, NY 12180, United States article info Article history: Received 11 October 2010 Received in revised form 17 November 2010 Available online 21 December 2010 Keywords: Allometry Metabolism Pareto distribution Probability calculus abstract The allometric relationship between the basal metabolic rate B and total body mass M is B = aM b , where the allometry coefficient a and the allometry exponent b have been fit to various data sets for over 150 years. The best fit of the allometry exponent to 391 mammalian species is given by Heusner [7] to be midway between the leading theoretical values of 2/3 and 3/4. Most theoretical investigations have focused on determining the proper value of b entailed by an appropriate biological model and with some notable exceptions ignored the allometry coefficient a altogether. Herein, we shift the focus and use the above data to settle on an empirical value of b that gives rise to an allometry coefficient with random variability described by a Pareto distribution. This new perspective suggests an interesting biological interpretation of the statistical fluctuations of the allometry coefficient. The time distribution of the intermittent fluctuations in a are determined to be of the same statistical form as those of speciation found in the punctuated equilibrium theory of macroevolution (Eldredge and Gould [3], Sneppen et al. [5] and Rikvold and Zia [17]). Published by Elsevier B.V. 1. Background Allometry is the study of size and its consequences, and allometryrelations among properties within and across species are ubiquitous in Natural Science [1,2]. In addition to being a useful tool for comparative physiology, allometry may also provide insight into biological macroevolution, insight that extends beyond the engineer’s ‘law of similarity’. Gould and Eldredge [3] argued that punctuated change dominates the history of life and that relatively rapid events of speciation constitute biological macroevolution. The intermittency of speciation in time has been explained by one group as punctuated equilibria [4], and has been indirectly related to fractal statistics by identifying it as a self-organized critical phenomenon [5]. Herein, we provide contemporary empirical evidence in the form of a Pareto probability density function (pdf ) for the variability of the allometry coefficient. We argue that this pdf directly supports the theory of punctuated equilibria. The most studied of the allometric relations is that between the basal metabolic rate (BMR) B measured in watts to the total body mass (TBM) M measured in kilograms across multiple species in the same taxa: B = aM b . (1) In 1932, Kleiber [6] established using observational data that b ≈ 3 4 ; Heusner [7], using a more extended data set, obtained b ≈ 2/3; and today the empirical value of the allometry exponent b remains controversial [8]. Controversy also arises in the theoretical explanation as to why the allometry exponent b should take on a specific value. Simple dimensional ∗ Corresponding author. E-mail addresses: Bruce.J.West@us.army.mil, bwest@nc.rr.com (B.J. West). 0378-4371/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.physa.2010.11.031