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First published online October 31, 2008
Journal of Experimental Biology 211, 3581-3587 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.023317

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Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates

Gary C. Packard^1,* and Geoffrey F. Birchard²

¹ Department of Biology, Colorado State University, Fort Collins, CO 80523, USA
² Department of Environmental Science and Policy, George Mason University, Fairfax, VA 22030, USA

^* Author for correspondence (e-mail: packard{at}lamar.colostate.edu)

Accepted 23 September 2008

The field of biological allometry was energized by the publication in 1997 of a theoretical model purporting to explain 3/4-power scaling of metabolic rate with body mass in mammals. This 3/4-power scaling exponent, which was first reported by Max Kleiber in 1932, has been derived repeatedly in empirical research by independent investigators and has come to be known as `Kleiber's Law'. The exponent was estimated in virtually every instance, however, by fitting a straight line to logarithmic transformations of data and by then re-expressing the resulting equation in the arithmetic scale. Because this traditional method may yield inaccurate and misleading estimates for parameters in the allometric equation, we re-examined the comprehensive data set that led Savage and colleagues to reaffirm the view that the metabolic rate of mammals scales to the 3/4-power of body mass. We found that a straight line fitted to logged data for the basal metabolic rate (BMR) of mammals ranging in size from a 2.4 g shrew to a 3672 kg elephant does not satisfy assumptions underlying the analysis and that the allometric equation obtained by back-transformation underestimates BMR for the largest species in the sample. Thus, the concept of 3/4-power scaling of metabolic rate to body mass is not well supported because the underlying statistical model does not apply to mammalian species spanning the full range in body size. Our findings have important implications with respect to methods and results of other studies that used the traditional approach to allometric analysis.

Key words: allometry, scaling, logarithms, transformations, metabolic rates

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