Mammalian basal metabolic rate is proportional to body mass^2/3

Abstract

The relationship between mammalian basal metabolic rate (BMR, ml of O 2 per h) and body mass (M, g) has been the subject of regular investigation for over a century. Typically, the relationship is expressed as an allometric equation of the form BMR ‫؍‬ aM b . The scaling exponent (b) is a point of contention throughout this body of literature, within which arguments for and against geometric (b ‫؍‬ 2/3) and quarter-power (b ‫؍‬ 3/4) scaling are made and rebutted. Recently, interest in the topic has been revived by published explanations for quarter-power scaling based on fractal nutrient supply networks and four-dimensional biology. Here, a new analysis of the allometry of mammalian BMR that accounts for variation associated with body temperature, digestive state, and phylogeny finds no support for a metabolic scaling exponent of 3/4. Data encompassing five orders of magnitude variation in M and featuring 619 species from 19 mammalian orders show that BMR ؔ M 2/3 . P ioneering work published by Max Rubner (1) in the 1880s reported that mammalian basal metabolic rate (BMR) was proportional to M 2/3 . In accordance with simple geometric and physical principles, it was therefore thought that an animal's rate of metabolic heat production was matched to the rate at which heat was dissipated through its body surface. However, Max Kleiber's influential monograph (2), published in 1932, concluded that basal metabolic rate scaled not in proportion with surface area, but with an exponent significantly greater than that of Rubner's surface law. Kleiber's work was later supported by Brody's (3) famous mouse-to-elephant curve, and an exponent of 3/4 (henceforth referred to as Kleiber's exponent) remains in widespread use. Quarter-power scaling is often regarded as ubiquitous in biology: metabolic rate has been reported as proportional to M 3/4 in organisms ranging from simple unicells to plants and endothermic vertebrates (4, 5). Kleiber's exponent has become so widely accepted that metabolic scaling relationships that deviate from an exponent of 3/4 are often considered somehow flawed or are summarily dismissed. However, examination of the species compositions of early studies (2, 3) shows that they poorly reflect Mammalia. Most data points are derived from domestic species, which have been under artificial energetic constraints for many generations (6). Additionally, the order Artiodactyla is consistently over-represented; both Kleiber's (2) and Brody's (3) data sets include Ϸ20% artiodactyls, but only Ϸ5% of Recent mammals are artiodactyls (7). Being near the upper mass limit of the regressions, these animals exert a disproportionate influence on the scaling exponent. Their inclusion is problematic, because microbial fermentation of cellulose may delay or prohibit entrance into a postabsorptive state (8). This elevates metabolic rate above basal levels and, when coupled with a large body mass, artificially inflates the calculated scaling exponent. Examination of Brody's (3) data reveals the same problems (6). Because meas...

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