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...

Body size and temperature are primary determinants of metabolic rate, and the standard metabolic rate (SMR) of animals ranging in size from unicells to mammals has been thought to be proportional to body mass (M ) raised to the power of three-quarters for over 40 years. However, recent evidence from rigorously selected datasets suggests that this is not the case for birds and mammals. To determine whether the influence of body mass on the metabolic rate of vertebrates is indeed universal, we compiled SMR measurements for 938 species spanning six orders of magnitude variation in mass. When normalized to a common temperature of 38 8C, the SMR scaling exponents of fish, amphibians, reptiles, birds and mammals are significantly heterogeneous. This suggests both that there is no universal metabolic allometry and that models that attempt to explain only quarterpower scaling of metabolic rate are unlikely to succeed.

SUMMARY The importance of size as a determinant of metabolic rate (MR) was first suggested by Sarrus and Rameaux over 160 years ago. Max Rubner's finding of a proportionality between MR and body surface area in dogs (in 1883) was consistent with Sarrus and Rameaux's formulation and suggested a proportionality between MR and body mass (Mb) raised to the power of 2/3. However, interspecific analyses compiled during the first half of the 20th century concluded that mammalian basal MR (BMR, ml O2 h-1) was proportional to Mb3/4, a viewpoint that persisted for seven decades, even leading to its common application to non-mammalian groups. Beginning in 1997, the field was re-invigorated by three new theoretical explanations for 3/4-power BMR scaling. However, the debate over which theory accurately explains 3/4-power scaling may be premature, because some authors maintain that there is insufficient evidence to adopt an exponent of 3/4 over 2/3. If progress toward understanding the non-isometric scaling of BMR is ever to be made, it is first essential to know what the relationship actually is. We re-examine previous investigations of BMR scaling by standardising units and recalculating regression statistics. The proportion of large herbivores in a data set is positively correlated both with the scaling exponent(b, where BMR=aMbb) and the coefficient of variation (CV: the standard deviation of ln-ln residuals) of the relationship. Inclusion of large herbivores therefore both inflates b and increases variation around the calculated trendline. This is related to the long fast duration required to achieve the postabsorptive conditions required for determination of BMR, and because peak post-feeding resting MR (RMRpp) scales with an exponent of 0.75±0.03 (95%CI). Large herbivores are therefore less likely to be postabsorptive when MR is measured, and are likely to have a relatively high MR if not postabsorptive. The 3/4 power scaling of RMRpp is part of a wider trend where,with the notable exception of cold-induced maximum MR(b=0.65±0.05), b is positively correlated with the elevation of the relationship (higher MR values scale more steeply). Thus exercise-induced maximum MR (b=0.87±0.05) scales more steeply than RMRpp, field MR (b=0.73±0.04), thermoneutral resting MR (RMRt, b=0.712±0.013) and BMR. The implication of this observation is that contamination of BMR data with non-basal measurements is likely to increase the BMR scaling exponent even if the contamination is randomly distributed with respect to Mb. Artificially elevated scaling exponents can therefore be accounted for by the inclusion of measurements that fail to satisfy the requirements for basal metabolism, which are strictly defined (adult,non-reproductive, postabsorptive animals resting in a thermoneutral environment during the inactive circadian phase). Similarly, a positive correlation between Mb and body temperature(Tb) and between Tb and mass-independent BMR contributes to elevation of b. While not strictly a defined condition for the measurement of BMR, the normalisation of BMR measurements to a common Tb (36.2°C) to achieve standard metabolic rate (SMR) further reduces the CV of the relationship. Clearly the value of the exponent depends on the conditions under which the data are selected. The exponent for true BMR is 0.686 (±0.014), Tb normalised SMR is 0.675 (±0.013) and RMRt is 0.712 (±0.013).

In neotropical forests, adults of many large scarab beetle species spend most of their time inside the floral chambers of heat-producing flowers, where they feed and mate throughout the night and rest during the following day, before briefly flying to another flower. Here we measure floral temperatures in Philodendron solimoesense (Araceae) in French Guiana and the respiration rates of Cyclocephala colasi beetles at floral and ambient temperatures, and show that the the beetles' extra energy requirements for activity are 2.0-4.8 times greater outside the flower than inside it. This finding indicates that heat produced by the flower constitutes an important energy reward to pollinators, allowing them to feed and mate at a fraction of the energy cost that would be required outside the flower.

Basal metabolic rate (BMR) is the rate at which a nonreproductive animal consumes energy when postabsorptive and at rest during the inactive circadian phase (McNab 1997;Frappell and Butler 2004). BMR is a benchmark measurement in comparative physiology, and represents 13 to 63% of daily energy turnover (Speakman 2000), suggesting that it might be an important focus for natural selection. Indeed, BMR is correlated with a range of ecological and physiological variables, including population density, maximum metabolic rate, field metabolic rate, reproductive output, cold tolerance, and over-winter survival (Jackson et al. 2001;Rezende et al. 2002; White and Seymour 2004;Blackmer et al. 2005;Swanson and Liknes 2006).A consistent theme of the comparative physiological literature since its early days has been consideration of the form of the relationship between BMR and body mass, which is usually in the form of an exponential equation, BMR = a M b , where M is body 2 6 5 8

Maximum left ventricular wall stress is calculated at end-diastolic volume and systemic arterial diastolic blood pressure, according to a thick-walled model for the principle of Laplace. Stress is independent of body mass and averages 13.9 kPa (+/-2.3; 95% confidence interval) in 24 species of mammals weighing 0.025-4,000 kg and 15.5 kPa (+/-4.7) in 12 birds weighing 0.014-110 kg. Birds have higher arterial blood pressures and larger hearts than mammals. Systolic and diastolic arterial blood pressures increase with body mass according to M(0.05) in mammals, and heart mass increases according to M(1.06) in the same species, further supporting the principle. However, blood pressure in birds is independent of body mass, and heart mass scales isometrically. End-diastolic stress values, calculated according to Laplace, are about one-third of peak stresses recorded in isolated mammalian myocardial preparations.

Basal metabolic rate (BMR, mL O2 h(-1)) is a useful measurement only if standard conditions are realised. We present an analysis of the relationship between mammalian body mass (M, g) and BMR that accounts for variation associated with body temperature, digestive state, and phylogeny. In contrast to the established paradigm that BMR proportional to M3/4, data from 619 species, representing 19 mammalian orders and encompassing five orders of magnitude variation in M, show that BMR proportional to M2/3. If variation associated with body temperature and digestive state are removed, the BMRs of eutherians, marsupials, and birds do not differ, and no significant allometric exponent heterogeneity remains between orders. The usefulness of BMR as a general measurement is supported by the observation that after the removal of body mass effects, the residuals of BMR are significantly correlated with the residuals for a variety of physiological and ecological variables, including maximum metabolic rate, field metabolic rate, resting heart rate, life span, litter size, and population density.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. ABSTRACT Physiological, anatomical, and developmental features of the crocodilian heart support the paleontological evidence that the ancestors of living crocodilians were active and endothermic, but the lineage reverted to ectothermy when it invaded the aquatic, ambush predator niche. In endotherms, there is a functional nexus between high metabolic rates, high blood flow rates, and complete separation of high systemic blood pressure from low pulmonary blood pressure in a four-chambered heart. Ectotherms generally lack all of these characteristics, but crocodilians retain a four-chambered heart. However, crocodilians have a neurally controlled, pulmonary bypass shunt that is functional in diving. Shunting occurs outside of the heart and involves the left aortic arch that originates from the right ventricle, the foramen of Panizza between the left and right aortic arches, and the cog-tooth valve at the base of the pulmonary artery. Developmental studies show that all of these uniquely crocodilian features are secondarily derived, indicating a shift from the complete separation of blood flow of endotherms to the controlled shunting of ectotherms. We present other evidence for endothermy in stem archosaurs and suggest that some dinosaurs may have inherited the trait. The University of Chicago Press