Roger S. Seymour

Mammalian basal metabolic rate is proportional to body mass2/3

The relationship between mammalian basal metabolic rate (BMR, ml of O2 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 = aMb. 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 ∝ M2/3.

Allometric scaling of mammalian metabolism

SUMMARY The importance of size as a determinant of metabolic rate (MR) was first suggested by Sarrus and Rameaux over 160 years ago. Max Rubners finding of a proportionality between MR and body surface area in dogs (in 1883) was consistent with Sarrus and Rameauxs 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).

The scaling and temperature dependence of vertebrate metabolism

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 °C, 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 quarter-power scaling of metabolic rate are unlikely to succeed.

PHYLOGENETICALLY INFORMED ANALYSIS OF THE ALLOMETRY OF MAMMALIAN BASAL METABOLIC RATE SUPPORTS NEITHER GEOMETRIC NOR QUARTER‐POWER SCALING

The form of the relationship between the basal metabolic rate (BMR) and body mass (M) of mammals has been at issue for almost seven decades, with debate focusing on the value of the scaling exponent (b, where BMR &agr; Mb) and the relative merits of b = 0.67 (geometric scaling) and b = 0.75 (quarter-power scaling). However, most analyses are not phylogenetically informed (PI) and therefore fail to account for the shared evolutionary history of the species they consider. Here, we reanalyze the most rigorously selected and comprehensive mammalian BMR dataset presently available, and investigate the effects of data selection and phylogenetic method (phylogenetic generalized least squares and independent contrasts) on estimation of the scaling exponent relating mammalian BMR to M. Contrary to the results of a non-PI analysis of these data, which found an exponent of 0.67–0.69, we find that most of the PI scaling exponents are significantly different from both 0.67 and 0.75. Similarly, the scaling exponents differ between lineages, and these exponents are also often different from 0.67 or 0.75. Thus, we conclude that no single value of b adequately characterizes the allometric relationship between body mass and BMR.

Does basal metabolic rate contain a useful signal? Mammalian BMR allometry and correlations with a selection of physiological, ecological, and life-history variables.

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 ∝ M3/4, data from 619 species, representing 19 mammalian orders and encompassing five orders of magnitude variation in M, show that BMR ∝ 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.

Heat-producing flowers

The flowers of some plants produce enough heat to raise their temperatures as much as 35°C above air temperature. Three species have been shown to regulate flower temperature within a narrow range by an unknown physiological mechanism that increases the rate of heat production as air temperature decreases. Thermogenic plants occur only in ancient families of seed plants, and have apparently evolved in association with beetle pollinators. Because many beetles require high body temperatures for activity, the warm environment inside thermoregulating flowers may be an energetic reward during their visits.

Evidence for Endothermic Ancestors of Crocodiles at the Stem of Archosaur Evolution

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.

Energy Metabolism of Dormant Spadefoot Toads (Scaphiopus)

Rates of oxygen consumption of Scaphiopus couchii and S. hammondii during dormancy beneath the soil averaged approximately 1/5 those of awake toads resting on the surface during the same season. Oxygen consumption decreased gradually when S. couchii entered dormancy in autumn and stabilized after two to three weeks. In contrast, oxygen consumption leveled off after a few days in toads which were temporarily aroused and allowed to become dormant again in winter. Oxygen consumption of awake animals resting on the surface were similar during the seasons of activity (July-August) and dormancy (September-June) in both species. However, awake S. hammondii showed a decrease in Qlo of oxygen consumption during the seasons of dormancy. Most spadefoots had minute fat bodies and diminished total body lipid when they emerged in the summer. Feeding during July and August led to rapid fat deposition and egg development. Large increases in oxygen consumption following feeding of recently emerged S. hammondii suggested that food was rapidly converted into non-protein products. The ovarian eggs of both species were well developed by September and continued to enlarge during dormancy. About half of the energy required during dormancy came from the fat bodies. Changes in total body lipid from September to July correlated with rates of oxygen consumption of buried dormant toads at field temperatures. That at least some toads could survive two or more years of starvation is indicated by the presence of large fat bodies in a few individuals emerging in the summer, the ability to reabsorb gametes if reproduction is prevented, the potential utilization of body parts containing protein and low metabolic rates during dormancy.

The Principle of Laplace and Scaling of Ventricular Wall Stress and Blood Pressure in Mammals and Birds

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 M0.05 in mammals, and heart mass increases according to M1.06 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.

Respiration and heat production by the inflorescence of Philodendron selloum Koch

During a 2-d sequence of anthesis, the spadices of the thermogenic arum lily, Philodendron selloum, regulated maximum temperature within a small range (37–44°C) by reversible thermal inhibition of respiratory heat production. This response protects the inflorescence and the attracted insects from thermal damage. Heat production by whole spadices, measured by O2 respirometry, equalled heat loss, measured by gradient layer calorimetry, which confirmed the heat equivalence of O2 consumption (20.4 J ml-1). This also indicated that there was no net phosphorylation during thermogenesis, heat production being the primary function of high rates of respiration. The sterile male florets consumed about 30 ml g-1 h-1 and the average 124-g spadix produced about 7 W to maintain a 30°C difference between spadix and ambient temperature. Most of the energy for thermogenesis is present in the florets before anthesis. Despite high respiratory rates, thermogenesis is an energetically inexpensive component of the reproductive process.