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This meta-study investigated the relationships between blood flow rate ( Q̇ ; cm 3  s -1 ), wall shear stress (τ w ; dyn cm -2 ) and lumen radius ( r i ; cm) in 20 named systemic arteries of nine species of mammals, ranging in mass from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varied between 3.7 µm in a cremaster artery of a rat and 11.2 mm in the aorta of a human. The 92 logged data points of [Formula: see text] and r i are described by a single second-order polynomial curve with the equation: [Formula: see text] The slope of the curve increased from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci's rule ([Formula: see text]) applies to the main arteries and Murray's law ([Formula: see text]) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which [Formula: see text] is fairly constant, yielded the allometric power equation: [Formula: see text] These empirical equations allow calculation of resting perfusion rates from arterial lumen size alone, without reliance on theoretical models or assumptions on the scaling of wall shear stress in relation to body mass. As expected, [Formula: see text] of individual named arteries is strongly affected by body mass; however, [Formula: see text] of the common carotid artery from six species (mouse to horse) is also sensitive to differences in whole-body basal metabolic rate, independent of the effect of body mass., Competing Interests: Competing interestsThe authors declare no competing or financial interests., (© 2019. Published by The Company of Biologists Ltd.)

Due in part to their large size, aggressive temperament, and difficulty in handling, there are few physiological studies of adult crocodilians in the literature. As a result, studies comparing individuals across an ontogenetic series and comparisons among species are also lacking. We addressed this gap in knowledge by measuring standard metabolic rates (SMR) of three species of crocodilians (Crocodylus porosus, C. johnsoni, and Alligator mississippiensis), and included individuals that ranged from 0.22 to 114 kg. Allometric scaling of SMR with body mass was similar among the species, but C. porosus had significantly higher SMR than did C. johnsoni or A. mississippiensis. Differences in SMR among species are potentially related to behavioural differences in levels of aggression; C. porosus are the most aggressive of the crocodilians measured, and have rates of standard metabolism that are approximately 36% higher at the grand mean body size than those measured for C. johnsoni or A. mississippiensis, which are among the least aggressive crocodilians., Competing Interests: The authors have declared that no competing interests exist.

Standard metabolic rate (SMR, ml O2 min(-1)) of captive Crocodylus porosus at 30 °C scales with body mass (kg) according to the equation, SMR = 1.01 M(0.829), in animals ranging in body mass of 3.3 orders of magnitude (0.19-389 kg). The exponent is significantly higher than 0.75, so does not conform to quarter-power scaling theory, but rather is likely an emergent property with no single explanation. SMR at 1 kg body mass is similar to the literature for C. porosus and for alligators. The high exponent is not related to feeding, growth, or obesity of captive animals. The log-transformed data appear slightly curved, mainly because SMR is somewhat low in many of the largest animals (291-389 kg). A 3-parameter model is scarcely different from the linear one, but reveals a declining exponent between 0.862 and 0.798. A non-linear model on arithmetic axes overestimates SMR in 70% of the smallest animals and does not satisfactorily represent the data.

Flying insects achieve the highest mass-specific aerobic metabolic rates of all animals. However, few studies attempt to maximise the metabolic cost of flight and so many estimates could be sub-maximal, especially where insects have been tethered. To address this issue, oxygen consumption was measured during tethered flight in adult locusts Locusta migratoria, some of which had a weight attached to each wing (totalling 30-45% of body mass). Mass-specific metabolic rate increased from 28±2 μmol O(2) g(-1) h(-1) at rest to 896±101 μmol O(2)g(-1) h(-1) during flight in weighted locusts, and to 1032±69 μmol O(2) g(-1) h(-1) in unweighted locusts. Maximum metabolic rate of locusts during tethered flight (m(O(2)); μmol O(2) h(-1)) increased with body mass (M(b); g) according to the allometric equation m(O(2))=994M(b)(0.75±0.19), whereas published metabolic rates of moths and orchid bees during hovering free flight (h(O(2))) are approximately 2.8-fold higher, h(O(2))=2767M(b)(0.72±0.08). The modest flight metabolic rate of locusts is unlikely to be an artefact of individuals failing to exert themselves, because mean maximum lift was not significantly different from that required to support body mass (95±8%), mean wingbeat frequency was 23.7±0.6 Hz, and mean stroke amplitude was 105±5 deg in the forewing and 96±5 deg in the hindwing - all of which are close to free-flight values. Instead, the low cost of flight could reflect the relatively small size and relatively modest anatomical power density of the locust flight motor, which is a likely evolutionary trade-off between flight muscle maintenance costs and aerial performance.

The physiological mechanisms that determine basal metabolic rate (BMR) of endotherms have long been debated. This journal has recently presented a new model, based on biophysical principles of heat flux through the tissues of mammals, that attempts to explain the allometric relationship between BMR and body size. We offer a critique of the model and conclude that although the model may describe the physics of heat transfer through the body, it cannot explain mechanistically the level of BMR. BMR determines some of the key variables of the model, but no combination of the variables determines BMR. The model arrives at an equation relating BMR to body mass that is similar to descriptive empirical equations, but this coincidence results from the geometry of the model and the empirical values put into it.

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 is proportional to M(b)) 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.

Routine metabolic rate (RMR) was measured in fasting southern bluefin tuna, Thunnus maccoyii, the largest tuna species studied so far (body mass=19.6 kg (+/-1.9 SE)). Mean mass-specific RMR was 460 mg kg(-1) h(-1) (+/-34.9) at a mean water temperature of 19 degrees C. When evaluated southern bluefin tuna standard metabolic rate (SMR) is added to published values of other tuna species, there is a strong allometeric relationship with body mass (423 M(0.86), R(2)=0.97). This demonstrates that tuna interspecific SMR scale with respect to body mass similar to that of other active teleosts, but is approximately 4-fold higher. However, RMR (not SMR) is most appropriate in ram-ventilating species that are physiologically unable to achieve complete rest. Respiration was measured in a large (250,000 l) flexible polypropylene respirometer (mesocosm respirometer) that was deployed within a marine-farm sea cage for 29 days. Fasted fish were maintained within the respirometer up to 42 h while dissolved oxygen dropped by 0.056 (+/-0.004) mg l(-1) h(-1). Fish showed no obvious signs of stress. They swam at 1.1 (+/-0.1) fork lengths per second and several fed within the respirometer immediately after measurements.

Examination of the energetics of sound production usually requires measurement of species that will produce normal calls under unnatural circumstances. Such measurements are potentially compromised by stress-related changes in calling input (through a reduction in calling effort) or output (through forced use of sub-optimal singing burrows). To determine if such measurements are indeed affected by abstraction from a natural setting, we measured the energetics of song production in undisturbed mole crickets Gryllotalpa monanka and employed a new approach where the animal's singing chamber replaces the respirometry chamber normally used in studies of this type. It was therefore possible to measure metabolic rate (MR) of calling crickets in situ for animals within self-constructed burrows under natural conditions. Calling MR measured under these conditions averaged 13.5-fold higher than standard MR and 2.2-fold higher than MR measured during burrowing in the lab. The calling MR of G. monanka was similar to that measured for other calling insects, and to endothermic insects, but was only 10% of that allometrically predicted for a similarly sized insect (0.89 g) during flight. A male mole cricket is estimated to consume 5.9 ml of oxygen during construction of a calling burrow and a 1-h calling bout; by comparison, a flying female would consume a similar volume in less than 6 min.

The controversial relationship between body mass and basal metabolic rate in animals revolves around two questions: what is the allometric scaling exponent and what is the functional basis for it? For mammals, the first question could be resolved if measurements from all 4600 extant species were available, but this study shows that data for only 150 species, spanning three to four orders of magnitude variation in body mass, are sufficient to accurately determine the exponent. Because the currently available data set includes about 600 species that vary over five orders of magnitude in body size, further increases in sample size are unlikely to change the estimate of the scaling exponent.

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=aMb b) 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 degrees 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).

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.

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 proportional, variant M(2/3).