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 ∝ 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.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

Phenotypic plasticity in the scaling of avian basal metabolic rate

Many birds exhibit short-term, reversible adjustments in basal metabolic rate (BMR), but the overall contribution of phenotypic plasticity to avian metabolic diversity remains unclear. The available BMR data include estimates from birds living in natural environments and captive-raised birds in more homogenous, artificial environments. All previous analyses of interspecific variation in BMR have pooled these data. We hypothesized that phenotypic plasticity is an important contributor to interspecific variation in avian BMR, and that captive-raised populations exhibit general differences in BMR compared to wild-caught populations. We tested this hypothesis by fitting general linear models to BMR data for 231 bird species, using the generalized least-squares approach to correct for phylogenetic relatedness when necessary. The scaling exponent relating BMR to body mass in captive-raised birds (0.670) was significantly shallower than in wild-caught birds (0.744). The differences in metabolic scaling between captive-raised and wild-caught birds persisted when migratory tendency and habitat aridity were controlled for. Our results reveal that phenotypic plasticity is a major contributor to avian interspecific metabolic variation. The finding that metabolic scaling in birds is partly determined by environmental factors provides further support for models that predict variation in scaling exponents, such as the allometric cascade model.     

Coevolution of body size and metabolic rate in vertebrates: a life‐history perspective

Despite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non‐linearity of the relationship between MR and body mass. This ‘statistical’ view must be replaced with the life‐history perspective that ‘allows’ organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation ‘decisions’ that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those ‘decisions’ form a wealth of life‐history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single‐cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life‐history evolution is the best way forward.     

Power and metabolic scope of bird flight: a phylogenetic analysis of biomechanical predictions

For flying animals aerodynamic theory predicts that mechanical power required to fly scales as P proportional, variant m (7/6) in a series of isometric birds, and that the flight metabolic scope (P/BMR; BMR is basal metabolic rate) scales as P (scope) proportional, variant m (5/12). I tested these predictions by using phylogenetic independent contrasts from a set of 20 bird species, where flight metabolic rate was measured during laboratory conditions (mainly in wind tunnels). The body mass scaling exponent for P was 0.90, significantly lower than the predicted 7/6. This is partially due to the fact that real birds show an allometric scaling of wing span, which reduces flight cost. P (scope) was estimated using direct measurements of BMR in combination with allometric equations. The body mass scaling of P (scope) ranged between 0.31 and 0.51 for three data sets, respectively, and none differed significantly from the prediction of 5/12. Body mass scaling exponents of P (scope) differed significantly from 0 in all cases, and so P (scope) showed a positive body mass scaling in birds in accordance with the prediction.     

Basal metabolic rate of endotherms can be modeled using heat-transfer principles and physiological concepts: reply to "can the basal metabolic rate of endotherms be explained by biophysical modeling?"

Our recent article (Roberts et al. 2010 ) proposes a mechanistic model for the relation between basal metabolic rate (BMR) and body mass (M) in mammals. The model is based on heat-transfer principles in the form of an equation for distributed heat generation within the body. The model can also be written in the form of the allometric equation BMR = aM(b), in which a is the coefficient of the mass term and b is the allometric exponent. The model generates two interesting results: it predicts that b takes the value 2/3, indicating that BMR is proportional to surface area in endotherms. It also provides an explanation of the physiological components that make up a, that is, respiratory heat loss, core-skin thermal conductance, and core-skin thermal gradient. Some of the ideas in our article have been questioned (Seymour and White 2011 ), and this is our response to those questions. We specifically address the following points: whether a heat-transfer model can explain the level of BMR in mammals, whether our test of the model is inadequate because it uses the same literature data that generated the values of the physiological variables, and whether geometry and empirical values combine to make a "coincidence" that makes the model only appear to conform to real processes.     

异速生长模型研究概述

最近,关于异速生长模型的讨论再次成为焦点,讨论热点为异速生长指数的取值及其理论解释.本文综述了WBE 97、BMR(99)模型的相关研究,重点介绍了MGL模型及由此模型得到的结果:个体整体的新陈代谢率与个体的质量没有明显依赖关系,其标度指数不是一个固定的值,而是一个区间[2/3,1].考虑的视角从个体整体的新陈代谢率转到单位质量的新陈代谢率,通过对不同物种、不同环境的单位质量新陈代谢率的研究,发现对大多数物种,其值落在一个具有普适性的上、下界的区间内;认为存在单位质量的新陈代谢率最小值确定了个体的大小,并建立基于该最小值的描述个体大小与温度关系的数学模型,该模型得到实验数据验证.     

Basal metabolic rate: history, composition, regulation, and usefulness

The concept of basal metabolic rate (BMR) was developed to compare the metabolic rate of animals and initially was important in a clinical context as a means of determining thyroid status of humans. It was also important in defining the allometric relationship between body mass and metabolic rate of mammals. The BMR of mammals varies with body mass, with the same allometric exponent as field metabolic rate and with many physiological and biochemical rates. The membrane pacemaker theory proposes that the fatty acid composition of membrane bilayers is an important determinant of a species BMR. In both mammals and birds, membrane polyunsaturation decreases and monounsaturation increases with increasing body mass and a decrease in mass-specific BMR. The secretion and production of thyroid hormones in mammals are related to body mass, with the allometric exponent similar to BMR; yet there is no body size-related variation in either total or free concentrations of thyroid hormones in plasma of mammals. It is suggested that in different-sized mammals, the secretion/production of thyroid hormones is a result of BMR differences rather than their cause. BMR is a useful concept in some situations but not in others.     

Environmental correlates of physiological variables in marsupials

We analyzed body temperature (T(b)), basal metabolic rate (BMR), wet thermal conductance (C(wet)), and evaporative water loss (EWL) of marsupials by conventional and phylogenetically corrected regression. Allometric effects were substantial for BMR, C(wet), and EWL but not T(b). There was a strong phylogenetic signal for mass and all physiological traits. A significant phylogenetic signal remained for BMR, C(wet), and EWL even after accounting for the highly significant phylogenetic signal of mass. T(b), BMR, C(wet), and EWL allometric residuals were correlated with some diet, distribution, and climatic variables before and after correction for phylogeny. T(b) residuals were higher for marsupials from arid environments (high T(a) and more variable rainfall). The fossorial marsupial mole had a lower-than-expected T(b) residual. The allometric slope for BMR was 0.72-0.75. Residuals were consistently related to distribution aridity and rainfall variability, with species from arid and variable rainfall habitats having a low BMR, presumably to conserve energy in a low-productivity environment. The nectarivorous honey possum had a higher-than-expected BMR. For C(wet), the allometric slope was 0.55-0.62; residuals were related to diet, with folivores having low and insectivores high C(wet) residuals. The allometric slope for EWL was 0.68-0.73. EWL residuals were consistently correlated with rainfall variability, presumably facilitating maintenance of water balance during dry periods.     

Phylogenetic analysis of the allometric scaling of therapeutic regimes for birds

The use of allometric scaling to estimate drug doses, regimes, and clearance rates (metabolic dosing) is based on the principle that the amount of drug to be administered is more closely related to daily energy use than to body mass (kg). Thus, by using the allometric estimations of minimal energy consumption (MEC) in kcal day⁻¹ based on the formula MEC= kM _b ^b , where b =3, it is thought to be possible to extrapolate appropriate drug dosage regimens to species for which direct MEC data are unavailable. However, the allometric equations for respiratory variables in birds were developed 30 years ago, and were based on a very small sample size, while the appropriate scaling exponent for the allometry of energy use is a matter of considerable debate. Hence, we revisit the issue of the scaling of therapeutic regimes in birds using the most current expanded database available (resting metabolic rate data for 296 species across 17 bird orders), taking account of the non-independence of species in this process using a phylogenetically independent approach. We show that the use of caloric values to estimate daily energy consumption introduces significant error into the formula, as there are a number of assumptions that are made when converting rate of oxygen consumption to a caloric value. We also show that there are significant differences in the proportionality or Hainsworth coefficients k across taxa when the data are examined in a phylogenetic context, although the allometric scaling exponent does not vary. We therefore recommend the use of only data based on oxygen consumption values, and not caloric values, and a multi-order phylogenetic model when calculating the appropriate drug dosage regime.     

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 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.     

Effects of body mass and reproduction on the basal metabolic rate of brown long-eared bats (Plecotus auritus)

We measured basal metabolic rate (BMR) of nonreproductive and of breeding (pregnant and lactating) female brown long-eared bats (Plecotus auritus) to investigate the effects of intra- and interindividual variation in body mass and of reproduction on metabolism. The BMR of six nonreproductive females was measured between five and seven times at approximately 2-wk intervals over a period of 2.5 mo. There was a highly significant effect (P<0.001) of body mass on BMR of these nonreproductive females. The pooled within-individual scaling exponent (1.88) significantly exceeded the established mammalian interspecific exponent (0.75). In addition, we made single observations on 14 nonreproductive females to establish the effects of differences in mass between individuals. The mean BMR across all 14 individuals was 82 mW (+/-24 SD). There was a significant positive relationship between BMR and body mass across these individuals (r2=0.39), with a between-individual scaling exponent of 0.75. Inter- and intraindividual effects of mass on BMR were combined in a regression analysis that included mean body mass and deviation from mean mass on any given day as predictors. This regression model explained 55% of the variation in BMR. We made longitudinal measurements of BMR throughout reproduction and compared these with the predicted BMR of nonreproductive bats of the same body mass. Reproductive females exhibited temporal flexibility in BMR. BMR during pregnancy increased on a whole-animal basis but was significantly lower (by, on average, 15%) than BMR predicted for nonreproductive females of the same mass. Over a period of 1-75 d following birth, whole-animal BMR was greater than that during pregnancy, even though body mass declined after parturition. Hence, postbirth BMR was greater than the level predicted for nonreproductive females of the same mass. This study indicates that the scaling of BMR with body mass differs significantly within and between individuals and that there is a reduction of BMR in pregnancy and an elevation of BMR during lactation.     

Modeling the influence of body size on V(O2) peak: effects of model choice and body composition.

This study examined the bivariate relationship between peak oxygen uptake (V(O2) peak); l/min) and body size in adult men (n = 1,314, age 17-66 yr), using both "simple" and "full" iterative nonlinear allometric models. The simple model was described by V(O2) peak = M(b) (or FFM(b)) exp(c SR-PA) exp(a + d age) epsilon (where M is body mass in kg; FFM is fat-free mass in kg; SR-PA is self-reported physical activity; epsilon is a multiplicative error term; and exp indicates natural antilogarithms). The full model was described by V(O2) peak = M(b) (or FFM(b)) exp(c SR-PA) exp(a + d age) + e (epsilon), where e is a permitted Y-intercept term. The M exponent obtained from simple allometry was 0.65 [95% confidence interval (CI), 0.59-0.71], suggestive of a curvilinear relationship constrained to pass through the origin. This "zero Y-intercept" assumption was examined via the full allometric model, which revealed an M exponent of 1.00 (95% CI, 0.7-1.31), together with a positive Y-intercept term (e) of 1.13 (95% CI, 0.54-1.73). The FFM exponents were not significantly different from unity in either the simple or full allometric models. It appears that the curvilinearity of the simple allometric model (using total M) is fictitious and is due to the inappropriate forcing of the regression line through the origin. Utilizing FFM as the body-size variable revealed a linear relationship between body size and V(O2) peak, irrespective of model choice. We conclude that the population mass exponent for V(O2) peak is close to unity.     

Active and resting metabolism in birds: allometry, phylogeny and ecology

Variation in resting metabolic rate is strongly correlated with differences in body weight among birds. The lowest taxonomic level at which most of the variance in resting metabolic rate and body weight is evident for the sample is among families within orders. The allometric exponent across family points is 0.67. This exponent accords with the surface area interpretation of metabolic scaling based on considerations of heat loss. Deviations of family points from this allometric line are used to examine how resting metabolic rates differ among taxa, and whether variation in resting metabolic rate is correlated with broad differences in ecology and behaviour. Despite the strong correlation between resting metabolic rate and body weight, there is evidence for adaptive departures from the allometric line, and possible selective forces are discussed.
The allometric scaling of active metabolic rate is compared with that of resting metabolic rate. The allometric exponents for the two levels of energy expenditure differ, demonstrating that active small-bodied birds require proportionately more energy per unit time above resting levels than do active large-bodied birds. No consistent evidence was found to indicate that the different methods used to estimate active metabolic rate result in systematic bias. Birds require more energy relative to body size when undertaking breeding activities than at other stages of the annual cycle.     

Metabolic scaling: a many-splendoured thing

Animals at rest and during exercise display rates of aerobic metabolism, VO2, that represent mainly the sum of mitochondrial respiration rates in various organs. The relative contributions of these organs change with physiological state such that internal organs such as liver, kidney and brain account for most of the whole-body VO2 at rest, while locomotory muscles account for >90% of the maximum rate, VO2max, during maximal aerobic exercise. Mechanisms that regulate VO2 are complex and the relative importance of each step in a series, estimated by metabolic control analysis, depends upon the level of biological organization under consideration as well as physiological state. Despite this complexity, prominent single-cause models propose that metabolic rates are supply-limited and that the scaling of supply systems provides a sufficient explanation for the allometric scaling of metabolism. We argue that some assumptions, as well as current interpretations of the meaning (or consequences) of these constraints are flawed, i.e., elephants do not have lower mass-specific basal or maximal rates of aerobic metabolism because their mitochondria are more supply-limited than those of shrews. Animals do not violate the laws of physics, and the allometric scaling of supply systems would be expected, to some extent, to be matched by capacities for (and rates of) energy expenditure. But life is not so simple. Animals are so diverse that to do justice to metabolic scaling, it is also necessary to consider the scaling of energy expenditure. It is by doing so that models of metabolic scaling can be consistent with current paradigms in metabolic regulation and accommodate the range of inter- and intraspecific exponents found in nature. The "allometric cascade," a first attempt at such an accounting, was a source of great satisfaction to Peter Hochachka. It was the last door that he helped open to comparative physiologists before he said goodbye.     

Structural support, not insulation, is the primary driver for avian cup-shaped nest design

The nest micro-environment is a widely studied area of avian biology, however, the contribution of nest conductance (the inverse of insulation) to the energetics of the incubating adult and offspring has largely been overlooked. Surface-specific thermal conductance (W °C(-1) cm(-2)) has been related to nest dimensions, wall porosity, height above-ground and altitude, but the most relevant measure is total conductance (G, W °C(-1)). This study is the first to analyse conductance allometrically with adult body mass (M, g), according to the form G = aM(b). We propose three alternative hypotheses to explain the scaling of conductance. The exponent may emerge from: heat loss scaling (M(0.48)) in which G scales with the same exponent as thermal conductance of the adult bird, isometric scaling (M(0.33)) in which nest shape is held constant as parent mass increases, and structural scaling (M(0.25)) in which nests are designed to support a given adult mass. Data from 213 cup-shaped nests, from 36 Australian species weighing 8-360 g, show conductance is proportional to M(0.25). This allometric exponent is significantly different from those expected for heat loss and isometric scaling and confirms the hypothesis that structural support for the eggs and incubating parent is the primary factor driving nest design.     

Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals

In this review I show that the '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy-using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional) and ultimate (evolutionary) causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b<1); and Type IV: nonlinear, ontogenetic shift from positively allometric (b>1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e. growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)-specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body-size range, and activity level. A 'metabolic-level boundaries hypothesis' focusing on two major constraints (surface-area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species. Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico-chemical and ecological constraints.     

Metabolic and thermal physiology of pigeons and doves

Pigeons and doves (Columbidae) are an interesting group to examine for physiological adaptations to climate and diet because this cosmopolitan family comprises more than 300 species that are mostly granivores, although some are specialized frugivores. We determined allometric and phylogenetic effects on body temperature (T(b)), basal metabolic rate (BMR; J h(-1)), and wet thermal conductance (C(wet); J h(-1) C(-1)), and we examined mass (M) and phylogenetically corrected residuals for further effects of climate, diet, and landmass size (mainland or island). Independent contrasts, correlograms, autoregression, and phylogenetic eigenvector regression (PVR) were used to examine phylogenetically related effects. We found a small but significant phylogenetic pattern for body mass of columbids. For T(b), there was no significant effect of mass or phylogeny. There was a significant effect of climate on T(b) and no significant effects of diet or landmass without mass or phylogenetic correction, but after mass and phylogenetic correction, there were no effects of climate, diet, or landmass. For BMR, there was a strong allometric effect, and residuals were significantly lower for arid and tropical species but not for temperate species, compared to predictions for nonpasserine birds. There was a nearly significant autoregressive phylogenetic relationship for BMR parl0;r=0.44), and the strong allometry of BMR remained for independent contrasts (slope=0.731), autoregressive residuals (0.698), and PVR (0.705). Residuals, from regression of autoregression and PVR residuals of M and BMR, were significantly associated with climate: arid pigeons had a lower BMR residual than tropical and temperate pigeons. PVR residuals were significantly affected by landmass (island columbids had a smaller residual than mainland columbids), but autoregression residuals were not. There was no association of autoregression or PVR residuals with diet. For C(wet), there was a strong allometric effect, and residuals for columbids were significantly higher compared to other birds. There was no significant relationship for C(wet) of columbids to climate, diet, or landmass. There was no significant autoregressive or PVR relationship for C(wet), and the strong allometry remained after phylogenetic analysis by independent contrasts (slope=0.501), autoregression (0.509), and PVR (0.514). Residuals from autoregression and PVR were not significantly correlated with climate, diet, or landmass (mainland/island).     

The ratio and allometric scaling of speed, power, and strength in elite male rugby union players

This study compared the effectiveness of ratio and allometric scaling for normalizing speed, power, and strength in elite male rugby union players. Thirty rugby players (body mass [BM] 107.1 ± 10.1 kg, body height [BH] 187.8 ± 7.1 cm) were assessed for sprinting speed, peak power during countermovement jumps and squat jumps, and horizontal jumping distance. One-repetition maximum strength was assessed during a bench press, chin-up, and back squat. Performance was normalized using ratio and allometric scaling (Y/X), where Y is the performance, X, the body size variable (i.e., BM or BH), and b is the power exponent. An exponent of 1.0 was used during ratio scaling. Allometric scaling was applied using proposed exponents and derived exponents for each data set. The BM and BH variables were significantly related, or close to, performance during the speed, power and/or strength tests (p < 0.001-0.066). Ratio scaling and allometric scaling using proposed exponents were effective in normalizing performance (i.e., no significant correlations) for some of these tests. Allometric scaling with derived exponents normalized performance across all the tests undertaken, thereby removing the confounding effects of BM and BH. In terms of practical applications, allometric scaling with derived exponents may be used to normalize performance between larger rugby forwards and smaller rugby backs, and could provide additional information on rugby players of similar body size. Ratio scaling may provide the best predictive measure of performance (i.e., strongest correlations).     

Allometric estimation of metabolic rates in animals

The relationship between body mass (M) and metabolic rate (MR) typically accounts for most (>90%) of the inter-specific variation in MR. As such, when measurement of a species of interest is not possible, its MR can often be predicted using M. However, choosing an appropriate relationship to make such predictions is critical, and the choice is complicated by ongoing debate about the structure of the relationship between M and MR. The present study examines a range of methods including ordinary least squares (OLS), reduced major axis (RMA), and phylogenetically-informed (PI) approaches for estimating log(MR) from log(M), as well as non-linear approaches for estimating the relationship between MR and M without the need for log-transformation. Using data for the basal metabolic rates of mammals, it is shown that RMA regression overestimates the scaling exponent of MR (b, where MR=aM(b)), suggesting that OLS regression is appropriate for these data. PI approaches are preferred over non-PI ones, and the best estimates of log(MR) are obtained by including information on body temperature, climate, habitat, island endemism, and use of torpor in addition to log(M). However, the use of log-transformed data introduces bias into estimates of MR, while the use of non-linear regression underestimates MR for small mammals. This suggests that no single relationship is appropriate for describing the relationship between MR and M for all mammals, and that relationships for more narrow taxonomic groups or body mass ranges should be used when predicting MR from M.