The effectiveness of scaling procedures for comparing ground reaction forces

Various scaling methods are used when attempting to remove the influence of anthropometric differences on ground reaction forces (GRF) when comparing groups. Though commonly used, ratio scaling often results in an over-correction. Allometric scaling has previously been suggested for kinetic variables but its effectiveness in partialing out the effect of anthropometrics is unknown due to a lack of consistent application. This study examined the effectiveness of allometric scaling vertical, braking and propulsive GRF and loading rate for 84 males and 47 females while running at 4.0 m/s. Raw, unfiltered data were ratio scaled by body mass (BM), height (HT), and BM multiplied by HT (BM1HT). Gender specific exponents for allometric scaling were determined by performing a log-linear (for BM and HT individually) or log-multilinear regression (BMHT). Pearson productmoment correlations were used to assess the effectiveness of each scaling method. Ratio scaling by BM, HT, or BM1HT resulted in an over-correction of the data for most variables and left a considerable portion of the variance still attributable to anthropometrics. Allometric scaling by BM successfully removed the effect of BM and HT for all variables except for braking GRF in males and vertical GRF in females. However, allometric scaling for BMHT successfully removed the effect of BM and HT for all reactionary forces in both genders. Based on these results, allometric scaling for BMHT was the most appropriate scaling method for partialing out the effect of BM and HT on kinetic variables to allow for effective comparisons between groups or individuals.     

Models of ontogenetic allometry in cladoceran morphology studies

Ontogenetic variation of morphological traits in cladocerans is usually analysed by a simple allometry function. We found that common cyclomorphic and inducible traits in Bosmina and Daphnia sometimes deviate from simple allometry, however. Consequently, simple allometric analysis may at times be inadequate since important aspects of the ontogenetic development may not be revealed. We suggest that other allometric models should be used more extensively in ontogenetic studies of cladocerans morphology. Especially, complex allometric functions may help analyse the effects of size-selective predation on morphological defence traits when predators prefer prey of intermediate size. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

Allometry and adaptation of body proportions and stature in African pygmies

We have analyzed the growth allometry of external body proportions in Efe pygmies from Zaire and combined these data with values from the literature for comparable dimensions in adult pygmies and nonpygmies. We sequentially tested the hypotheses that adult proportion differences between 1) male vs. female Efe, and 2) pygmies vs. nonpygmies result from ontogenetic scaling, or the differential extension of common patterns of growth allometry. Results indicate an almost complete concordance of allometric trajectories for male and female Efe. These preliminary analyses also strongly suggest that adult nonpygmy Africans generally differ from pygmies in their terminal size and correlated allometric consequences, rather than in more fundamental alterations of underlying patterns of growth. Biacromial diameter emerges as the measurement most likely to depart from this general pattern. These results provide further evidence that shifts in systemic growth hormones yielding differences in terminal overall body size may be accompanied by global and coordinated allometric transformations. Certain proportion differences previously interpreted by some as specific evidence of primitive retention in pygmies in fact reflect simple growth allometric correlates of the derived rapid size decrease in these groups. Selected divergent body proportions characterizing adult pygmies, previously interpreted by some as independent evidence of climatic adaptation, also reflect such allometric correlates of ontogenetic scaling. We critically assess arguments that the small overall body size of pygmies was specifically selected for reasons of thermoregulatory efficiency, and consider an alternative or complementary scenario, based on selection for small size in order to reduce caloric requirements. © 1996 Wiley-Liss, Inc.     

Variation in the ontogenetic allometry of horn length in bovids along a body mass continuum

Allometric relationships describe the proportional covariation between morphological, physiological, or life‐history traits and the size of the organisms. Evolutionary allometries estimated among species are expected to result from species differences in ontogenetic allometry, but it remains uncertain whether ontogenetic allometric parameters and particularly the ontogenetic slope can evolve. In bovids, the nonlinear evolutionary allometry between horn length and body mass in males suggests systematic changes in ontogenetic allometry with increasing species body mass. To test this hypothesis, we estimated ontogenetic allometry between horn length and body mass in males and females of 19 bovid species ranging from ca. 5 to 700 kg. Ontogenetic allometry changed systematically with species body mass from steep ontogenetic allometries over a short period of horn growth in small species to shallow allometry with the growth period of horns matching the period of body mass increase in the largest species. Intermediate species displayed steep allometry over long period of horn growth. Females tended to display shallower ontogenetic allometry with longer horn growth compared to males, but these differences were weak and highly variable. These findings show that ontogenetic allometric slope evolved across species possibly as a response to size‐related changes in the selection pressures acting on horn length and body mass.     

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).     

Nutrient‐dependent allometric plasticity in a male‐diphenic mite

Male secondary sexual traits often scale allometrically with body size. These allometries can be variable within species and may shift depending on environmental conditions, such as food quality. Such allometric plasticity has been hypothesized to initiate local adaptation and evolutionary diversification of scaling relationships, but is under‐recorded, and its eco‐evolutionary effects are not well understood. Here, we tested for allometric plasticity in the bulb mite (Rhizoglyphus robini), in which large males tend to develop as armed adult fighters with thickened third legs, while small males become adult scramblers without thickened legs. We first examined the ontogenetic timing for size‐ and growth‐dependent male morph determination, using experimentally amplified fluctuations in growth rate throughout juvenile development. Having established that somatic growth and body size determine male morph expression immediately before metamorphosis, we examined whether the relationship between adult male morph and size at metamorphosis shifts with food quality. We found that the threshold body size for male morph expression shifts toward lower values with deteriorating food quality, confirming food‐dependent allometric plasticity. Such allometric plasticity may allow populations to track prevailing nutritional conditions, potentially facilitating rapid evolution of allometric scaling relationships.     

Stochastic ontogenetic allometry: the statistical dynamics of relative growth

Background

In the absence of stochasticity, allometric growth throughout ontogeny is axiomatically described by the logarithm-transformed power-law model, , where and are the logarithmic sizes of two traits at any given time t. Realistically, however, stochasticity is an inherent property of ontogenetic allometry. Due to the inherent stochasticity in both and , the ontogenetic allometry coefficients, and k, can vary with t and have intricate temporal distributions that are governed by the central and mixed moments of the random ontogenetic growth functions, and . Unfortunately, there is no probabilistic model for analyzing these informative ontogenetic statistical moments.

Methodology/Principal Findings

This study treats and as correlated stochastic processes to formulate the exact probabilistic version of each of the ontogenetic allometry coefficients. In particular, the statistical dynamics of relative growth is addressed by analyzing the allometric growth factors that affect the temporal distribution of the probabilistic version of the relative growth rate, , where is the expected value of the ratio of stochastic to stochastic , and and are the numerator and the denominator of , respectively. These allometric growth factors, which provide important insight into ontogenetic allometry but appear only when stochasticity is introduced, describe the central and mixed moments of and as differentiable real-valued functions of t.

Conclusions/Significance

Failure to account for the inherent stochasticity in both and leads not only to the miscalculation of k, but also to the omission of all of the informative ontogenetic statistical moments that affect the size of traits and the timing and rate of development of traits. Furthermore, even though the stochastic process and the stochastic process are linearly related, k can vary with t.     

Scaling of maximal oxygen uptake by lower leg muscle volume in boys and men.

The aim of this study was to critically examine the influence of body size on maximal oxygen uptake (VO2 max) in boys and men using body mass (BM), estimated fat-free mass (FFM), and estimated lower leg muscle volume (Vol) as the separate scaling variables. VO2 max and an in vivo measurement of Vol were assessed in 15 boys and 14 men. The FFM was estimated after percentage body fat had been predicted from population-specific skinfold measurements. By using nonlinear allometric modeling, common body size exponents for BM, FFM, and Vol were calculated. The point estimates for the size exponent (95% confidence interval) from the separate allometric models were: BM 0.79 (0.53-1.06), FFM 1.00 (0.78-1.22), and Vol 0.64 (0.40-0.88). For the boys, substantial residual size correlations were observed for VO2 max/BM0.79 and VO2 max/FFM1.00, indicating that these variables did not correctly partition out the influence of body size. In contrast, scaling by Vol0.64 led to no residual size correlation in boys or men. Scaling by BM is confounded by heterogeneity of body composition and potentially substantial differences in the mass exponent between boys and men. The FFM is precluded as an index of involved musculature because Vol did not represent a constant proportion of FFM [Vol proportional, variantFFM1.45 (95% confidence interval, 1.13-1.77)] in the boys (unlike the men). We conclude that Vol, as an indicator of the involved muscle mass, is the most valid allometric denominator for the scaling of VO2 max in a sample of boys and men heterogeneous for body size and composition.     

Joint multiple quantitative trait loci mapping for allometries of body compositions and metabolic traits to body weights in broiler

In order to map quantitative trait loci (QTLs) for allometries of body compositions and metabolic traits in chicken, we phenotypically characterize the allometric growths of multiple body components and metabolic traits relative to BWs using joint allometric scaling models and then establish random regression models (RRMs) to fit genetic effects of markers and minor polygenes derived from the pedigree on the allometric scalings. Prior to statistically inferring the QTLs for the allometric scalings by solving the RRMs, the LASSO technique is adopted to rapidly shrink most of marker genetic effects to zero. Computer simulation analysis confirms the reliability and adaptability of the so-called LASSO-RRM mapping method. In the F₂ population constructed by multiple families, we formulate two joint allometric scaling models of body compositions and metabolic traits, in which six of nine body compositions are tested as significant, while six of eight metabolic traits are as significant. For body compositions, a total of 14 QTLs, of which 9 dominant, were detected to be associated with the allometric scalings of drumstick, fat, heart, shank, liver and spleen to BWs; while for metabolic traits, a total of 19 QTLs also including 9 dominant be responsible for the allometries of T4, IGFI, IGFII, GLC, INS, IGR to BWs. The detectable QTLs or highly linked markers can be used to regulate relative growths of the body components and metabolic traits to BWs in marker-assisted breeding of chickens.     

Does allometry account for shape variability in <Emphasis Type="Italic">Ephedrus persicae</Emphasis> Froggatt (Hymenoptera: Braconidae: Aphidiinae) parasitic wasps?

We analysed linear measurements on various parts of the body and the configuration of 11 landmarks on the wing in a large sample of Ephedrus persicae that had emerged from 13 aphid host species, to assess whether static allometry (a measure of the scaling relationship between traits in a population of individuals at the same ontogenetic stage) accounts for variation in body shape. The analysed specimens came from several localities in Europe, Asia Minor, Japan and South America, and cover a large portion of the distribution area of E. persicae. We found that allometry accounts for variation in body shape among different biotypes within the E. persicae group. The allometric slopes for head size (HD), petiolus width (PETW), mesoscutum width (MSC), and ovipositor sheath length (OVPL) diverged significantly among biotypes, indicating biotype-specific allometries. The analysis of allometric variation in wing shape showed that the pattern and direction of allometric changes also differed among individuals that had emerged from different hosts. Our results (observed divergences in the directions of allometric slopes of particular morphometric traits and wing shape) suggest that allometric relations within E. persicae are not conserved, so that allometry itself changes, evolving differently in aphid parasitoids that emerge from different hosts.     

Interspecific allometry of morphological traits among trematode parasites: selection and constraints

Developmental constraints and selective pressures interact to determine the strength of allometric scaling relationships between body size and the size of morphological traits among related species. Different traits are expected to relate to body size with different scaling exponents, depending on how their function changes disproportionately with increasing body size. For trematodes parasitic in vertebrate guts, the risk of being dislodged should increase disproportionately with body size, whereas basic physiological functions are more likely to increase in proportion to changes in body size. Allometric scaling exponents for attachment structures should thus be higher than those for other structures and should be higher for trematode families using endothermic hosts than for those using ectotherms, given the feeding and digestive characteristics of these hosts. These predictions are tested with data on 363 species from 13 trematode families. Sizes of four morphological structures were investigated, two associated with attachment (oral and ventral suckers) and the other two with feeding and reproduction (pharynx and cirrus sac). The scaling exponents obtained were generally low, the majority falling between 0.2 and 0.5. There were no consistent differences within families between the magnitude of scaling exponents for different structures. Also, there was no difference in the values of scaling exponents between families exploiting endothermic hosts and those using ectotherms. There were strong correlations across families between the values of the scaling exponents for the oral sucker, the ventral sucker and the pharynx: in families where the size of one trait increases relatively steeply as a function of body size, the same is generally true of the other traits. These results suggest either that developmental constraints link several morphological features independently of their specific roles or that similar selection pressures operate on different structures, leading to covariation of scaling exponents. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 96 , 533–540.     

The influence of body size on measurements of overall cardiac function

The purpose of this study was to determine the best scaling method to account for the effects of body size on measurements of overall cardiac function and subsequently the interpretation of data based on cardiac power output (CPO). CPO was measured at rest (CPO(rest)) and at maximal exercise (CPO(max)) on 88 and 103 healthy but untrained men and women, respectively, over the age range of 20-70 yr. Cardiac reserve (CR) was calculated as CPO(max) - CPO(rest). CPO(rest), CPO(max), and CR were all significantly related to body mass (BM), body surface area (BSA), and lean body mass (LBM). The linear regression model failed to completely normalize these measurements. In contrast, the allometric model produced size-independent values of CPO. Furthermore, all the assumptions associated with the allometric model were achieved. For CPO(rest), mean body size exponents were BM(0.33), BSA(0.60), and LBM(0.47). For CPO(max), the exponents were BM(0.41), BSA(0.81), and LBM(0.71). For CR, mean body size exponents were BM(0.44), BSA(0.87), and LBM(0.79). LBM was identified (from the root-mean-squares errors of the separate regression models) as the best physiological variable (based on its high metabolic activity) to be scaled in the allometric model. Scaling of CPO to LBM(b) (where b is the scaling exponent) dramatically reduced the between-gender differences with only a 7% difference in CPO(rest) and CPO(max) values. In addition, the gender difference in CR was completely removed. To avoid erroneous interpretations and conclusions being made when comparing data between men and women of different ages, the allometric scaling of CPO to LBM(b) would seem crucial.     

A common genetic basis to the origin of the leaf economics spectrum and metabolic scaling allometry

Many facets of plant form and function are reflected in general cross‐taxa scaling relationships. Metabolic scaling theory (MST) and the leaf economics spectrum (LES) have each proposed unifying frameworks and organisational principles to understand the origin of botanical diversity. Here, we test the evolutionary assumptions of MST and the LES using a cross of two genetic variants of Arabidopsis thaliana. We show that there is enough genetic variation to generate a large fraction of variation in the LES and MST scaling functions. The progeny sharing the parental, naturally occurring, allelic combinations at two pleiotropic genes exhibited the theorised optimum ¾ allometric scaling of growth rate and intermediate leaf economics. Our findings: (1) imply that a few pleiotropic genes underlie many plant functional traits and life histories; (2) unify MST and LES within a common genetic framework and (3) suggest that observed intermediate size and longevity in natural populations originate from stabilising selection to optimise physiological trade‐offs.     

Intersexual allometry differences and ontogenetic shifts of coloration patterns in two aquatic turtles,Graptemys oculifera and Graptemys flavimaculata

Coloration can play critical roles in a species' biology. The allometry of color patterns may be useful for elucidating the evolutionary mechanisms responsible for shaping the traits. We measured characteristics relating to eight aspects of color patterns from Graptemys oculifera and G. flavimaculata to investigate the allometric differences among male, female, and unsexed juvenile specimens. Additionally, we investigated ontogenetic shifts by incorporating the unsexed juveniles into the male and female datasets. In general, male color traits were isometric (i.e., color scaled with body size), while females and juvenile color traits were hypoallometric, growing in size more slowly than the increase in body size. When we included unsexed juveniles in our male and female datasets, our linear regression analyses found all relationships to be hypoallometric and our model selection analysis found support for nonlinear models describing the relationship between body size and color patterns, suggestive of an ontogenetic shift in coloration traits for both sexes at maturity. Although color is critical for many species' biology and therefore under strong selective pressure in many other species, our results are likely explained by an epiphenomenon related to the different selection pressures on body size and growth rates between juveniles and adults and less attributable to the evolution of color patterns themselves.     

Is there an influence of body mass on digesta mean retention time in herbivores? A comparative study on ungulates

The relation between body mass (BM) and digesta mean retention time (MRT) in herbivores was the focus of several studies in recent years. It was assumed that MRT scaled with BM(0.25) based on the isometric scaling of gut capacity (BM(1.0)) and allometric scaling of energy intake (BM(0.75)). Literature studies that tested this hypothesis produced conflicting results, arriving sometimes at higher or lower exponents than the postulated 0.25. This study was conducted with 8 ruminants (n=2-6 per species) and 6 hindgut fermenting species/breeds (n=2-6, warthog n=1) with a BM range of 60-4000 kg. All animals received a ration of 100% grass hay with ad libitum access. Dry matter intake was measured and the MRT was estimated by the use of a solute and a particle (1-2 mm) marker. No significant scaling of MRT(particle) with BM was observed for all herbivores (32 BM(0.04), p=0.518) and hindgut fermenters (32 BM(0.00), p=1.00). The scaling exponent for ruminants only showed a tendency towards significance (29 BM(0.12), p=0.071). Ruminants on average had an MRT(particle) 1.61-fold longer than hindgut fermenters. Whereas an exponent of 0.25 is reasonable from theoretical considerations, much lower exponents were found in this and other studies. The energetic benefit of increasing MRT is by no means continuous, since the energy released from a given food unit via digestion decreases over time. The low and non-significant scaling factors for both digestion types suggest that in ungulates, MRT is less influenced by BM (maximal allometric exponent ≤0.1) than often reported.     

Allometric scaling of seed retention time in seed dispersers and its application to estimation of seed dispersal potentials of theropod dinosaurs

Seed retention time (SRT), the time interval between seed ingestion and defaecation, is a critical parameter that determines the spatial pattern of seed dispersal created by an animal, and is therefore, an essential component of trait‐based modelling of seed dispersal functions. However, no simple predictive model of SRT for any given animal exists. We explored the linkage between animal traits and SRT. We collected previously published data on mean SRT for 112 species of birds, mammals, reptiles and fishes and investigated the general allometric scaling of mean SRT with body mass for each taxon. Moreover, we analysed the effects of food habit and digestive strategy on mean SRT for birds and mammals. In general, mean SRT increased with body mass in all four taxa, whereas the pattern of allometric scaling varied greatly among the taxa. Birds had a smaller intercept and larger slope than those of mammals, whereas reptiles had a much larger intercept and smaller slope than those of either birds or mammals. For birds, food habit was also detected as an important factor affecting SRT. We applied the allometric scaling that was obtained for birds to estimate mean SRT of extinct Mesozoic dinosaurs (Theropoda) – few of which are assumed to have acted as seed dispersers. SRT for large carnivorous theropods was estimated to be 4–5 days, when considering only body mass. The present study provides allometric scaling parameters of mean SRT for a variety of seed‐dispersing animals, and highlights large variations in scaling among taxa. The allometric scaling obtained could be a critical component of further trait‐based modelling of seed dispersal functions. Further, the potential and limitations of the scaling of animal SRT with body mass and a future pathway to the development of trait‐based modelling are discussed.     

Intraspecific mating system evolution and its effect on complex male secondary sexual traits: Does male–male competition increase selection on size or shape?

Sexual selection is generally held responsible for the exceptional diversity in secondary sexual traits in animals. Mating system evolution is therefore expected to profoundly affect the covariation between secondary sexual traits and mating success. Whereas there is such evidence at the interspecific level, data within species remain scarce. We here investigate sexual selection acting on the exaggerated male fore femur and the male wing in the common and widespread dung flies Sepsis punctum and S. neocynipsea (Diptera: Sepsidae). Both species exhibit intraspecific differences in mating systems and variation in sexual size dimorphism (SSD) across continents that correlates with the extent of male–male competition. We predicted that populations subject to increased male–male competition will experience stronger directional selection on the sexually dimorphic male foreleg. Our results suggest that fore femur size, width and shape were indeed positively associated with mating success in populations with male‐biased SSD in both species, which was not evident in conspecific populations with female‐biased SSD. However, this was also the case for wing size and shape, a trait often assumed to be primarily under natural selection. After correcting for selection on overall body size by accounting for allometric scaling, we found little evidence for independent selection on any of these size or shape traits in legs or wings, irrespective of the mating system. Sexual dimorphism and (foreleg) trait exaggeration is therefore unlikely to be driven by direct precopulatory sexual selection, but more so by selection on overall size or possibly selection on allometric scaling.     

Environmental and Ontogenetic Effects on Intraspecific Trait Variation of a Macrophyte Species across Five Ecological Scales

Although functional trait variability is increasingly used in community ecology, the scale- and size-dependent aspects of trait variation are usually disregarded. Here we quantified the spatial structure of shoot height, branch length, root/shoot ratio and leaf number in a macrophyte species Potamogeton maackianus, and then disentangled the environmental and ontogenetic effects on these traits. Using a hierarchical nested design, we measured the four traits from 681 individuals across five ecological scales: lake, transect, depth stratus, quadrat and individual. A notable high trait variation (coefficient variation: 48–112%) was observed within species. These traits differed in the spatial structure, depending on environmental factors of different scales. Shoot height and branch length were most responsive to lake, transect and depth stratus scales, while root/shoot ratio and leaf number to quadrat and individual scales. The trait variations caused by environment are nearly three times higher than that caused by ontogeny, with ontogenetic variance ranging from 21% (leaf number) to 33% (branch length) of total variance. Remarkably, these traits showed non-negligible ontogenetic variation (0–60%) in each ecological scale, and significant shifts in allometric trajectories at lake and depth stratus scales. Our results highlight that environmental filtering processes can sort individuals within species with traits values adaptive to environmental changes and ontogenetic variation of functional traits was non-negligible across the five ecological scales.     

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.