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.     

Bioenergetics of reproduction and pup development in a subterranean rodent (Ctenomys talarum)

The objective of this study was to evaluate the maternal costs of reproduction and pup development in the subterranean rodent Ctenomys talarum (Thomas 1898). Statistical differences were detected in whole-animal metabolic rates between nonreproductive and pregnant or lactating females. Whole-animal metabolic rates during pregnancy and lactation were 128% and 151% of the resting metabolic rate (RMR) observed in nonreproductive females. The total additional energy cost of reproduction (above the nonreproductive level) was similar for both the gestation and lactation periods. Mass-specific RMR revealed an upregulation of cell or tissue metabolism during lactation but not during gestation. The mass-specific metabolic rate of pups was 237% of the adults' metabolic rates. No differences were observed in body temperature among nonreproductive, pregnant, or lactating females. No differences were detected in body mass at birth among pups from litters with different numbers of nestlings. Pups increased their body temperature, reaching adult temperature at 30 d of age, when they were near weaning. Milk constituted the exclusive food for pups until they started eating solid food at 10 d old. Suckling time decreased with age of pups, and at the same time, mother chases directed toward their pups increased. These reproductive characteristics may contribute to successful existence in a subterranean habitat.     

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.     

Rate of metabolism during lactation in small terrestrial mammals (Crocidura russula, Mus domesticus and Microtus arvalis)

Basal rate of metabolism (BMR) and resting maternal rate of metabolism around peak lactation (RMR(L)) were measured in Crocidura russula, Mus domesticus and Microtus arvalis. These species have a moderate or high BMR relative to the scaling relationship of Kleiber. One goal of the study was to check whether females of these species show elevated rates of metabolism during lactation. A second goal was to test for a possible intraspecific correlation between the level of BMR and the change in rate of metabolism associated with lactation. RMR(L) was significantly higher than BMR in all species when changes in body mass between the two states were taken into account. Data available on other small mammals are in accordance with this finding, which does not support the hypothesis that low-BMR mammal species increase their rate of metabolism during reproduction because Kleiber's relationship represents an optimal level for therian reproduction. Within C. russula and M. domesticus, a significant and negative correlation was found between the level of BMR and the change in rate of metabolism associated with lactation. This pattern is presumably due to the fact that low-BMR females undergo more extensive physiological and anatomical changes during lactation than high-BMR females.     

Plasticity in body composition in breeding birds: what drives the metabolic costs of egg production?

Body composition in vertebrates is known to show phenotypic plasticity, and changes in organ masses are usually rapid and reversible. One of the most rapid and reversible changes is the transformation of the female avian reproductive organs before breeding. This provides an excellent system to investigate the effects of plasticity in organ size on basal metabolic rate (BMR) through relationships between organ masses and BMR. We compared body composition of female European starlings (Sturnus vulgaris) during various reproductive stages over 3 yr and investigated the pattern of changes in reproductive and nonreproductive organ mass during follicular development and ovulation. Furthermore, we analyzed the relationship between organ mass and resting metabolic rate (RMR) in nonbreeding, laying, and chick-rearing females. Our analysis revealed marked variation in organ masses between breeding stages but no consistent pattern among years except for kidney and pectoralis muscle. Furthermore, changes in nonreproductive organs did not parallel the cycle of growth and regression of the reproductive organs. The oviduct gained 62% of its 22-fold increase in mass in only 3 d, and oviduct regression was just as rapid and began even before the final egg of the clutch was laid, with 42% of the oviduct mass lost before laying of the final egg. In laying females, 18% of variation in mass-corrected RMR was explained by the mass of the oviduct (r2=0.18, n=80, P<0.0005), while pectoralis muscle mass in nonbreeding individuals and liver and gizzard mass in chick-rearing females were the only organs significantly related to RMR (r2=0.31-0.44). We suggest that the nonreproductive organs are affected more by changes in local ecological conditions than the reproductive state itself and that the activity and maintenance cost of the oviduct is high enough that selection has led to a very tight size-function relationship for this organ.     

Variation in intensity of a parasitic mite (Spinturnix myoti) in relation to the reproductive cycle and immunocompetence of its bat host (Myotis myotis)

Given the intimate association in host–parasite systems, parasites are expected to initiate their own reproduction when vulnerable hosts become abundant and/or when adult hosts are less resistant. In this study, we examined the variation in the intensities of a blood-sucking mite ( Spinturnix myoti , Acarina) with respect to the reproductive cycle and immunocompetence of its host, the greater mouse-eared bat Myotis myotis . Reproductive, pregnant females were less immunocompetent and harboured more parasites than nonreproductive females, whilst, during lactation, immunocompetence was positively associated with female body mass. There was a dramatic increase in the T-cell response of gravid females with the advancement of gestation, which coincided with a diminution of individual parasite loads and a progressive switch of parasites from adults to juveniles. The latter not only harboured greater numbers of mites than adult female bats, but they also exhibited gravid parasites in higher proportions, indicating that juvenile hosts are more attractive for parasite reproduction than adult females.     

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.     

Repeatability of basal metabolism in breeding female kittiwakes Rissa tridactyla

We studied kittiwakes (Rissa tridactyla) breeding near Ny-Ålesund (79° N, 12° E) on Svalbard. In 1997, the basal metabolic rates (BMRs) of 17 breeding females were measured during the incubation and chick-rearing periods. The mean body mass of the kittiwakes decreased significantly (by 10%) between the incubation and chick-rearing periods. At the same time, both the whole-body and mass-specific BMRs decreased significantly. There was a positive and significant relationship between the BMR residuals from the incubation period and those from the chick-rearing period. Thus, the BMR of incubating female kittiwakes is a significant predictor of their BMR during the chick-rearing period. New BMR data were collected in 1998 from ten of these females, measured around the chick-hatching date. Repeatability values were calculated using either (i) the data for eight individuals for which three BMR measurements existed, or (ii) all the data from both years, yielding significant repeatabilities of 0.52 and 0.35, respectively. These values indicate that between 48 and 65% of the observed variation in BMR is due to intraindividual variability, while between-individual variability accounts for 35 to 52% of the variation in the BMR. This is the first report of a significant repeatability of the BMR of an endothermic organism across an elapsed time of more than one day.     

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.     

Mass,phylogeny, and temperature are sufficient to explain differences in metabolic scaling across mammalian orders?

Whether basal metabolic rate‐body mass scaling relationships have a single exponent is highly discussed, and also the correct statistical model to establish relationships. Here, we aimed (1) to identify statistically best scaling models for 17 mammalian orders, Marsupialia, Eutheria and all mammals, and (2) thereby to prove whether correcting for differences in species’ body temperature and their shared evolutionary history improves models and their biological interpretability. We used the large dataset from Sieg et al. (The American Naturalist 174 , 2009, 720) providing species’ body mass (BM), basal metabolic rate (BMR) and body temperature (T). We applied different statistical approaches to identify the best scaling model for each taxon: ordinary least squares regression analysis (OLS) and phylogenetically informed analysis (PGLS), both without and with controlling for T. Under each approach, we tested linear equations (log‐log‐transformed data) estimating scaling exponents and normalization constants, and such with a variable normalization constant and a fixed exponent of either ? or ¾, and also a curvature. Only under temperature correction, an additional variable coefficient modeled the influence of T on BMR. Except for Pholidata and Carnivora, in all taxa studied linear models were clearly supported over a curvature by AICc. They indicated no single exponent at the level of orders or at higher taxonomic levels. The majority of all best models corrected for phylogeny, whereas only half of them included T. When correcting for T, the mathematically expected correlation between the exponent (b) and the normalization constant (a) in the standard scaling model y = a x ^b was removed, but the normalization constant and temperature coefficient still correlated strongly. In six taxa, T and BM correlated positively or negatively. All this hampers a disentangling of the effect of BM, T and other factors on BMR, and an interpretation of linear BMR‐BM scaling relationships in the mammalian taxa studied.     

Scaling of metabolic rate in the lesser wax moth Achroia grisella does not fit the 3/4‐power law and shows significant sex differences

Allometric scaling of metabolic rates is commonly described as a power function and 0.75 is a widely accepted exponent. The universality of this exponent is in doubt and, particularly for insects, contradictory results have been obtained. Furthermore, sexual differences in scaling exponents are observed for several species that could lead to artefacts when they are not considered in intra‐ and interspecific scaling. Whether the metabolic scaling exponent in the lesser wax moth Achroia grisella differs significantly from 0.75 is tested, as well as whether it differs between the sexes. Adults of this moth neither feed nor drink, rendering them as suitable subjects for a study of metabolic rates. Neglecting sex differences, a metabolic scaling exponent of 0.8 is recorded. However, there are significant differences in metabolic scaling between the sexes. When considered separately, males scale with 0.96 and females with 0.67. Thus, in this species, a scaling exponent of 0.75 does not appear to exist either for males or females. The body size optimization model offers a potential explanation for the sex differences in metabolic scaling, although it remains to be tested in wax moths. With insects in particular, there is the need for more detailed studies on the scaling of metabolic rates that also take sexual differences into account.     

Expanding the body mass range: associations between BMR and tissue morphology in wild type and mutant dwarf mice (<Emphasis Type="Italic">David</Emphasis> mice)

We sought to identify associations of basal metabolic rate (BMR) with morphological traits in laboratory mice. In order to expand the body mass (BM) range at the intra-strain level, and to minimize relevant genetic variation, we used male and female wild type mice (C3HeB/FeJ) and previously unpublished ENU-induced dwarf mutant littermates (David mice), covering a body mass range from 13.5 g through 32.3 g. BMR was measured at 30°C, mice were killed by means of CO₂ overdose, and body composition (fat mass and lean mass) was subsequently analyzed by dual X-ray absorptiometry (DEXA), after which mice were dissected into 12 (males) and 10 (females) components, respectively. Across the 44 individuals, 43% of the variation in the basal rates of metabolism was associated with BM. The latter explained 47% to 98% of the variability in morphology of the different tissues. Our results demonstrate that sex is a major determinant of body composition and BMR in mice: when adjusted for BM, females contained many larger organs, more fat mass, and less lean mass compared to males. This could be associated with a higher mass adjusted BMR in females. Once the dominant effects of sex and BM on BMR and tissue mass were removed, and after accounting for multiple comparisons, no further significant association between individual variation in BMR and tissue mass emerged. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Quantitative genetics and fitness effects of basal metabolism

The physiological requirements of reproduction are predicted to generate a link between energy, physiology and life history traits. Simultaneously, low maintenance costs, measured by energy consumption, are expected to be advantageous. Here we investigated fitness relatedness of traits by estimating genetic correlations between, and inbreeding depression for, body mass, basal metabolic rate (BMR) and other life history characters in a wild rodent, Myodes glareolus. The narrow-sense heritability of absolute and mass corrected BMRs were high for females (h² = 0.48 and 0.42) but low and non-significant for males (0.32 and 0.09). A significant positive genetic correlation between BMR and litter size suggests that traits connected to female fecundity might favour higher metabolism (i.e. support increased intake hypothesis). However, the estimates of inbreeding depression indicate that, while higher values of body mass and female litter size could be positively associated with overall fitness, the association between BMR and overall fitness in bank voles would be negative (i.e. support compensation hypothesis). This result suggests that the advantages of larger litters and larger body mass might be evolutionary constrained by high costs of maintenance of those traits, as reflected by the level of basal metabolism.     

Fit females and fat polygynous males: seasonal body mass changes in the grey-headed flying fox

When females and males differ in their timing of maximum reproductive effort, this can result in sex-specific seasonal cycles in body mass. Such cycles are undoubtedly under strong selection, particularly in bats, where they affect flying ability. Flying foxes (Old World fruit bats, Pteropus spp.) are the largest mammals that can sustain powered flight and therefore face critical trade-offs in managing body reserves for reproduction, yet little is known about body mass dynamics in this group. I investigated body mass changes in relation to reproductive behaviour in a large colony of grey-headed flying foxes (Pteropus poliocephalus). In this polygynous mammal, females were predicted to maximise reproductive effort during lactation and males during the breeding season. As predicted, female body condition declined during the nursing period, but did not vary in relation to sexual activity. By contrast, males accumulated body reserves prior to the breeding season, but subsequently lost over 20% of their body mass on territory defence and courtship, and lost foraging opportunities as they also defended their day roost territories at night. Males in better condition had larger testes, particularly during territory establishment, prior to maximum sexual activity. Thus, the seasonality of female mass reflected the high metabolic load that lactation imposes on mothers. However, male mass followed a pattern akin to the "fatted male phenomenon", which is commonly observed in large polygynous mammals with seasonal reproduction, but not in bats. This shows the importance of body reserves for reproduction in flying foxes, despite their severe constraints on body mass.     

Changes in body temperature influence the scaling of VO2max and aerobic scope in mammals

Debate on the mechanism(s) responsible for the scaling of metabolic rate with body size in mammals has focused on why the maximum metabolic rate (VO2max ) appears to scale more steeply with body size than the basal metabolic rate (BMR). Consequently, metabolic scope, defined as VO2max/BMR, systematically increases with body size. These observations have led some to suggest that VO2max, and BMR are controlled by fundamentally different processes, and to discount the generality of models that predict a single power-law scaling exponent for the size dependence of the metabolic rate. We present a model that predicts a steeper size dependence for VO2max than BMR based on the observation that changes in muscle temperature from rest to maximal activity are greater in larger mammals. Empirical data support the model's prediction. This model thus provides a potential theoretical and mechanistic link between BMR and VO2 max.     

Allometric cascade: a model for resolving body mass effects on metabolism

Expanding upon a preliminary communication (Nature 417 (2002) 166), we here further develop a "multiple-causes model" of allometry, where the exponent b is the sum of the influences of multiple contributors to control. The relative strength of each contributor, with its own characteristic value of b(i), is determined by c(i), the control contribution or control coefficient. A more realistic equation for the scaling of metabolism with body size thus can be written as BMR=MR(0)Sigmac(i)(M/M(0))(bi), where MR(0) is the "characteristic metabolic rate" of an animal with a "characteristic body mass", M(0). With M(0) of 1 unit mass (usually kg), MR(0) takes the place of the value a, found in the standard scaling equation, b(i) is the scaling exponent of the process i, and c(i) is its control contribution to overall flux, or the control coefficient of the process i. One can think of this as an allometric cascade, with the b exponent for overall energy metabolism being determined by the b(i) and c(i) values for key steps in the complex pathways of energy demand and energy supply. Key intrinsic factors (such as neural and endocrine processes) or ecological extrinsic factors are considered to act through this system in affecting allometric scaling of energy turnover. Applying this model to maximum vs. BMR data for the first time explains the differing scaling behaviour of these two biological states in mammals, both in the absence and presence of intrinsic regulators such as thyroid hormones (for BMR) and catecholamines (for maximum metabolic rate).     

Basal rate of metabolism and temperature regulation in Goeldi's monkey (Callimico goeldii)

Basal rate of metabolism (BMR) and temperature regulation are described for Goeldi's monkey (Callimico goeldii), a threatened New World primate species of the family Callitrichidae. Measurements were conducted on sleeping individuals during the night, using a special nestbox designed to serve as a respirometry chamber, such that test animals remained undisturbed in their customary surroundings. Oxygen consumption was measured at ambient temperatures between 17.5 and 32 degrees C for 10 individuals with an average body mass of 557 g. Average BMR was 278+/-41 ml O(2) h(-1), which is lower than the value predicted on the basis of body mass. Individual differences in BMR were significant even when body mass was accounted for. Body temperature was measured in five individuals below thermoneutrality and averaged 36+/-0.3 degrees C. The corresponding thermal conductance averaged 29.3+/-2.2 ml O(2) h(-1) degrees C(-1), which is similar to the expected value. The metabolic and thermoregulatory patterns observed in C. goeldii resemble those of the closely related marmosets and tamarins. Low BMR is presumably associated with limited access to energy resources and may be directly linked with phylogenetic dwarfing in the family Callitrichidae.     

Intraspecific mass scaling of metabolic rates in grass carp (Ctenopharyngodon idellus)

We assessed the intraspecific mass scaling of standard metabolic rate (SMR), maximum metabolic rate (MMR), excess post-exercise oxygen consumption (EPOC), and erythrocyte size in grass carp (Ctenopharyngodon idellus), with body masses ranging from 4.0 to 459 g. SMR and MMR scaled with body mass with similar exponents, but neither exponent matched the expected value of 0.75 or 1, respectively. Erythrocyte size scaled with body mass with a very low exponent (0.090), suggests that while both cell number and cell size contribute to the increase in body mass, cell size plays a smaller role. The similar slopes of MMR and SMR in grass carp suggest a constant factorial aerobic scope (FAS) as the body grows. SMR was negatively correlated with FAS, indicating a tradeoff between SMR and FAS. Smaller fish recovered faster from the exhaustive exercises, and the scaling exponent of EPOC was 1.075, suggesting a nearly isometric increase in anaerobic capacity. Our results provide support for the cell size model and suggest that variations of erythrocyte size may partly contribute to the intraspecific scaling of SMR. The scaling exponent of MMR was 0.863, suggesting that the metabolism of non-athletic fish species is less reliant on muscular energy expenditure, even during strenuous exercise.     

Mitochondrial function and bioenergetic trade‐offs during lactation in the house mouse (Mus musculus)

Energy allocation theory predicts that a lactating female should alter the energetic demands of its organ systems in a manner that maximizes nutrient allocation to reproduction while reducing nutrient use for tasks that are not vital to immediate survival. We posit that organ‐specific plasticity in the function of mitochondria plays a key role in mediating these energetic trade‐offs. The goal of this project was to evaluate mitochondrial changes that occur in response to lactation in two of the most energetically demanding organs in the body of a rodent, the liver and skeletal muscle. This work was conducted in wild‐derived house mice (Mus musculus) kept in seminatural enclosures that allow the mice to maintain a natural social structure and move within a home range size typical of wild mice. Tissues were collected from females at peak lactation and from age‐matched nonreproductive females. Mitochondrial respiration, oxidative damage, antioxidant, PGC‐1α, and uncoupling protein levels were compared between lactating and nonreproductive females. Our findings suggest that both liver and skeletal muscle downregulate specific antioxidant proteins during lactation. The liver, but not skeletal muscle, of lactating females displayed higher oxidative damage than nonreproductive females. The liver mass of lactating females increased, but the liver displayed no change in mitochondrial respiratory control ratio. Skeletal muscle mass and mitochondrial respiratory control ratio were not different between groups. However, the respiratory function of skeletal muscle did vary among lactating females as a function of stage of concurrent pregnancy, litter size, and mass of the mammary glands. The observed changes are predicted to increase the efficiency of skeletal muscle mitochondria, reducing the substrate demands of skeletal muscle during lactation. Differences between our results and prior studies highlight the role that an animals’ social and physical environment could play in how it adapts to the energetic demands of reproduction.     

Energy In-Equivalence in Australian Marsupials: Evidence for Disruption of the Continent’s Mammal Assemblage,or Are Rules Meant to Be Broken?

The energy equivalence rule (EER) is a macroecological hypothesis that posits that total population energy use (PEU) should be independent of species body mass, because population densities and energy metabolisms scale with body mass in a directly inverse manner. However, evidence supporting the EER is equivocal, and the use of basal metabolic rate (BMR) in such studies has been questioned; ecologically-relevant indices like field metabolic rate (FMR) are probably more appropriate. In this regard, Australian marsupials present a novel test for the EER because, unlike eutherians, marsupial BMRs and FMRs scale differently with body mass. Based on either FMR or BMR, Australian marsupial PEU did not obey an EER, and scaled positively with body mass based on ordinary least squares (OLS) regressions. Importantly, the scaling of marsupial population density with body mass had a slope of −0.37, significantly shallower than the expected slope of −0.75, and not directly inverse of body-mass scaling exponents for BMR (0.72) or FMR (0.62). The findings suggest that the EER may not be a causal, universal rule, or that for reasons not yet clear, it is not operating for Australia’s unique native fauna.