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 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.     

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.     

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.     

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.     

On the relation between basal and maximum metabolic rate in mammals

Basal and maximum metabolic rates, measured by oxygen consumption, for 18 species of wild mammals have been obtained from a search of literature records. The mass exponent of the allometric regression equation for maximum metabolic rate is significantly higher than that for BMR (0.841 and 0.745, respectively; P less than 0.05) in the group of animals examined. No significant correlation between mass-independent basal and maximum metabolic rates has been found. These results do not support the 'aerobic capacity' model of the origin of endothermy.     

Intraspecific allometry of basal metabolic rate: relations with body size, temperature, composition, and circadian phase in the kestrel, Falco tinnunculus

The relationship between body size and basal metabolic rate (BMR) in homeotherms has been treated in the literature primarily by comparison between species of mammals or birds. This paper focuses on the intraindividual changes in BMR when body mass (W) varies with different maintenance regimens. BMR varied in individual kestrels in proportion to W1.67, which is considerably steeper than the mass exponents for homomorphic change (0.667; Heusner, 1984) for interspecific comparison among all birds (0.677) or raptors (0.678), for interindividual comparison of kestrels on ad libitum maintenance regimens (0.786), and for mass proportionality (1.00). The circadian range of telemetered core temperature also varied more strongly with intraindividual than with interspecific (Aschoff, 1981a) variation in mass. This was due to reduced nocturnal core temperature at low-maintenance regimens, which was, however, insufficient to account for the excessive reduction in BMR. kidney lean mass at Carcass analysis of eight birds sacrificed revealed a disproportionate reduction in heart and kidney lean mass at low-maintenance regimens. We surmise that variation in BMR primarily reflects variation in these metabolically highly active tissues. This may account for positive correlations found between heart, kidney, and BMR residuals relative to interspecific allometric prediction, and between alpha and rho residuals, as expected on the basis of the constant excess of BMR during alpha above BMR during rho (Aschoff & Pohl, 1970a).     

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.     

Mammalian metabolism, longevity and parasite species richness

Basal metabolic rate (BMR) scales allometrically with body mass in mammals, but the reasons why some species have higher or lower metabolic rates than predicted from their body mass remain unclear. We tested the idea that parasite species richness may be a contributory factor by performing a comparative analysis on 23 species of mammals for which data were available on parasite species richness, BMR, body mass and two potentially confounding variables, i.e. host density and host longevity. Parasite species richness was positively correlated with BMR and negatively correlated with host longevity independent of body mass.     

Phylogenetic differences of mammalian basal metabolic rate are not explained by mitochondrial basal proton leak

Metabolic rates of mammals presumably increased during the evolution of endothermy, but molecular and cellular mechanisms underlying basal metabolic rate (BMR) are still not understood. It has been established that mitochondrial basal proton leak contributes significantly to BMR. Comparative studies among a diversity of eutherian mammals showed that BMR correlates with body mass and proton leak. Here, we studied BMR and mitochondrial basal proton leak in liver of various marsupial species. Surprisingly, we found that the mitochondrial proton leak was greater in marsupials than in eutherians, although marsupials have lower BMRs. To verify our finding, we kept similar-sized individuals of a marsupial opossum (Monodelphis domestica) and a eutherian rodent (Mesocricetus auratus) species under identical conditions, and directly compared BMR and basal proton leak. We confirmed an approximately 40 per cent lower mass specific BMR in the opossum although its proton leak was significantly higher (approx. 60%). We demonstrate that the increase in BMR during eutherian evolution is not based on a general increase in the mitochondrial proton leak, although there is a similar allometric relationship of proton leak and BMR within mammalian groups. The difference in proton leak between endothermic groups may assist in elucidating distinct metabolic and habitat requirements that have evolved during mammalian divergence.     

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.     

Allometry of thermal variables in mammals: consequences of body size and phylogeny

A large number of analyses have examined how basal metabolic rate (BMR) is affected by body mass in mammals. By contrast, the critical ambient temperatures that define the thermo‐neutral zone (TNZ), in which BMR is measured, have received much less attention. We provide the first phylogenetic analyses on scaling of lower and upper critical temperatures and the breadth of the TNZ in 204 mammal species from diverse orders. The phylogenetic signal of thermal variables was strong for all variables analysed. Most allometric relationships between thermal variables and body mass were significant and regressions using phylogenetic analyses fitted the data better than conventional regressions. Allometric exponents for all mammals were 0.19 for the lower critical temperature (expressed as body temperature ‐ lower critical temperature), ?0.027 for the upper critical temperature, and 0.17 for the breadth of TNZ. The small exponents for the breadth of the TNZ compared to the large exponents for BMR suggest that BMR per se affects the influence of body mass on TNZ only marginally. However, the breadth of the TNZ is also related to the apparent thermal conductance and it is therefore possible that BMR at different body masses is a function of both the heat exchange in the TNZ and that encountered below and above the TNZ to permit effective homeothermic thermoregulation.     

Locomotor mode, maximum running speed, and basal metabolic rate in placental mammals

The locomotor performance (absolute maximum running speed [MRS]) of 120 mammals was analyzed for four different locomotor modes (plantigrade, digitigrade, unguligrade, and lagomorph-like) in terms of body size and basal metabolic rate (BMR). Analyses of conventional species data showed that the MRS of plantigrade and digitigrade mammals and lagomorphs increases with body mass, whereas that of unguligrade mammals decreases with body mass. These trends were confirmed in plantigrade mammals and lagomorphs using phylogenetically independent contrasts. Multiple regression analyses of MRS contrasts (dependent variable) as a function of body mass and BMR contrasts (predictor variables) revealed that BMR was a significant predictor of MRS in the complete data set, as well as in plantigrade and nonplantigrade mammals. However, there was severe multicollinearity in the nonplantigrade model that may influence the interpretation of these models. Although these data show mass-independent correlation between BMR and MRS, they are not necessarily indicative of a cause-effect relationship. However, the analyses do identify a negligible role of body size associated with MRS once phylogenetic and BMR effects are controlled, suggesting that the body size increase in large mammals over time (i.e., Cope's rule) can probably rule out MRS as a driving variable.     

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.     

The allometry of avian basal metabolic rate: good predictions need good data

Basal metabolic rate (BMR) is often predicted by allometric interpolation, but such predictions are critically dependent on the quality of the data used to derive allometric equations relating BMR to body mass (Mb). An examination of the metabolic rates used to produce conventional and phylogenetically independent allometries for avian BMR in a recent analysis revealed that only 67 of 248 data unambiguously met the criteria for BMR and had sample sizes with n>/=3. The metabolic rates that represented BMR were significantly lower than those that did not meet the criteria for BMR or were measured under unspecified conditions. Moreover, our conventional allometric estimates of BMR (W; logBMR=-1.461+0.669logMb) using a more constrained data set that met the conditions that define BMR and had n>/=3 were 10%-12% lower than those obtained in the earlier analysis. The inclusion of data that do not represent BMR results in the overestimation of predicted BMR and can potentially lead to incorrect conclusions concerning metabolic adaptation. Our analyses using a data set that included only BMR with n>/=3 were consistent with the conclusion that BMR does not differ between passerine and nonpasserine birds after taking phylogeny into account. With an increased focus on data mining and synthetic analyses, our study suggests that a thorough knowledge of how data sets are generated and the underlying constraints on their interpretation is a necessary prerequisite for such exercises.     

Sample size and mass range effects on the allometric exponent of basal metabolic rate

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

Thermogenic effect of food in physically well-trained elderly men

Basal metabolic rate (BMR) and the thermogenic effect of food (TEF) after a liquid mixed meal of 2092 kJ (500 kcal) were examined in physically well-trained, elderly men in comparison with sedentary weight- and age-matched controls. BMR tended to be higher and TEF was significantly higher in the physically well-trained men than in the controls. No certain differences were found in plasma thyroid hormones or catecholamines. BMR correlated with whole body potassium while TEF did not. The tendency to elevated BMR in the well-trained men might therefore be due to their greater muscle mass. The elevated TEF, however, probably has other causes and might be associated with the elevated catecholamine sensitivity associated with the physically trained condition.     

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.     

Causes and significance of variation in mammalian basal metabolism

Mammalian basal metabolic rates (BMR) increase with body mass, whichs explains approximately 95% of the variation in BMR. However, at a given mass, there remains a large amount of variation in BMR. While many researchers suggest that the overall scaling of BMR with body mass is due to physiological constraints, variation at a given body mass may provide clues as to how selection acts on BMR. Here, we examine this variation in BMR in a broad sample of mammals and we test the hypothesis that, across mammals, body composition explains differences in BMR at a given body mass. Variation in BMR is strongly correlated with variation in muscle mass, and both of these variables are correlated with latitude and ambient temperature. These results suggest that selection alters BMR in response to thermoregulatory pressures, and that selection uses muscle mass as a means to generate this variation.