Intraspecific Scaling of the Resting and Maximum Metabolic Rates of the Crucian Carp (Carassius auratus)

The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M ^0.776 and MMR = 0.753M ^0.785. The scaling exponents for RMR (b _r) and MMR (b _m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.     

Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

Scaling segmental moments of inertia for individual subjects

The purpose of this investigation was to validate methods of scaling human segmental moments of inertia for the transverse principal axis. Firstly, two methods of scaling Chandler et al.'s (Pamphlets DOT HS-801 430 and AMRL TR-74-137, Wright Patterson Air Force Base, OH, 1975) mean subject data to estimate the segmental moments of inertia were used. Chandler et al.'s data were scaled using body mass and segment length (formula 1) or body mass and standing height (formula 2). These data were then compared with a procedure of using the cadaver whose anthropometric measurements most closely match those of the subject. The difference between the criterion data (Chandler's subject data) and scaled values were plotted on scatter diagrams with confidence limits of p less than 0.05 at d.f. = 17. For procedure 1, 43% of the scaled values were plotted within the confidence limits using formula (2) (mass and standing height), compared with 26% for formula (1) (mass and segment length). Formula (1) markedly underestimated the tallest and heaviest subjects. In procedure 2, only 16% and 21% of the scaled values, using formula (1) and (2), respectively, fell within the confidence limits. Results suggested that scaling formulae approximate the moment of inertia of body segments with only limited accuracy. However, if scaling was to be adopted then mean moment of inertia data from an appropriate data set, using the formula that incorporates subject mass and standing height, gave results closest to the criterion value.     

Energetics of the smallest: Do bacteria breathe at the same rate as whales?

Power laws describing the dependence of metabolic rate on body mass have been established for many taxa, but not for prokaryotes, despite the ecological dominance of the smallest living beings. Our analysis of 80 prokaryote species with cell volumes ranging more than 1,000,000-fold revealed no significant relationship between mass-specific metabolic rate q and cell mass. By absolute values, mean endogenous mass-specific metabolic rates of non-growing bacteria are similar to basal rates of eukaryote unicells, terrestrial arthropods and mammals. Maximum mass-specific metabolic rates displayed by growing bacteria are close to the record tissue-specific metabolic rates of insects, amphibia, birds and mammals. Minimum mass-specific metabolic rates of prokaryotes coincide with those of larger organisms in various energy-saving regimes: sit-and-wait strategists in arthropods, poikilotherms surviving anoxia, hibernating mammals. These observations suggest a size-independent value around which the mass-specific metabolic rates vary bounded by universal upper and lower limits in all body size intervals.     

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.     

Supply-Side Constraints Are Insufficient to Explain the Ontogenetic Scaling of Metabolic Rate in the Tobacco Hornworm,Manduca sexta

Explanations for the hypoallometric scaling of metabolic rate through ontogeny generally fall into two categories: supply-side constraints on delivery of oxygen, or decreased mass-specific intrinsic demand for oxygen. In many animals, supply and demand increase together as the body grows, thus making it impossible to tease apart the relative contributions of changing supply and demand to the observed scaling of metabolic rate. In larval insects, the large components of the tracheal system are set in size at each molt, but then remain constant in size until the next molt. Larvae of Manduca sexta increase up to ten-fold in mass between molts, leading to increased oxygen need without a concomitant increase in supply. At the molt, the tracheal system is shed and replaced with a new, larger one. Due to this discontinuous growth of the tracheal system, insect larvae present an ideal system in which to examine the relative contributions of supply and demand of oxygen to the ontogenetic scaling of metabolic rate. We observed that the metabolic rate at the beginning of successive instars scales hypoallometrically. This decrease in specific intrinsic demand could be due to a decrease in the proportion of highly metabolically active tissues (the midgut) or to a decrease in mitochondrial activity in individual cells. We found that decreased intrinsic demand, mediated by a decrease in the proportion of highly metabolically active tissues in the fifth instar, along with a decrease in the specific mitochondrial activity, contribute to the hypoallometric scaling of metabolic rate.     

Relative growth of organs and parts of a marine teleost,the porgy,Pagrus major,with special reference to metabolism-size relationships

Organ-body mass relationships were examined for 36 different organs and parts in porgies,Pagrus major, ranging in body mass from 0.0033 to 1200 g. Organs with high metabolic activity, e.g. brain, intestine, pyloric caeca and heart showed negative allometry except during very early stages in the life history. On the other hand, the trunk, which comprised mainly musculature with low metabolic activity, showed positive allometry. These results support our idea that the decline in mass-specific metabolic rate in animals with increasing body mass can be explained, partly at least, by tissues with low metabolic rates becoming heavier in proportion to the whole body with growth.     

The development of thermoregulation in turkey and guinea fowl hatchlings: similarities and differences

The development of thermoregulation was studied in turkeys (Meleagris gallopavo, 60.5 g) and guinea fowl (Numida meleagris, 33.5 g) from 2 to 24 h after hatching. Thermoregulation was measured at different ages during 1 h of cold exposure (20°C). Final body temperature rose linearly with age in turkeys, but reached a plateau in guinea fowl between 12 and 16 h. At 2 h after hatch final body temperature was highest in guinea fowl, while at 24 h after hatch there was no difference between the species. The development of mass-specific metabolic rate with age resembled the pattern of final body temperature. At 2 h post-hatch mass-specific metabolic rate was highest in guinea fowl; however, at 24 h post-hatch there was no difference between the species. since mass-specific metabolic rate reached a plateau in guinea fowl at 16 h. In turkeys mass-specific dry thermal conductance decreased with age initially, while in guinea fowl it remained stable. Nevertheless, at both 2 and 24 h after hatch mass-specific wet conductance did not differ significantly between the species. In turkeys mass-specific wet conductance increased initially. This increase in mass-specific wet conductance may be due to the rapid onset of feather growth in turkeys. The O₂ consumption per breath doubled during the first 24 h in turkeys but remained stable in guine fowl. This suggests that at least two different developmental patterns of O₂ intake exist within Galliformes. The results show that 2 h post-hatch the thermoregulatory ability was lowest in turkeys, despite their larger body mass. However, at 24 h post-hatch the difference between the species was not significant, because the thermoregulatory ability had increased more in turkeys.Abbreviations B _f breathing frequency - BM body mass - BMR basal metabolic rate - C _D mass-specific dry thermal conductance - C _w mass-specific wet thermal conductance - HI homeothermy index - H _E evaporative heat loss - H _B loss of stored body heat - MR metabolic rate - M _MS mass-specific metabolic rate - RH relative humidity - I _A ambient temperature - T _Bi initial body temperature - T _Bf final body temperature - VO₂ volume oxygen consumed - VCO₂ volume carbon dioxide produced     

Routine metabolic rate of southern bluefin tuna (Thunnus maccoyii)

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

Abundance-body size relationships: the roles of metabolism and population dynamics

1. Species' abundance scales approximately as an inverse power of body mass. This property has been explained on the basis of metabolic rates of organisms of different sizes. 2. This paper considers the additional effect of population dynamics on the abundance-body size relationship, on the grounds that mass flow through food webs also depends on interactions between predators and their prey. To do this, an analysis of simple dynamical food-chain models was carried out, using rate parameters which scaled with body mass according to empirically based rules. 3. The analysis shows that a function for the abundance-body size relationship derived from metabolic theory is a good first approximation to a function derived for food chains at dynamic equilibrium, although the mechanistic interpretation of terms in the functions is not the same. 4. The results are sensitive to assumptions about the scaling of the self-limitation of basal species with respect to body size. Depending on the assumption made, the abundance-body size relationship may have a power parameter -1 at all trophic levels, or be described by different functions at different trophic levels.     

Metabolic rate in the whip-spider, Damon annulatipes (Arachnida: Amblypygi)

Metabolic rate estimates as well as a measure of their repeatability and response to laboratory acclimation are provided for the amblypygid Damon annulatipes (Wood). This species (mean +/- S.E. mass: 640+/-66 mg) shows continuous gas exchange, as might be expected from its possession of book lungs, and at 21 degrees C has a metabolic rate of 30.22+/-2.87 microl CO2 h(-1) (approximately 229.6+/-21.8 microW, R.Q. = 0.72). The intraclass correlation coefficient (r=0.74-0.89) indicated substantial repeatability in metabolic rate which did not change with laboratory acclimation over a period of 2 weeks. By contrast, absolute metabolic rate declined by c. 16-33%, although this was not a consequence of changes in mass (which were non-significant over the same period). Rather, it appears that a reduction in overall stress or activity in the laboratory might have been responsible for the decline in mass-independent metabolic rate. At the intraspecific level, metabolic rate scaled as microW = 342 M(0.857), where mass is in grams. Metabolic rates of this species are in keeping with its sedentary behaviour such that for a given body size they are lower than those of most arthropods (spiders and insects), higher than the very sedentary ticks, and equivalent to scorpions. These findings have implications for the understanding of the evolution of metabolic rates in arthropods.     

Trade-offs between the metabolic rate and population density of plants

The energetic equivalence rule, which is based on a combination of metabolic theory and the self-thinning rule, is one of the fundamental laws of nature. However, there is a progressively increasing body of evidence that scaling relationships of metabolic rate vs. body mass and population density vs. body mass are variable and deviate from their respective theoretical values of 3/4 and -3/4 or -2/3. These findings questioned the previous hypotheses of energetic equivalence rule in plants. Here we examined the allometric relationships between photosynthetic mass (M(p)) or leaf mass (M(L)) vs. body mass (beta); population density vs. body mass (delta); and leaf mass vs. population density, for desert shrubs, trees, and herbaceous plants, respectively. As expected, the allometric relationships for both photosynthetic mass (i.e. metabolic rate) and population density varied with the environmental conditions. However, the ratio between the two exponents was -1 (i.e. beta/delta = -1) and followed the trade-off principle when local resources were limited. Our results demonstrate for the first time that the energetic equivalence rule of plants is based on trade-offs between the variable metabolic rate and population density rather than their constant allometric exponents.     

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.     

High-Throughput Tissue Bioenergetics Analysis Reveals Identical Metabolic Allometric Scaling for Teleost Hearts and Whole Organisms

Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO₂), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO₂ scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO₂) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism’s vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate—a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in toxicology, evolutionary physiology, and biomedical sciences, particularly in the context of investigating pathogenesis of mitochondrial diseases.     

Modelling energetic costs of fish swimming

The oxygen consumption rates of two cyprinid fishes, carp (Cyprinus carpio L.) and roach (Rutilus rutilus (L.)), were analysed for a wide range of body mass and swimming speed by computerized intermittent-flow respirometry. Bioenergetic models were derived, based on fish mass (M) and swimming speed (U), to predict the minimal speed and mass-specific active metabolic rate (AMR) in these fishes (AMR=aMbUc). Mass and speed together explained more than 90% of the variance in total swimming costs in both cases. The derived models show that carp consume far more oxygen at a specific speed and body mass, thus being less efficient in energy use during swimming than roach. It was further found that in carp (AMR=0.02M0.8U0.95) the metabolic increment during swimming is more strongly effected by speed, whereas in roach (AMR=0.02M0.93U0.6) it is more strongly effected by body mass. The different swimming traits of carp and roach are suitable for their respective lifestyles and ecological demands.     

Energetic inequivalence in eusocial insect colonies

The energetic equivalence rule states that population-level metabolic rate is independent of average body size. This rule has been both supported and refuted by allometric studies of abundance and individual metabolic rate, but no study, to my knowledge, has tested the rule with direct measurements of whole-population metabolic rate. Here, I find a positive scaling of whole-colony metabolic rate with body size for eusocial insects. Individual metabolic rates in these colonies scaled with body size more steeply than expected from laboratory studies on insects, while population size was independent of body size. Using consumer-resource models, I suggest that the colony-level metabolic rate scaling observed here may arise from a change in the scaling of individual metabolic rate resulting from a change in the body size dependence of mortality rates.     

The scaling rule for environmental organizing systems in a gravitational field

A recent thermodynamics and information study examined the basis of a scaling rule for simple living organisms. The present paper examines a scaling rule for the relationship between the integrated scaled metabolic energy and the mass of a system for a wide range of masses, from animals to the 4He cores of main-sequence stars, considering the effect of gravitational energy. The expected specific scaled energy for animals and the 4He cores of main-sequence stars is 1600 times greater than the specific scaled energy for fundamental living organisms, such as unicellular organisms. This difference results from their organization in a gravitational field or the lack thereof.     

The scaling and temperature dependence of vertebrate metabolism

Body size and temperature are primary determinants of metabolic rate, and the standard metabolic rate (SMR) of animals ranging in size from unicells to mammals has been thought to be proportional to body mass (M) raised to the power of three-quarters for over 40 years. However, recent evidence from rigorously selected datasets suggests that this is not the case for birds and mammals. To determine whether the influence of body mass on the metabolic rate of vertebrates is indeed universal, we compiled SMR measurements for 938 species spanning six orders of magnitude variation in mass. When normalized to a common temperature of 38 degrees C, the SMR scaling exponents of fish, amphibians, reptiles, birds and mammals are significantly heterogeneous. This suggests both that there is no universal metabolic allometry and that models that attempt to explain only quarter-power scaling of metabolic rate are unlikely to succeed.     

Metabolism, body size and life span: a case study in evolutionarily divergent populations of the garter snake (Thamnophis elegans)

We present a case study of metabolism, life history and aging in the western terrestrial garter snake (Thamnophis elegans). Early research in the field supported the rate-of-living hypothesis as an explanation of aging, which was based on an apparent negative relationship between mass-specific metabolic rate and lifespan in endotherms. This hypothesis in its original form has not withstood additional tests and comparisons between the two main lineages of endotherms-birds and mammals, but there is still much to be discovered of the causative links among rate of oxygen consumption, physiology and life history, particularly in ectothermic reptiles. We present data that show adult short-lived snakes, from naturally occurring ecotypes of garter snakes, have higher mass-specific resting metabolic rates at any given body mass (metabolic intensity) across a series of normal activity temperatures (15-32°C). The short-lived ecotype in this geographic region reaches a larger body size, and has life-history traits that place it at the fast end of a pace-of-life continuum (fast growth, early maturation, high reproductive output) relative to individuals of the small-bodied long-lived ecotype. The difference between ecotypes in metabolic intensity, even after acclimation to identical conditions, may reflect evolutionary divergence and genetic differences between ecotypes. The difference in metabolic intensity is not, however, present at birth, so an alternative is that developmental environment may permanently influence metabolic rate and life history. Such developmental canalization could lead to altered gene expression via environmental influences on the epigenome and result in altered metabolic trajectories in the snakes' natural habitats.     

Origin of the scaling rule for fundamental living organisms based on thermodynamics

The regular relationships between metabolic energy and body mass M of unicellular organisms, poikilotherms and homeotherms were well known as general equations. The metabolic energy rate and the life span are proportional to M(0.75) and to M(0.25), respectively. As a result, the product of the metabolic energy rate and the life time, namely, life metabolic energy, is proportional to the mass of the living organism. The origin of the scaling rules for environmental organizing systems is as follows: (1) the scaling rules for internal energy, activation energy and free energy as a function of temperature and mass of a mole of molecules. (2) The majority of species of the living organisms have the same molecules such as polysaccharides, lipids, proteins and nucleic acids in nearly same the ratio. (3) The internal energy of reactants in living organisms is equilibrium with the internal energy of water. Then, the integrated metabolic energy over the synthesizing time depends on internal energy of water and is proportional to mass M, despite the synthesizing time of the system depending on reaction rate. The proportional constant is obtained based on the thermodynamics for fundamental living organisms such as unicellular organisms and plants. Information on the environmental organizing system is also discussed.