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.     

Dichotomy of eutherian reproduction and metabolism

How anatomical, physiological and ecological (life history) features scale with body mass is a fundamental question in biology. There is an ongoing debate in the scientific literature whether allometric scaling follows a universal pattern that can be described in a single model, or differs between groups. However, recently some analyses were published demonstrating a change in scaling across the body mass range: brain‐size allometry of mammals indicates that scaling follows a curvilinear pattern in double‐logarithmic space, and a quadratic pattern in double‐logarithmic space was found in one of the largest physiological datasets, on basal metabolic rate (MR) in mammals. Here, we analysed a variety of independent datasets on anatomical, physiological and ecological characteristics in mammals, birds and reptiles to answer the question whether the quadratic scaling is a universal biological law, or a pattern unique to mammals. The pattern was present in mammalian basal and field MR, brain size, and reproduction parameters, but neither in other organ allometries in mammals, nor in the scaling of MR in birds and reptiles. However, the curvature was better explained by separate allometric scaling of three different mammalian reproduction strategies: marsupials, and eutherian mammals with one and with many offspring. The two latter strategies are distributed unequally over the body mass range in eutherian mammals. Our findings show that a quadratic model, as well as a traditional allometric model with a universal scaling exponent (such as 0.67 or 0.75), may be inappropriate in mammals as they are a result of different scalings within these three reproductive groups. We propose that the observed distribution pattern is the result of the eutherian mammal clade's uniquely pronounced dichotomy of reproductive strategies.     

Brain size, development and metabolism in birds and mammals

Recent hypotheses that variation in brain size among birds and mammals result from differences in metabolic allocation during ontogeny are tested.
Indices of embryonic and post-embryonic brain growth are defined. Precocial birds and mammals have high embryonic brain growth indices which are compensated for by low post-embryonic indices (with the exception of Homo supiens ). In contrast, altricial birds and mammals have low embryonic and high post-embryonic indices. Altricial birds have relatively small brains at hatching and develop relatively large brains as adults, but among mammals there is no equivalent correlation between variation in adult relative brain sizes and state of neonatal development.
Compensatory brain development in both birds and mammals is associated with compensatory parental metabolic allocation. In comparison with altricial development, precocial development is characterized by higher levels of brain growth and parental metabolic allocation prior to hatching or birth and lower levels subsequently. Differences between degrees of postnatal investment by the parents in the young of precocial birds versus precocial mammals may result in the different patterns of adult brain size associated with precociality versus altriciality in the two groups.
The allometric exponent scaling brain on body size differs among taxonomic levels in birds. The exponent is higher for some parts of the brain than others, irrespective of taxonomic level. Unlike mammals, the exponents for birds do not show a general increase with taxonomic level. These pattcrns call into question recent interpretations of the allometric exponent in birds. and the reason for changes in exponent with taxonomic level.     

Scaling of Na+,K+-ATPase molecular activity and membrane fatty acid composition in mammalian and avian hearts

We have examined Na(+),K(+)-ATPase molecular activity and membrane fatty acid composition in the heart of six mammalian and eight avian species ranging in size from 30 g in mice to 280 kg in cattle and 13 g in zebra finches to 35 kg in emus, respectively. Na(+),K(+)-ATPase activity scaled negatively with body mass in both mammals and birds. In small mammals, the elevated enzyme activity was related to allometric changes in both the concentration and molecular activity (turnover rate) of Na(+),K(+)-ATPase enzymes, while in small birds, higher Na(+),K(+)-ATPase activity appeared to result primarily from an increased molecular activity of individual enzymes. The unsaturation index of cardiac phospholipids scaled negatively with body mass in both groups, while a significant allometric increase in monounsaturate content was observed in the larger mammals and birds. In particular, the relative content of the highly polyunsaturated docosahexaenoic acid (22:6n-3) displayed the greatest variation, scaling negatively with body mass and varying greater than 40-fold in both mammals and birds. Membrane fatty acid profile was correlated with Na(+),K(+)-ATPase molecular activity in both mammals and birds, suggesting a potential association between membrane lipid composition and the activity of membrane-bound enzymes in the hearts of endotherms.     

Resting breathing frequency in aquatic birds: a comparative analysis with terrestrial species

Several studies have indicated that in birds breathing frequency ( f , breaths min⁻¹) scales to the −1/3 of body weight ( W , kg); this is different from the −1/4 of mammals. We wondered if this discrepancy was due to the peculiar scaling pattern of aquatic birds, as is the case of aquatic mammals. In fact, we had noted previously that the allometric scaling of f differs considerably between aquatic and terrestrial mammals, respectively, W ^−0.42 and W ^−0.25. Measurements of f were obtained in 48 aquatic birds of 22 species and in 35 terrestrial birds of 27 species, during resting conditions on land. Additional data from 11 aquatic and 14 terrestrial species, different from the ones measured, were obtained from the literature. The allometric curve of all species combined (terrestrial and aquatic, n =74) was f =13.3 W ^−0.36, similar to what is reported in previous studies. However, the allometric curve of the aquatic species ( n =33, f =14.5 W ^−0.56) differed greatly ( P <0.001) from that of the terrestrial species ( n =41, f =13.4 W ^−0.26). On average, f of aquatic birds of the 3–5 kg range was 63%, and that of birds of larger size was 57%, of the values of terrestrial birds of similar W . We conclude that, as in mammals, also in terrestrial birds f scales to the −1/4 exponent of W . The similarity of the scaling patterns of f between aquatic birds and mammals suggests a common breathing adaptation to life in the aquatic environment irrespective of phylogenetic relations.     

A phylogenetic analysis of the allometry of diving

The oxygen store/usage hypothesis suggests that larger animals are able to dive for longer and hence deeper because oxygen storage scales isometrically with body mass, whereas oxygen usage scales allometrically with an exponent <1 (typically 0.67-0.75). Previous tests of the allometry of diving tend to reject this hypothesis, but they are based on restricted data sets or invalid statistical analyses (which assume that every species provides independent information). Here we apply information-theoretic statistical methods that are phylogenetically informed to a large data set on diving variables for birds and mammals to describe the allometry of diving. Body mass is strongly related to all dive variables except dive:pause ratio. We demonstrate that many diving variables covary strongly with body mass and that they have allometric exponents close to 0.33. Thus, our results fail to falsify the oxygen store/usage hypothesis. The allometric relationships for most diving variables are statistically indistinguishable for birds and mammals, but birds tend to dive deeper than mammals of equivalent mass. The allometric relationships for all diving variables except mean dive duration are also statistically indistinguishable for all major taxonomic groups of divers within birds and mammals, with the exception of the procellariiforms, which, strictly speaking, are not true divers.     

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.     

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).     

Stoichiometry of endothermy: shifting the quest from nitrogen to carbon

For many animals, notably herbivores, plants are often an inadequate food source given the low content of protein and high content of C-rich material. This conception is mainly based on studies on ectotherms. The validity of this conception for endotherms is unclear given their much higher carbon requirements for maintenance energy metabolism than ectotherms. Applying stoichiometric principles, we hypothesized that endotherms can cope with diets with much higher (metabolizable) carbon to nitrogen ratios than ectotherms. Using empirical data on birds, eutherian mammals, marsupials and reptiles, we compiled and compared measurements and allometric equations for energy metabolism as well as nitrogen requirements. Our analysis supports our hypothesis that plants, and especially their leaves, are generally sufficiently rich in nitrogen to fulfil protein demands in endotherms, at least during maintenance conditions, but less so in ectotherms. This has important implications with respect to community functioning and the evolution of endothermy.     

Projecting human pharmacokinetics of therapeutic antibodies from nonclinical data

The pharmacokinetics (PK) of therapeutic antibodies is determined by target and non-target mediated mechanisms. These antibody-specific factors need to be considered during prediction of human PK based upon preclinical information. Principles of allometric scaling established for small molecules using data from multiple animal species cannot be directly applied to antibodies. Here, different methods for projecting human clearance (CL) from animal PK data for 13 therapeutic monoclonal antibodies (mAbs) exhibiting linear PK over the tested dose ranges were examined: simple allometric scaling (CL versus body weight), allometric scaling with correction factors, allometric scaling based on rule of exponent and scaling from only cynomolgus monkey PK data. A better correlation was obtained between the observed human CL and the estimated human CL based on cynomolgus monkey PK data and an allometric scaling exponent of 0.85 for CL than other scaling approaches. Human concentration-time profiles were also reasonably predicted from the cynomolgus monkey data using species-invariant time method with a fixed exponent of 0.85 for CL and 1.0 for volume of distribution. In conclusion, we expanded our previous work and others and further confirmed that PK from cynomolgus monkey alone can be successfully scaled to project human PK profiles within linear range using simplify allometry and Dedrick plots with fixed exponent.     

Projecting human pharmacokinetics of therapeutic antibodies from nonclinical data: What have we learned?

The pharmacokinetics (PK) of therapeutic antibodies is determined by target and non-target mediated mechanisms. These antibody-specific factors need to be considered during prediction of human PK based upon preclinical information. Principles of allometric scaling established for small molecules using data from multiple animal species cannot be directly applied to antibodies. Here, different methods for projecting human clearance (CL) from animal PK data for 13 therapeutic monoclonal antibodies (mAbs) exhibiting linear PK over the tested dose ranges were examined: simple allometric scaling (CL versus body weight), allometric scaling with correction factors, allometric scaling based on rule of exponent and scaling from only cynomolgus monkey PK data. A better correlation was obtained between the observed human CL and the estimated human CL based on cynomolgus monkey PK data and an allometric scaling exponent of 0.85 for CL than other scaling approaches. Human concentration-time profiles were also reasonably predicted from the cynomolgus monkey data using species-invariant time method with a fixed exponent of 0.85 for CL and 1.0 for volume of distribution. In conclusion, we expanded our previous work and others and further confirmed that PK from cynomolgus monkey alone can be successfully scaled to project human PK profiles within linear range using simplify allometry and Dedrick plots with fixed exponent.Key words: monoclonal antibody, pharmacokinetics, clearance, allometric scaling, species-invariant time method     

Power isn't everything: muscle function and energetic costs during steady swimming in Atlantic cod (Gadus morhua)

Power produced by red myotomal muscles of fish during cruise swimming appears seldom maximized, so we sought to investigate whether economy may impact or dominate muscle function. We measured cost of transport (COT) using oxygen consumption and the strain trajectories and electromyographic activity of red muscle measured at anterior (ANT) and posterior (POST) locations while Atlantic cod (Gadus morhua) swam steadily at speeds between 0.3 and 1.0 body lengths (BL) s(-1). We then measured the power produced by isolated segments of red muscle when activated either as in the swimming cod or such that maximal net power was produced. Patterns of activation during swimming were not optimal for power output and were highly variable between tail beats, particularly at the ANT location and at slow swim speeds. Muscle strain amplitude did not increase until swimming speed reached 0.9 (ANT) versus 0.5 (POST) BL s(-1). These limited power to only 53% (ANT) and 71% (POST) of maximum at slower swim speeds and to 70%-80% of maximum at high swim speeds. COT (resting metabolism subtracted) was minimal at the slowest swim speed, surprisingly, where power was most impaired by activation and strain. Thus, production of powered forces for maneuverability/stability appeared to greatly impact red muscle function during cruise swimming in cod, particularly at slow speeds and in ANT muscle.     

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.     

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).     

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

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

Phylogenetic analysis of the allometric scaling of therapeutic regimes for birds

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

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.     

Near Isometric Biomass Partitioning in Forest Ecosystems of China

Based on the isometric hypothesis, belowground plant biomass (M_B) should scale isometrically with aboveground biomass (M_A) and the scaling exponent should not vary with environmental factors. We tested this hypothesis using a large forest biomass database collected in China. Allometric scaling functions relating M_B and M_A were developed for the entire database and for different groups based on tree age, diameter at breast height, height, latitude, longitude or elevation. To investigate whether the scaling exponent is independent of these biotic and abiotic factors, we analyzed the relationship between the scaling exponent and these factors. Overall M_B was significantly related to M_A with a scaling exponent of 0.964. The scaling exponent of the allometric function did not vary with tree age, density, latitude, or longitude, but varied with diameter at breast height, height, and elevation. The mean of the scaling exponent over all groups was 0.986. Among 57 scaling relationships developed, 26 of the scaling exponents were not significantly different from 1. Our results generally support the isometric hypothesis. M_B scaled near isometrically with M_A and the scaling exponent did not vary with tree age, density, latitude, or longitude, but increased with tree size and elevation. While fitting a single allometric scaling relationship may be adequate, the estimation of M_B from M_A could be improved with size-specific scaling relationships.     

The allometric approach to species differences in brain size

Allometric methods can be used to test quantitative theories of the relationship between brain size and body size across species, and to search for ecological, behavioural, life history, and ontogenetic correlates of brain size. Brain size scales with an allometric exponent of around 0.75 against body size across mammals, but is closer to 0.56 for birds and for reptiles. The slope of the allometric line often varies depending upon the taxonomic level of analysis. However, this phenomenon, at least in mammals, may be a statistical artifact. Brain size for a given body size (relative brain size) varies among orders in birds and mammals, and some dietary associations with relative brain size have been found in particular taxa. Developmental status at birth is the most consistent correlate of relative brain size: precocial neonates have larger brains for a given maternal size than altricial neonates in both birds and mammals. Altricial neonates, however, have more brain growth following birth, and in birds also have larger relative adult brain sizes. Energetic explanations for differences in neonatal brain growth, although attractive on theoretical grounds, have largely failed to stand up to empirical tests.     

An exploration of differences in the scaling of life history traits with body mass within reptiles and between amniotes

Allometric relationships linking species characteristics to body size or mass (scaling) are important in biology. However, studies on the scaling of life history traits in the reptiles (the nonavian Reptilia) are rather scarce, especially for the clades Crocodilia, Testudines, and Rhynchocephalia (single extant species, the tuatara). Previous studies on the scaling of reptilian life history traits indicated that they differ from those seen in the other amniotes (mammals and birds), but so far most comparative studies used small species samples and also not phylogenetically informed analyses. Here, we analyzed the scaling of nine life history traits with adult body mass for crocodiles (n = 22), squamates (n = 294), turtles (n = 52), and reptiles (n = 369). We used for the first time a phylogenetically informed approach for crocodiles, turtles, and the whole group of reptiles. We explored differences in scaling relationships between the reptilian clades Crocodilia, Squamata, and Testudines as well as differences between reptiles, mammals, and birds. Finally, we applied our scaling relationships, in order to gain new insights into the degree of the exceptionality of the tuatara's life history within reptiles. We observed for none of the life history traits studied any difference in their scaling with body mass between squamates, crocodiles, and turtles, except for clutch size and egg weight showing small differences between these groups. Compared to birds and mammals, scaling relationships of reptiles were similar for time‐related traits, but they differed for reproductive traits. The tuatara's life history is more similar to that of a similar‐sized turtle or crocodile than to a squamate.