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.     

Egg mass and incubation period allometry in birds and reptiles: effects of phylogeny

Here we test the hypothesis that the relationship between egg mass at oviposition (IEM) and incubation period ( I _p) is a function of the taxonomic relatedness of bird and reptile species. Allometric relationships between IEM and I _p were examined for 1525 bird species and 201 reptilian species. Treating species as independent data revealed the allometric exponent linking I _p to IEM to be 0.234 for birds and 0.138 for reptiles. However, ANCOVA revealed that within both birds and reptiles the elevation and slope of the regression lines were dependent on the taxonomic order studied, indicating that the exponents were confounded by the phylogenetic relatedness of species. Thus, allometric exponents were recalculated based on the method of comparative analysis using independent contrasts. This technique revealed that the allometric exponent in both birds and reptiles was confounded by phylogeny. In birds the allometric relationship between I _p and IEM was almost halved to 0.122, whereas in reptiles the exponent increased to 0.185. Importantly, the results demonstrate that some results of allometric analyses can be artefacts of the method of analysis of the dataset. That for bird eggs I _p is not determined in large part by egg mass allows new questions to be posed regarding the ecological and physiological factors affecting the length of incubation, and hence rates of embryonic growth, for different taxa and habitats.     

Wing-bone length allometry in birds

A comparative analysis using both independent contrasts (CAIC) and a species level analysis was used to investigate the allometric scaling of avian wing-bone lengths. Total arm ( ta =humerus+ulna+manus) scaled with positive allometry as body mass ( M )^0.37–0.39. Similarly, and in accordance with previous studies, wing-span ( b ) was positively allometric, but CAIC suggested a lower allometric exponent ( M ^0.35) than found using species as independent data points ( M ^0.39). Contrary to previous studies, individual wing-bones appear to scale with similar exponents against M and scale isometrically with ta . In addition to a general trend for larger birds to have longer wings, wing-bones and ta , their ta was a larger proportion of their b . A detailed study of primary feather length and elbow joint angle across a wide range of bird species and bird size, however, is required before a conclusive explanation for this increase in ta relative to b in larger birds can be established. Scaling equations are presented that can be used to predict M , ta and b from individual wing-bone lengths, which may be of use to palaeontologists wishing to reconstruct whole animals from single bones.     

Allometry of human fertility and energy use

The flux of energy and materials constrains all organisms, and allometric relationships between rates of energy consumption and other biological rates are manifest at many levels of biological organization. Although human ecology is unusual in many respects, human populations also face energetic constraints. Here we present a model relating fertility rates to per capita energy consumption rates in contemporary human nations. Fertility declines as energy consumption increases with a scaling exponent of ?1/3 as predicted by allometric theory. The decline may be explained by parental trade‐offs between the number of children and the energetic investment in each child. We hypothesize that the ?1/3 exponent results from the scaling properties of the networked infrastructure that delivers energy to consumers. This allometric analysis of human fertility offers a framework for understanding the demographic transition to smaller family sizes, with implications for human population growth, resource use and sustainability.     

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.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

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.     

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.     

Scaling of respiratory variables and the breathing pattern in birds: an allometric and phylogenetic approach

Allometric equations can be useful in comparative physiology in a number of ways, not the least of which include assessing whether a particular species deviates from the norm for its size and phylogenetic group with respect to some specific physiological process or determining how differences in design among groups may be reflected in differences in function. The allometric equations for respiratory variables in birds were developed 30 yr ago by Lasiewski and Calder and presented as "preliminary" because they were based on a small number of species. With the expanded data base now available to reconstruct these allometries and the call for taking account of the nonindependence of species in this process through a phylogenetically independent contrasts (PIC) approach, we have developed new allometric equations for respiratory variables in birds using both the traditional and PIC approaches. On the whole, the new equations agree with the old ones with only minor changes in the coefficients, and the primary difference between the traditional and PIC approaches is in the broader confidence intervals given by the latter. We confirm the lower VE/VO2 ratio for birds compared to mammals and observe a common scaling of inspiratory flow and oxygen consumption for birds as has been reported for mammals. Use of allometrics and comparisons among avian groups are also discussed.     

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     

7种木本植物的分支指数与代谢指数

West、Brown和Enquist提出的植物分形网络模型(简称WBE模型)认为: 植物的分支指数(1/a, 1/b)决定植物的代谢指数, 当分支指数1/a、1/b分别为理论值2.0、3.0时, 代谢速率与个体大小的3/4次幂成正比, 但是恒定的3/4代谢指数并不能全面地反映植物的代谢情况。基于分支指数的协同变化, Price、Enquist和Savage对WBE模型进行扩展, 提出植物分支参数协同变化模型(简称PES模型)。该文借助于PES模型分析了7种木本植物的分支指数和代谢指数。结果表明: 物种间叶面积与叶生物量呈异速生长关系, 基于叶面积得到的分支指数1/a和代谢指数θ在物种间无显著差异, 基于叶生物量得到的分支指数1/a、1/b和代谢指数θ在物种间均存在显著差异, 但基于叶面积和叶生物量分别拟合出的整体分支指数1/a、1/b和代谢指数θ与理论值均无显著差异, 且用叶面积作为代谢速率的替代指标比用叶生物量分析得出的代谢指数与理论值更接近。今后研究应当关注植物叶面积与叶生物量的异速生长关系对植物代谢速率及相关功能特性的影响。     

Branching and metabolic exponents in seven woody plants

West、Brown和Enquist提出的植物分形网络模型(简称WBE模型)认为: 植物的分支指数(1/a, 1/b)决定植物的代谢指数, 当分支指数1/a、1/b分别为理论值2.0、3.0时, 代谢速率与个体大小的3/4次幂成正比, 但是恒定的3/4代谢指数并不能全面地反映植物的代谢情况。基于分支指数的协同变化, Price、Enquist和Savage对WBE模型进行扩展, 提出植物分支参数协同变化模型(简称PES模型)。该文借助于PES模型分析了7种木本植物的分支指数和代谢指数。结果表明: 物种间叶面积与叶生物量呈异速生长关系, 基于叶面积得到的分支指数1/a和代谢指数θ在物种间无显著差异, 基于叶生物量得到的分支指数1/a、1/b和代谢指数θ在物种间均存在显著差异, 但基于叶面积和叶生物量分别拟合出的整体分支指数1/a、1/b和代谢指数θ与理论值均无显著差异, 且用叶面积作为代谢速率的替代指标比用叶生物量分析得出的代谢指数与理论值更接近。今后研究应当关注植物叶面积与叶生物量的异速生长关系对植物代谢速率及相关功能特性的影响。     

Model selection and logarithmic transformation in allometric analysis

The standard approach to most allometric research is to gather data on a biological function and a measure of body size, convert the data to logarithms, display the new values in a bivariate plot, and then fit a straight line to the transformations by the method of least squares. The slope of the fitted line provides an estimate for the allometric (or scaling) exponent, which often is interpreted in the context of underlying principles of structural and functional design. However, interpretations of this sort are based on the implicit assumption that the original data conform with a power function having an intercept of 0 on a plot with arithmetic coordinates. Whenever this assumption is not satisfied, the resulting estimate for the allometric exponent may be seriously biased and misleading. The problem of identifying an appropriate function is compounded by the logarithmic transformations, which alter the relationship between the original variables and frequently conceal the presence of outliers having an undue influence on properties of the fitted equation, including the estimate for the allometric exponent. Much of the current controversy in allometric research probably can be traced to substantive biases introduced by investigators who followed standard practice. We illustrate such biases with examples taken from the literature and outline a general methodology by which the biases can be minimized in future research.     

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.     

Scaling of swim speed in breath-hold divers

1. Breath-hold divers are widely assumed to descend and ascend at the speed that minimizes energy expenditure per distance travelled (the cost of transport (COT)) to maximize foraging duration at depth. However, measuring COT with captive animals is difficult, and empirical support for this hypothesis is sparse. 2. We examined the scaling relationship of swim speed in free-ranging diving birds, mammals and turtles (37 species; mass range, 0·5-90,000 kg) with phylogenetically informed statistical methods and derived the theoretical prediction for the allometric exponent under the COT hypothesis by constructing a biomechanical model. 3. Swim speed significantly increased with mass, despite considerable variations around the scaling line. The allometric exponent (0·09) was statistically consistent with the theoretical prediction (0·05) of the COT hypothesis. 4. Our finding suggests a previously unrecognized advantage of size in divers: larger animals swim faster and thus could travel longer distance, search larger volume of water for prey and exploit a greater range of depths during a given dive duration. 5. Furthermore, as predicted from the model, endotherms (birds and mammals) swam faster than ectotherms (turtles) for their size, suggesting that metabolic power production limits swim speed. Among endotherms, birds swam faster than mammals, which cannot be explained by the model. Reynolds numbers of small birds (<2 kg) were close to the lower limit of turbulent flow (～ 3 × 10(5) ), and they swam fast possibly to avoid the increased drag associated with flow transition.     

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.     

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

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

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.