A comparison of methods for fitting allometric equations to field metabolic rates of animals

We re-examined data for field metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for fitting the allometric equation can lead to very different estimates for the allometric coefficient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line fitted to logarithms of the data. Another two-parameter power function was then generated for each data-set by non-linear regression on values in the original arithmetic scale. Allometric equations obtained by non-linear regression described the metabolic rates of all animals in the samples. Equations estimated by back-transformation from logarithms, on the other hand, described the metabolic rates of small species but not large ones. Thus, allometric equations estimated in the traditional way for field metabolic rates of varanids and marsupials do not have general importance because they do not characterize rates for species spanning the full range in body size. Logarithmic transformation of predictor and response variables creates new distributions that may enable investigators to perform statistical analyses in compliance with assumptions underlying the tests. However, statistical models fitted to transformations should not be used to estimate parameters of equations in the arithmetic domain because such equations may be seriously biased and misleading. Allometric analyses should be performed on values expressed in the original scale, if possible, because this is the scale of interest.     

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.     

Allometry and prediction in hominoids: a solution to the problem of intervening variables.

To avoid misinterpretation of allometric exponents determined from interspecific allometric comparisons, specific conditions must be met with respect to the common reference variable. Body weight is considered to be the best general indication of overall size and is hence widely acknowledged to be the most suitable reference variable. However, because of the paucity of recorded body weights for museum specimens, various comparative studies have used other size indicators as intervening variables, although the allometric relationships to body size/weight were often unknown and possibly differed between species. Because of differences in the scaling properties of alternative intervening variables across the species investigated, conflicting conclusions may be drawn if different variables are chosen as substitutes for overall size. This is illustrated with two examples. In this study, series of skeletons with associated body weights of Gorilla, Pan, Pongo, and Homo were investigated. Both ontogenetic and static adult allometric relationships between several widely used reference variables and body weight were determined. Neither these variables nor additional estimators investigated in this study displayed allometric exponents and coefficients similar enough across species to justify direct interspecific comparison. To generate an alternative size estimator for both ontogenetic and static interspecific investigations, equations for combined sexes were derived to predict body weight from various long bone dimensions for individual hominoid species. From a total of 25 predictors, 12 prediction equations per species (six for nonadults and six for adults) were selected according to their relative suitability for reliable prediction of body weight. It is shown that the derived reference variable "predicted body weight" avoids problems of intervening variables, is valid for any interspecific ontogenetic and static allometric comparison, and displays less fluctuation in comparison to actual body weight.     

Resting metabolic rates of two orbweb spiders: a first approach to evolutionary success of ecribellate spiders

Spiders are considered conservative with regard to their resting metabolic rate, presenting the same allometric relation with body mass as the majority of land-arthropods. Nevertheless, web-building is thought to have a great impact on the energetic metabolism, and any modification that affects this complex behavior is expected to have an impact over the daily energetic budget. We analyzed the possibility of the presence of the cribellum having an effect on the allometric relation between resting metabolic rate and body mass for an ecribellate species (Zosis geniculata) and a cribellate one (Metazygia rogenhoferi), and employed a model selection approach to test if these species had the same allometric relationship as other land-arthropods. Our results show that M. rogenhoferi has a higher resting metabolic rate, while Z. geniculata fitted the allometric prediction for land arthropods. This indicates that the absence of the cribellum is associated with a higher resting metabolic rate, thus explaining the higher promptness to activity found for the ecribellate species. If our result proves to be a general rule among spiders, the radiation of Araneoidea could be connected to a more energy-consuming life style. Thus, we briefly outline an alternative model of diversification of Araneoidea that accounts for this possibility.     

Allometry and catastrophic regime shifts in food chains

Population dynamics can reflect the body mass distribution of species because there is an allometric relationship between the average body mass of species and its metabolic timescale. Since predators are generally larger than their prey, a hierarchical structure from fast timescales to slow timescales can be a general structure in food webs. In this paper, we show that changes of the metabolic timescale ratio can cause catastrophic shifts. Then, we investigate a two-dimensional parameter space with the timescale ratio and the carrying capacity of basal species, and reveal that the timescale ratio characterizes the response of the system to environmental variation. Finally, in a bistable regime, we try to clarify the relationship between the trophic position of a species and the extent to which the species induces attractor switching. We saw that, in a 4-species food chain, top predators and second consumers induce attractor switching easily compared to first consumers and basal species.     

Postcanine tooth size in female primates

The results of many allometric studies of postcanine tooth size in mammals have not corresponded to expectations of tooth size based on energy requirements and dental function. The purpose of this study is to investigate the relationship between postcanine occlusal surface area, body size, and the metabolic demands of pregnancy and lactation in female primates. Tooth and body sizes from 38 primate species were taken from the literature to test two hypotheses: 1) females should have relatively larger teeth than males in order to masticate additional food for the energetic costs of reproduction; 2) taxa with the largest neonatal size (a measure of average metabolic costs of pregnancy and lactation) should have females with a greater degree of relative dental enlargement. The results show that relatively large female teeth are not found consistently in primate species. Females have less occlusal surface area than expected on the basis of the male tooth and body size regression in 21% of the species, and there is no correlation between relative female tooth size and relative newborn size across higher primate taxa. The degree of female dental enlargement is most closely related to degree of sexual dimorphism in body weight. The correlation between degree of body weight dimorphism and relatively larger postcanine teeth in females than in males is 0.87 in the 38 species. Species that are monomorphic in weight tend to be monomorphic in tooth size even though females apparently require more food than males.(ABSTRACT TRUNCATED AT 250 WORDS)     

Gill surface area provides a clue for the respiratory basis of brain size in the blacktip shark (Carcharhinus limbatus)

Brain size varies dramatically, both within and across species, and this variation is often believed to be the result of trade-offs between the cognitive benefits of having a large brain for a given body size and the energetic cost of sustaining neural tissue. One potential consequence of having a large brain is that organisms must also meet the associated high energetic demands. Thus, a key question is whether metabolic rate correlates with brain size. However, using metabolic rate to measure energetic demand yields a relatively instantaneous and dynamic measure of energy turnover, which is incompatible with the longer evolutionary timescale of changes in brain size within and across species. Morphological traits associated with oxygen consumption, specifically gill surface area, have been shown to be correlates of oxygen demand and energy use, and thus may serve as integrated correlates of these processes, allowing us to assess whether evolutionary changes in brain size correlate with changes in longer-term oxygen demand and energy use. We tested how brain size relates to gill surface area in the blacktip shark Carcharhinus limbatus. First, we examined whether the allometric slope of brain mass (i.e., the rate that brain mass changes with body mass) is lower than the allometric slope of gill surface area across ontogeny. Second, we tested whether gill surface area explains variation in brain mass, after accounting for the effects of body mass on brain mass. We found that brain mass and gill surface area both had positive allometric slopes, with larger individuals having both larger brains and larger gill surface areas compared to smaller individuals. However, the allometric slope of brain mass was lower than the allometric slope of gill surface area, consistent with our prediction that the allometric slope of gill surface area could pose an upper limit to the allometric slope of brain mass. Finally, after accounting for body mass, individuals with larger brains tended to have larger gill surface areas. Together, our results provide clues as to how fishes may evolve and maintain large brains despite their high energetic cost, suggesting that C. limbatus individuals with a large gill surface area for their body mass may be able to support a higher energetic turnover, and, in turn, a larger brain for their body mass.     

Standard Metabolism and Macrotaxonomy of Crustaceans

The influence of temperature and other environmental factors on the rate of oxygen consumption has been studied in adult crustaceans. The allometric relationship between respiration and body weight was calculated for 15 crustacean orders on the basis of published data on the standard metabolic rate and body weight in 225 crustacean species. The macrotaxonomy of the studied crustacean orders was proposed on the basis of the obtained values of coefficient a from the allometric relationship.     

Effects of housing density and cage floor space on C57BL/6J mice

The Guide for the Care and Use of Laboratory Animals (the Guide) is widely accepted as the housing standard by most Institutional Animal Care and Use Committees. The recommendations are based on best professional judgment rather than experimental data. Current efforts are directed toward replacing these guidelines with data-driven, species-appropriate standards. Our studies were undertaken to determine the optimum housing density for C57BL/6J mice, the most commonly used inbred mouse strain. Four-week-old mice were housed for 8 weeks at four densities (the recommended approximately 12 in2 [ca. 77.4 cm2]/mouse down to 5.6 in2 [ca. 36.1 cm2]/mouse) in three cage types with various amounts of floor space. Housing density did not affect a variety of physiologic parameters but did affect certain micro-environmental parameters, although these remained within accepted ranges. A second study was undertaken housing C57BL/6J mice with as little as 3.2 in2/mouse (ca. 20.6 cm2). The major effect was elevated ammonia concentrations that exceeded limits acceptable in the workplace at increased housing densities; however, the nasal passages and eyeballs of the mice remained microscopically normal. On the basis of these results, we conclude that C57BL/6J mice as large as 29 g may be housed with 5.6 in2 of floor space per mouse. This area is approximately half the floor space recommended in the Guide. The role of the Guide is to ensure that laboratory animals are well treated and housed in a species-appropriate manner. Our data suggest that current policies could be altered in order to provide the optimal habitation conditions matched to this species' social needs.     

Causes of variation in wing loading among Drosophila species

We examined influences on wing and body size in 11 species (12 strains) of Drosophila. Six measures of wing length and width were closely correlated with wing area and suggested little variation in wing shape among the species. Among ten species wing loading, an important factor in flight costs and manoeuvrability, increased as body mass increased at a rate consistent with expectations from allometric scaling of wing area and body mass to body length. Intraspecific variation in wing loading showed similar relationships to body mass. Density and temperature during larval development influenced wing loading through general allometric relations of body size and wing area. Temperature during the pupal stage, but not during wing hardening after eclosion, influenced wing area independently of body size. Wing area increased as growth temperature decreased. Individuals reared at cooler temperatures thus compensated for a potential allometric increase in wing loading by differentially enlarging the wing area during pupal development.     

Ontogenic growth of the haemopoietic stem cell pool in humans

Recently, the size of the active stem cell pool has been predicted to scale allometrically with the adult mass of mammalian species with a 3/4 power exponent, similar to what has been found to occur for the resting metabolic rate across species. Here we investigate the allometric scaling of human haemopoietic stem cells (HSCs) during ontogenic growth and predict a linear scaling with body mass. We also investigate the allometric scaling of resting metabolic rate during growth in humans and find a linear scaling with mass similar to that of the haemopoietic stem cell pool. Our findings suggest a common underlying organizational principle determining the linear scaling of both the stem cell pool and resting metabolic rate with mass during ontogenic growth within the human species, combined with a 3/4 scaling with adult mass across mammalian species. It is possible that such common principles remain valid for haemopoiesis in other mammalian species.     

On the definition of variables in studies of primate dental allometry

Cranial and dental measurements are taken on 253 adult female primates from 32 species. Regression equations are calculated to determine allometric relationships between anterior tooth size, posterior tooth size, and body size. When cranial length or skull length is used as the measure of general size, the results of the equations differ from when body weight is the reference dimension. Similarly, using different definitions of posterior tooth size (such as mandibular second molar length and maxillary postcanine area) alters results substantially. The same occurs with different definitions of anterior tooth size. It has been common in studies of primate dental allometry to generalize from the specific variables measured to broad functional interpretations. However, highly correlated variables cannot be substituted one for another in allometric analyses without important changes in the results of the equation. Interpretation of allometric data is more highly restricted to the precise variables measured in a particular study than has been generally recognized.     

Structural allometry of the femur and tibia in Hominoidea and Macaca

Allometric scaling relationships between body weight, bone length, and cross-sectional dimensions of the lower limb bones which measure structural strength and rigidity (area, second moments of area) are investigated in Homo, Gorilla, Pan, Pongo, and Macaca. Cross-sectional dimensions are slightly positively allometric and highly correlated with body weight; within-bone proportional differences are largely a result of differences in relative bone length to body weight. Orangutans show the greatest deviation from general scaling relationships between lower limb bone structural strength and weight, probably due to habitual upper limb suspension. Formulas for the prediction of weight from cross-sectional dimensions are presented.     

Comparative allometric investigations on the skulls of wild cavies (Cavia aperea) versus domesticated guinea pigs (C. aperea f. porcellus) with comments on the domestication of this species

Bivariate allometric calculations were performed to quantitatively compare skulls of wild cavies with domesticated guinea pigs. Descendents of wild caught Cavia aperea from eastern regions of the species’ distribution area were used, as well as unselected domesticated breeds of guinea pigs differing in outer appearance. The individuals of both groups were kept under similar environmental conditions. Altogether 19 parameters on the skulls and the body weights were used for the analyses. These parameters were studied in relation to greatest skull length and to body size. As a general result the diverse parameters are in most cases significantly different between both groups which is interpreted as a special result of unconsciously selected and genetically determined intraspecific changes concomitant with domestication. The skull does not change in total under the domestication process but in a mosaic manner. However, for the mosaic changes of the diverse parameters in relation to skull length a different picture is valid as related to body weight. This is caused by the fact that the skull of guinea pigs is around 5% shorter independent of the body size, a common effect of domestication also described for other species. Thus, skull length is not an appropriate parameter for body size with respect to such intraspecific investigations, although normally used for the characterization of species in interspecific comparisons of museum materials.Altogether in relation to body weight most of the parameters describing the fascial portion of the skull are shorter in the guinea pig, especially the palatine, the diastema and the mandible but also the nasalia and frontalia lengths as well as the breadth of the rostrum and the zygomaticum are smaller. Most of the occipital skull measures are additionally smaller in the guinea pigs. This is clearly the case for the length and the breadth of the braincase and for the tympanic bulla. The braincase volume is 16.2% smaller, a value only slightly different when compared with the degree of brain size decrease due to domestication as reported for this species in other investigations.     

Rotational distortion in conventional allometric analyses

Three data sets from the recent literature were submitted to new analyses to illustrate the rotational distortion that commonly accompanies traditional allometric analyses and that often causes allometric equations to be inaccurate and misleading. The first investigation focused on the scaling of evaporative water loss to body mass in passerine birds; the second was concerned with the influence of body size on field metabolic rates of rodents; and the third addressed interspecific variation in kidney mass among primates. Straight lines were fitted to logarithmic transformations by Ordinary Least Squares and Generalized Linear Models, and the resulting equations then were re-expressed as two-parameter power functions in the original arithmetic scales. The re-expressed models were displayed on bivariate graphs together with tracings for equations fitted directly to untransformed data by nonlinear regression. In all instances, models estimated by back-transformation failed to describe major features of the arithmetic distribution whereas equations fitted by nonlinear regression performed quite well. The poor performance of equations based on models fitted to logarithms can be traced to the increased weight and leverage exerted in those analyses by observations for small species and to the decreased weight and leverage exerted by large ones. The problem of rotational distortion can be avoided by performing exploratory analysis on untransformed values and by validating fitted models in the scale of measurement.     

Cephalisation bei Caniden

Cephalisation in Canidae Studied were the intraspecific and interspecific relationships between brain weight and body weight in Canidae. Inclination values of the allometric lines: intraspecific – 0,25, interspecific 0,571. Most of the studied species have nearly the same degree of cephalisation, deviations from the interspecific allometric line are small; the cephalisation of Nyctereutes and Otocyon is less developed than in the other canid species. There is no difference in cephalisation between most canids and felids. Mustelids show a high variability in cephalisation. Criticized were the data of Bauchot (1985) and Gittleman (1986) on brain weight and body weight.     

Incisor size and diet revisited: The view from a platyrrhine perspective

Allometric relationships between incisor size and body size were determined for 26 species of New World primates. While previous studies have suggested that the incisors of Old World primates, and anthropoids in general, scale isometrically with body size, the data presented here indicate a negative allometric relationship between incisor size and body size among New World species. This negative allometry was exhibited by platyrrhines when either upper or lower incisor row length was regressed against body weight, and when either least-squares or bivariate principal axis equations were used. When upper incisor length was plotted against skull length, negative allometry could be sustained using both statistical techniques only when the full sample of 26 species was plotted. The choice of variables to represent incisor size and body size, and the choice of a statistical technique to effect the allometric equation, had a more pronounced impact on the location of individual species with regard to lines of best fit. Platyrrhines as a group have smaller incisors relative to body size than do catarrhines, regardless of diet. Among New World primates, small incisors represent a plausible primitive condition; species with relatively large incisors manifest a phyletic change associated with a dietary shift to foods that require increased incisal preparation. The opposite trend characterizes Old World primates. In spite of the taxonomic differences in relative incisor size between platyrrhine and catarrhine primates, inferences about diet derived from an allometric equation for all anthropoids should prove reliable as long as the species with unknown diet does not lie at the upper end of the body size range for platyrrhines or catarrhines.     

Static allometry of unicellular green algae: scaling of cellular surface area and volume in the genus Micrasterias (Desmidiales)

The surface area‐to‐volume ratio of cells is one of the key factors affecting fundamental biological processes and, thus, fitness of unicellular organisms. One of the general models for allometric increase in surface‐to‐volume scaling involves fractal‐like elaboration of cellular surfaces. However, specific data illustrating this pattern in natural populations of the unicellular organisms have not previously been available. This study shows that unicellular green algae of the genus Micrasterias (Desmidiales) have positive allometric surface‐to‐volume scaling caused by changes in morphology of individual species, especially in the degree of cell lobulation. This allometric pattern was also detected within most of the cultured and natural populations analysed. Values of the allometric S:V scaling within individual populations were closely correlated to the phylogenetic structure of the clade. In addition, they were related to species‐specific cellular morphology. Individual populations differed in their allometric patterns, and their position in the allometric space was strongly correlated with the degree of allometric S:V scaling. This result illustrates that allometric shape patterns are an important correlate of the capacity of individual populations to compensate for increases in their cell volumes by increasing the surface area. However, variation in allometric patterns was not associated with phylogenetic structure. This indicates that the position of the populations in the allometric space was not evolutionarily conserved and might be influenced by environmental factors.     

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.     

代谢异速生长理论及其在微生物生态学领域的应用

新陈代谢是生物的基本生理过程,影响生物在不同环境中参与物质循环和能量转化的过程.代谢速率作为生物体重要的生命过程指标,几乎影响所有的生物活性速率,且在很多研究中均表现出异速生长现象.所谓代谢异速是指生物体代谢速率与其个体大小(或质量)之间存在的幂函数关系.代谢异速生长理论的提出,从机制模型角度解释了代谢异速关系这一普遍存在的生命现象.该理论利用分形几何学及流体动力学等原理,从生物能量学角度阐释了异速生长规律的机理,证实了3/4权度指数的存在;但同时有研究表明,权度指数因环境因素等影响处于2/3-1范围之间而非定值.随着研究工作的深入,代谢异速生长理论研究从起初的宏观动植物领域拓展到了微生物领域,在研究微生物的代谢异速生长理论时,可将微生物的可操作分类单元(Operational taxonomic unit,OTU)或具有特定功能的功能群视为一个微生物个体,基于其遗传多样性和功能多样性特征进行表征,以便于将微生物群落多样性与其生态功能性联系起来,使该理论在微生物生态学领域得到有效的补充和完善.尽管细菌具有独特的生物学特性,但与宏观生物系统中观测到的现象表现出明显的一致性.有研究表明,3个农田土壤细菌基于遗传多样性的OTU数的平均周转率分别为0.71、0.80和0.84,介于2/3与1之间,可能与生物代谢异速指数有一定关联,为微生物代谢异速指数的研究提出了一个参考解决方案.鉴于微生物个体特征和生物学特性,在分析代谢速率与个体大小关系中,从微生物单位个体的定义、个体大小表征到计量单位的统一,仍需更多的理论支持.分析了代谢异速生长理论在微生物与生态系统功能关系研究中的可能应用,延伸了该理论的应用范围,并对尚待加强的研究问题进行了评述和展望.