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.     

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.     

Influence of food,body size,and fragmentation on metabolic rate in a sessile marine invertebrate

Metabolic rates vary among individuals according to food availability and phenotype, most notably body size. Disentangling size from other factors (e.g., age, reproductive status) can be difficult in some groups, but modular organisms may provide an opportunity for manipulating size experimentally. While modular organisms are increasingly used to understand metabolic scaling, the potential of feeding to alter metabolic scaling has not been explored in this group. Here, we perform a series of experiments to examine the drivers of metabolic rate in a modular marine invertebrate, the bryozoan Bugula neritina. We manipulated size and examined metabolic rate in either fed or starved individuals to test for interactions between size manipulation and food availability. Field collected colonies of unknown age showed isometric metabolic scaling, but those colonies in which size was manipulated showed allometric scaling. To further disentangle age effects from size effects, we measured metabolic rate of individuals of known age and again found allometric scaling. Metabolic rate strongly depended on access to food: starvation decreased metabolic rate by 20% and feeding increased metabolic rate by 43%. In comparison to other marine invertebrates, however, the increase in metabolic rate, as well as the duration of the increase (known as specific dynamic action, SDA), were both low. Importantly, neither starvation nor feeding altered the metabolic scaling of our colonies. Overall, we found that field‐collected individuals showed isometric metabolic scaling, whereas metabolic rate of size‐manipulated colonies scaled allometrically with body size. Thus, metabolic scaling is affected by size manipulation but not feeding in this colonial marine invertebrate.     

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.     

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.     

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.     

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.     

Models projecting the fate of fish populations under climate change need to be based on valid physiological mechanisms

Some recent modelling papers projecting smaller fish sizes and catches in a warmer future are based on erroneous assumptions regarding (i) the scaling of gills with body mass and (ii) the energetic cost of ‘maintenance’. Assumption (i) posits that insurmountable geometric constraints prevent respiratory surface areas from growing as fast as body volume. It is argued that these constraints explain allometric scaling of energy metabolism, whereby larger fishes have relatively lower mass‐specific metabolic rates. Assumption (ii) concludes that when fishes reach a certain size, basal oxygen demands will not be met, because of assumption (i). We here demonstrate unequivocally, by applying accepted physiological principles with reference to the existing literature, that these assumptions are not valid. Gills are folded surfaces, where the scaling of surface area to volume is not constrained by spherical geometry. The gill surface area can, in fact, increase linearly in proportion to gill volume and body mass. We cite the large body of evidence demonstrating that respiratory surface areas in fishes reflect metabolic needs, not vice versa, which explains the large interspecific variation in scaling of gill surface areas. Finally, we point out that future studies basing their predictions on models should incorporate factors for scaling of metabolic rate and for temperature effects on metabolism, which agree with measured values, and should account for interspecific variation in scaling and temperature effects. It is possible that some fishes will become smaller in the future, but to make reliable predictions the underlying mechanisms need to be identified and sought elsewhere than in geometric constraints on gill surface area. Furthermore, to ensure that useful information is conveyed to the public and policymakers about the possible effects of climate change, it is necessary to improve communication and congruity between fish physiologists and fisheries scientists.     

WBE 模型及其在生态学中的应用：研究概述

介绍了WBE模型,综述了该模型在生态学中的应用进展。WBE模型,以及以该模型为基础的MTE模型,假设生物体为自相似分形网络结构,提出代谢速率和个体大小之间存在3/4指数关系,分别预测了从个体到生物圈多个尺度上的生物属性之间的异速生长关系,而且部分得到了验证。WBE模型的应用涵盖了个体组织生物量、年生长率,种群密度和生态系统单位面积产量、能量流动率等多个方面;即使在生物圈大尺度上,WBE模型也可用来预测试验中无法直接测量的特征变量的属性,如全球碳储量的估算等。至今,关于WBE和MTE模型仍然存在各种褒贬争论,讨论焦点主要集中于模型建立的前提假设以及权度指数的预测。今后的研究工作应规范试验技术和方法,考虑物种多样性和环境等因素的影响,提出符合各类生物的模型结构体系,使其具有更广泛的应用性和预测性。     

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.     

Changes in body temperature influence the scaling of VO2max and aerobic scope in mammals

Debate on the mechanism(s) responsible for the scaling of metabolic rate with body size in mammals has focused on why the maximum metabolic rate (VO2max ) appears to scale more steeply with body size than the basal metabolic rate (BMR). Consequently, metabolic scope, defined as VO2max/BMR, systematically increases with body size. These observations have led some to suggest that VO2max, and BMR are controlled by fundamentally different processes, and to discount the generality of models that predict a single power-law scaling exponent for the size dependence of the metabolic rate. We present a model that predicts a steeper size dependence for VO2max than BMR based on the observation that changes in muscle temperature from rest to maximal activity are greater in larger mammals. Empirical data support the model's prediction. This model thus provides a potential theoretical and mechanistic link between BMR and VO2 max.     

Ontogenetic and interspecific scaling of consumption in insects

The uptake of resources from the environment is a basic feature of all life. Consumption rate has been found to scale with body size with an exponent close to unity across diverse organisms. However, past analyses have ignored the important distinction between ontogenetic and interspecific size comparisons. Using principles of dynamic energy budget theory, we present a mechanistic model for the body mass scaling of consumption, which separates interspecific size effects from ontogenetic size effects. Our model predicts uptake to scale with surface‐area (mass^2/3) during ontogenetic growth but more quickly (between mass^3/4 and mass¹) for interspecific comparisons. Available data for 41 insect species on consumption and assimilation during ontogeny provides strong empirical support for our theoretical predictions. Specifically, consumption rate scaled interspecifically with an exponent close to unity (0.89) but during ontogenetic growth scaled more slowly with an exponent of 0.70. Assimilation rate (consumption minus defecation) through ontogeny scaled more slowly than consumption due to a decrease in assimilation efficiency as insects grow. Our results highlight how body size imposes different constraints on metabolism depending on whether the size comparison is ontogenetic or inter‐specific. Synthesis One of the most robust patterns in biology is the effect of body size on metabolism – a relationship that underlies the rapidly emerging field of metabolic ecology. However, the precise energetic constraints imposed by body size have been notoriously difficult to entangle. Here we show that the constraints imposed on metabolism by body size are different depending on whether the size comparison is ontogenetic or interspecific. Using a single unifying theory of animal metabolism and a newly compiled data set on insect consumption and assimilation rates, we show that interspecific comparisons generally lead to the estimation of higher scaling exponents compared with ontogenetic comparisons. Our results help to explain large variation in estimated metabolic scaling exponents and will encourage future studies in metabolic ecology to make the important distinction between ontogenetic and evolutionary size changes.     

Intraspecific temperature dependence of the scaling of metabolic rate with body mass in fishes and its ecological implications

Metabolism constitutes a fundamental property of all organisms. Metabolic rate is commonly described to scale as a power function of body size and exponentially with temperature, thereby treating the effects of body size and temperature independently. Mounting evidence shows that the scaling of metabolic rate with body mass itself depends on temperature. Across‐species analyses in fishes suggest that the mass‐scaling exponent decreases with increasing temperature. However, whether this relationship holds at the within‐species level has rarely been tested. Here, we re‐analyse data on the metabolic rates of four freshwater fish species, two coregonids and two cyprinids, that cover wide ranges of body masses and their naturally experienced temperatures. We show that the standard metabolic rate of the coregonids is best fit when accounting for a linear temperature dependence of the scaling of metabolic rate with body mass, whereas a constant mass‐scaling exponent is supported in case of the cyprinids. Our study shows that phenotypic responses to temperature can result in temperature‐dependent scaling relationships at the species level and that these responses differ between taxa. Together with previous findings, these results indicate that evolutionarily adaptive and phenotypically plastic responses to temperature affect the scaling of metabolic rate with body mass in fishes.     

Body size in ecological networks

Body size determines a host of species traits that can affect the structure and dynamics of food webs, and other ecological networks, across multiple scales of organization. Measuring body size provides a relatively simple means of encapsulating and condensing a large amount of the biological information embedded within an ecological network. Recently, important advances have been made by incorporating body size into theoretical models that explore food web stability, the patterning of energy fluxes, and responses to perturbations. Because metabolic constraints underpin body-size scaling relationships, metabolic theory offers a potentially useful new framework within which to develop novel models to describe the structure and functioning of ecological networks and to assess the probable consequences of biodiversity change.     

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.     

Metabolic rate and food availability of the Antarctic amphipod <Emphasis Type="Italic">Gondogeneia antarctica</Emphasis> (Chevreux 1906): seasonal variation in allometric scaling and temperature dependence

Among the few existing works on seasonal variation in metabolic rate of polar species, most have been conducted during summer due to logistic constraints and have been focused on species that cease feeding during winter. In this work, we present the first extensive data set on the seasonal variation in metabolic rate of G. antarctica, an abundant amphipod that feeds throughout the year, and its relationship with body size, potential food availability and temperature. We measured the resting metabolic rate (RMR) of groups of individuals during 6 months from late summer through winter at 4 experimental temperatures and for a wide range of body size. RMR had a negative allometric scaling with body size and showed a tendency to increase with temperature as expected. However, temperature and body size effects on RMR showed a significant temporal variation, and an increase in temperature decreased scaling exponents. RMR at the mean seawater temperature throughout the study showed a strong seasonal variation following food availability: RMR decreased from the end of summer through winter, coinciding with a reduction in microphytobenthos stock, but recovered summer values in August, when an epontic algae boom occurred. The seasonal factorial aerobic scope (×2.37) is lower than benthic Antarctic invertebrates that cease feeding during winter, in agreement with what is expected based on theoretical grounds. Results suggest that seasonal variation of RMR would allow G. antarctica to achieve a high efficiency in energy utilization, while maintaining the ability to exploit sudden changes in food supply.     

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).     

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.     

幂指数异速生长机制模型综述

 个体大小对生物的各种生理属性有重要意义, 描述个体大小和生理属性关系的规律叫做异速生长。生物的异速生长通常以幂函数的形 式表示, 在众多的异速生长关系中, Kleiber定律所描述的新陈代谢率和个体大小的3/4幂指数关系最为重要和基本, 解释此有充分数据支持的 定律的机理也最具挑战性。围绕该著名的3/4幂指数异速生长关系, 该文回顾历史上主要的有关模型假说, 并重点介绍1990年代中期以来, 由 West等提出的分形分配网络模型和由其它研究人员建立的代表性模型: 最少载体网络模型、多因理论、最小总熵理论、构造理论、细胞优化生 长理论和能量消耗理论。