Scaling of metabolic rate in the lesser wax moth Achroia grisella does not fit the 3/4‐power law and shows significant sex differences

Allometric scaling of metabolic rates is commonly described as a power function and 0.75 is a widely accepted exponent. The universality of this exponent is in doubt and, particularly for insects, contradictory results have been obtained. Furthermore, sexual differences in scaling exponents are observed for several species that could lead to artefacts when they are not considered in intra‐ and interspecific scaling. Whether the metabolic scaling exponent in the lesser wax moth Achroia grisella differs significantly from 0.75 is tested, as well as whether it differs between the sexes. Adults of this moth neither feed nor drink, rendering them as suitable subjects for a study of metabolic rates. Neglecting sex differences, a metabolic scaling exponent of 0.8 is recorded. However, there are significant differences in metabolic scaling between the sexes. When considered separately, males scale with 0.96 and females with 0.67. Thus, in this species, a scaling exponent of 0.75 does not appear to exist either for males or females. The body size optimization model offers a potential explanation for the sex differences in metabolic scaling, although it remains to be tested in wax moths. With insects in particular, there is the need for more detailed studies on the scaling of metabolic rates that also take sexual differences into account.     

生态学中的尺度问题——尺度上推

尺度推绎是生态学理论和应用的核心。如何在一个异质景观中进行尺度推绎仍然是一个悬而未决的科学难题,是对当今生态学家在全球变化背景下研究环境问题的重大挑战。就目前的研究,一般可分为四大类尺度推绎途径:空间分析法(如分维分析法和小波分析法)、基于相似性的尺度上推方法、基于局域动态模型的尺度上推方法、随机(模型)法。基于相似性的尺度上推方法来源于生物学上的异量关联,可将其思想延伸至空间上,研究物种丰富度、自然河网、地形特征、生态学格局或过程变量和景观指数等。基于局域动态模型的尺度上推方法需要首先确定是否进行跨尺度推绎,以及是否考虑空间单元之间的水平相互作用和反馈,然后再应用具体的方法或途径,如简单聚合法、有效值外推法、直接外推法、期望值外推、显式积分法和空间相互作用模拟法等。随机(模型)法以其它尺度上推方法为基础,根据研究的是单个景观,还是多个景观,采用不同的途径。理解、定量和降低尺度推绎结果的不确定性已经变得越来越重要,但相关研究仍然极少。以上所有有关尺度推绎的方法、途径和结果分析共同构成了尺度推绎的概念框架。     

On the use of log‐transformation versus nonlinear regression for analyzing biological power laws

Xiao and colleagues re‐examined 471 datasets from the literature in a major study comparing two common procedures for fitting the allometric equation y = ax^b to bivariate data (Xiao et al., 2011). One of the procedures was the traditional allometric method, whereby the model for a straight line fitted to logarithmic transformations of the original data is back‐transformed to form a two‐parameter power function with multiplicative, lognormal, heteroscedastic error on the arithmetic scale. The other procedure was standard nonlinear regression, whereby a two‐parameter power function with additive, normal, homoscedastic error is fitted directly to untransformed data by nonlinear least squares. Xiao and colleagues articulated a simple (but explicit) protocol for fitting and comparing the alternative models, and then used the protocol to examine each of the datasets in their compilation. The traditional method was said to provide a better fit in 69% of the cases and an equivalent fit in another 15%, so the investigation appeared to validate findings from a large majority of prior studies on allometric variation. However, focus for the investigation by Xiao and colleagues was overly narrow, and statistical models apparently were not validated graphically in the scale of measurement. The present study re‐examined a subset of the cases using a larger pool of candidate models and graphical validation, and discovered complexities that were overlooked in their investigation. Some datasets that appeared to be described better by the traditional method actually were unsuited for use in an allometric analysis, whereas other datasets were not described adequately by a two‐parameter power function, regardless of how the model was fitted. Thus, conclusions reached by Xiao and colleagues are not well supported and their paradigm for fitting allometric equations is unreliable. Future investigations of allometric variation should adopt a more holistic approach and incorporate graphical validation on the original arithmetic scale. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1167–1178.     

The ontogeny of sexual dimorphism in the facial skeleton of the African apes

This paper aims to test the contribution of ontogenetic scaling to sexual dimorphism of the facial skeleton in the African apes. Specifically, it addresses whether males and females of each species share a common postnatal ontogenetic shape trajectory for the facial skeleton. Where trajectories are found to differ, it is tested whether male and female trajectories: 1) diverge early, or 2) diverge later after sharing a common trajectory earlier in the postnatal period. Where ontogenetic shape trajectories are found to be shared, it is also tested whether males and females are ontogenetically scaled. This study uses geometric morphometric analyses of 28 landmarks from the facial skeletons of 137 G. g. gorilla (62 adults; 75 juveniles), 95 P. paniscus (34 adults; 61 juveniles), and 115 P. t. troglodytes (58 adults; 57 juveniles). On average, males and females share a common ontogenetic shape trajectory until around the eruption of the second permanent molars. In addition, for the same period, males and females in each species share a common ontogenetic scaling trajectory. After this period, males and females diverge both from each other and from the common juvenile ontogenetic shape and scaling trajectories within each species. Thus, the male and female facial skeleton shows ontogenetic scaling until around the point of the eruption of the second molar (i.e., around puberty and the development of secondary sexual characteristics), but subsequent sexual dimorphism occurs via divergent trajectories and not via ontogenetic scaling.     

Allometric scaling relationship between above‐ and below‐ground biomass within and across five woody seedlings

Allometric biomass allocation theory predicts that leaf biomass (M_L) scaled isometrically with stem (M_S) and root (M_R) biomass, and thus above‐ground biomass (leaf and stem) (M_A) and root (M_R) scaled nearly isometrically with below‐ground biomass (root) for tree seedlings across a wide diversity of taxa. Furthermore, prior studies also imply that scaling constant should vary with species. However, litter is known about whether such invariant isometric scaling exponents hold for intraspecific biomass allocation, and how variation in scaling constants influences the interspecific scaling relationship between above‐ and below‐ground biomass. Biomass data of seedlings from five evergreen species were examined to test scaling relationships among biomass components across and within species. Model Type II regression was used to compare the numerical values of scaling exponents and constants among leaf, stem, root, and above‐ to below‐ground biomass. The results indicated that M_L and M_S scaled in an isometric or a nearly isometric manner with M_R, as well as M_A to M_R for five woody species. Significant variation was observed in the Y‐intercepts of the biomass scaling curves, resulting in the divergence for intraspecific scaling and interspecific scaling relationships for M_L versus M_S and M_L versus M_R, but not for M_S versus M_R and M_A versus M_R. We conclude, therefore, that a nearly isometric scaling relationship of M_A versus M_R holds true within each of the studied woody species and across them irrespective the negative scaling relationship between leaf and stem.     

Spatial modelling of nitrous oxide emissions at the national scale using soil, climate and land use information

Nitrous oxide (N₂O) is a powerful greenhouse gas. The UK government is committed to reducing all greenhouse gas emissions and is required to make an inventory of the sources and emissions of these gases. Here, we extend work from a pilot study at the catchment scale reported in an earlier paper. This paper reports on the upscaling measurements of emissions to derive annual emission rates for specific combinations of soil type, land management and fertiliser practices to the national scale. Digital soil, climate and land use maps were combined within Geographic Information Systems (GIS) software. Upscaling of field emissions measurements involves adjusting measured annual N₂O emissions to fit combinations of crop growth cycles, soil wetness and the amount and timing of fertiliser applications. We have also taken account of the differences in emission rates from grazed pasture land due to differences in land management between land utilised for dairy production and land utilised for beef production. Calculated annual emission rates were then spatially scaled to derive national figures through the use of a GIS modelling framework, termed NitOx. The annual emission of N₂O from Scotland was determined as approximately 6 000 000 kg N yr⁻¹ (2.8 Mt carbon dioxide (CO₂) equivalents) and compares favourably with other national scale estimates such as the IPCC (1997) . The combination of animal grazing, high N inputs, climatic warmth and poorly drained soils means that the south west contributes significantly to the national total N₂O emissions. Localised areas of high emission can also be identified, but identification could be improved by applying this modelling approach at a larger scale. It would be beneficial to target these areas with mitigation strategies.     

Estimating consumable biomass from body length and order in insects and spiders

1. Current models used to estimate insect prey biomass for diet studies use whole weight. However, a large proportion of an arthropod's body is taken up by an indigestible exoskeleton, leading to erroneous estimation of the food intake of insectivorous animals. 2. Linear mixed effect models were used to obtain equations to predict consumable biomass from body length for a variety of Neotropical insects and spiders. These data were obtained by feeding taxa of various orders to groups of 100 social spiders and comparing pre‐ and post‐consumption weights using size‐matched controls. 3. Significant linear relationships were found relating body size to consumed biomass for all orders, with slopes ranging from 1.276 to 4.011 and R² values from 0.476 to 0.929. For orders other than spiders and Orthoptera, the increase in weight with size exhibited negative allometric scaling, suggesting a decrease in tissue density, or an increase in internal air space, with size. 4. Although there were significant differences across taxonomic orders in the proportion of biomass consumed, within most orders the proportion consumed did not differ significantly with body size. The estimated regression coefficients may be used by other workers to estimate consumable biomass of arthropod prey for studies requiring large sample sizes or non‐lethal sampling of rare or endangered species.     

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.     

生态学中的尺度及尺度转换方法

尺度作为生态学的重要范式,已经引起了广泛重视,但对尺度问题的研究还不够成熟.尺度具有多维性特点,即功能尺度、空间尺度、时间尺度等,但生态学研究的重点是空间和时间尺度.并且时空尺度还具有复杂性、变异性特征.尺度研究的根本目的在于通过适宜的空间和时间尺度来揭示和把握复杂的生态学规律.为此,科学有效的尺度选择和尺度转换方法不可或缺.常见的尺度转换方法有图示法、回归分析、变异函数、自相关分析、谱分析、分形和小波变换,同时遥感和地理信息系统技术在尺度研究中也发挥着重要作用.结合实例对上述方法进行了分析和论述,认为各种方法都有其内在的优势和不足,新方法的引入和应用对于尺度转换方法体系的充实和完善非常重要.有关尺度的研究将进一步加强,研究的重点是尺度变异性、不同尺度间的相互作用机制以及尺度转换方法等.     

Metabolic scaling of antibiotics in reptiles: Basis and limitations

The allometric equation y = a · x^b has been used to scale many morphological and physiological attributes relative to body mass. For instance, in eutherian mammals, the equation P_met = 70M_b^0.75 has been used to describe the relationship between metabolic rate (P_met) and body mass (M_b). Similar equations have been derived for squamate reptiles. Recently, this relationship between metabolic rate and body mass has been used in determining appropriate dosages and dosing intervals of antibiotics both intraspecifically for different sized reptiles and interspecifically for those reptiles in which antibiotic pharmacokinetic studies have not been performed. Although this is a simple mathematical process, a number of problems surface when this approach is examined closely. First, the mass constant (a) in reptiles varies from 1–5 for snakes and 6–10 for lizards. No such information is available for chelonians or crocodilians. Unless the mass constant for the unknown species approximates that of the known species, inappropriate dosages and intervals of administration will be calculated. Second, pharmacokinetic differences may exist between widely divergent species, independent of metabolic rate. Third, all available pharmacokinetic studies and metabolic allometric equations are derived from clinically healthy reptiles. Differences more than likely exist between healthy and ill reptiles in regard to uptake, distribution, and elimination of drugs and overall metabolism. While metabolic scaling of antibiotics is a potentially useful and practical tool in drug dosing, these limitations must be considered when dosing an ill reptile. Until more scientifically derived information is available for demonstrating the accuracy of metabolic scaling of antibiotics in reptiles, the clinician will need to understand the limitations of this approach. © 1996 Wiley-Liss, Inc.     

水文尺度转换探讨

水文尺度问题是当今水文学研究的热点和前沿.水文尺度包括过程尺度、观测尺度和模拟尺度三方面含义.主导过程尺度作为尺度的特征量,是水文研究中的重点.水文尺度转换工作包括了对水文模式、参数、状态变量和输入的尺度转换四方面,每一方面都有其特殊的研究方法.水文系统的有组织复杂性、时空变异性和数据不足是当前水文研究的难点所在.自然河网的自相似特性使其成为水文尺度研究的重要组成部分.进一步深入研究水文尺度问题需要多种研究思路、技术手段和理论工具的结合.     

Blood pressure increases with body size in mammals

In a recent technical comment regarding our analysis of the scaling of blood pressure with body mass in mammals (White and Seymour 2014), Packard (2015) argues that the trends in our graphs do not accurately reflect the relationship between the original variables, and that neither the graphics nor the accompanying statistical analyses provide strong support for the conclusions from the study, namely that larger mammals have higher arterial blood pressures. Here we take the opportunity to respond to these criticisms.     

Importin α Partitioning to the Plasma Membrane Regulates Intracellular Scaling

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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。     

A scaling approach to spatial variability in early diagenetic processes

The traditional approach to understanding early diagenetic processes in sediments has generally been to analyze pore water and solid phases from a single core on depth scales of centimeters. The resulting data is then modeled using the approximations of lateral homogeneity and steady-state conditions. However, the continuing advancement of the field of benthic biogeochemistry and development of new microelectrode analytic techniques are clearly demonstrating that in many sedimentary environments a more sophisticated approach to measure the spatial and temporal variability is necessary. Although no one approach is appropriate for all situations, a scaling method is presented, with examples, in this study for determining appropriate sampling intervals in time and space that has considerable utility for investigating early changes in sediment geochemistry in complex natural systems. This approach is derived from scaling techniques that have been developed by physical oceanographers for the study of processes in the water column where many analogous sampling problems are encountered.     

Information and allometry

Many life-history parameters have condition-dependent optima, but individuals are often required to set the values of such parameters relatively early in development, before the relevant conditions can be assessed with full accuracy. If cues are available that predict such future conditions, then the condition-dependent parameter should evolve to assume values that deviate from the mean in the direction implied by the cues, but these deviations should regress towards the mean to the degree that the cues are less than fully reliable. Under mild assumptions, the slopes of the resulting relationships between condition-dependent life-history parameters and the variable conditions on which their optima depend will be the ideal slopes (those that would maximize fitness if the parameter could be chosen on the basis of full information) devalued by the squared correlation between the condition and the parameter.     

The size–grain hypothesis and interspecific scaling in ants

1. The size–grain hypothesis maintains that as terrestrial walking organisms decrease in size, their environment becomes less planar and more rugose. The benefits of long legs (efficient, speedy movement over a planar environment) may thus decrease with smaller body size, while the costs (larger cross-sectional area limiting access to the interstitial environment) are enhanced.
2. A prediction from this hypothesis – that leg size should increase proportionately with body mass – is examined. Ants are among the smallest walking animals and extend the size gradient five orders of magnitude beyond the traditional 'mouse to elephant' curve. The mass of 135 species of worker ants spans 3·7 orders of magnitude (0·008–53 mg). Larger ants tended to be slimmer and longer legged. Ant subfamilies varied in their scaling relationships, but four out of five showed a positive allometry for hind leg length ( b > 0·33). Mammals, in contrast, show isometry for leg length over six orders of magnitude.
3. It is suggested that ants make a transition from living in an interstitial environment when small to a planar environment when large, a habit continued by most terrestrial mammals. Head length and pronotum width are robust estimators of mass in ants.     

Evolution and inheritance of early embryonic patterning in Drosophila simulans and D. sechellia

Pattern formation in Drosophila is a widely studied example of a robust developmental system. Such robust systems pose a challenge to adaptive evolution, as they mask variation that selection may otherwise act upon. Yet we find variation in the localization of expression domains (henceforth "stripe allometry") in the pattern formation pathway. Specifically, we characterize differences in the gap genes giant and Kruppel, and the pair-rule gene even-skipped, which differ between the sibling species Drosophila simulans and D. sechellia. In a double-backcross experiment, stripe allometry is consistent with maternal inheritance of stripe positioning and multiple genetic factors, with a distinct genetic basis from embryo length. Embryos produced by F1 and F2 backcross mothers exhibit novel spatial patterns of gene expression relative to the parental species, with no measurable increase in positional variance among individuals. Buffering of novel spatial patterns in the backcross genotypes suggests that robustness need not be disrupted in order for the trait to evolve, and perhaps the system is incapable of evolving to prevent the expression of all genetic variation. This limitation, and the ability of natural selection to act on minute genetic differences that are within the "margin of error" for the buffering mechanism, indicates that developmentally buffered traits can evolve without disruption of robustness.     

Uncertainty/Safety Factors in Health Risk Assessment: Opportunities for Improvement

This paper presents the results of deliberations from participants who met on the second day of the Fourth Annual Workshop on the Evaluation of Uncertainty/Safety Factors in Health Risk Assessment. The group reviewed the previous day's presentations and implications for improvement in risk assessment. After much discussion, the group concluded that, in the short term, significant improvements could be made in the pharmacokinetic component of the inter-species uncertainty factor and developed a series of default options for this factor. These defaults consider route of exposure (oral or inhalation), and the form of the active compound (parent, metabolite, or very reactive metabolite). Several assumptions are key to this approach, such as a similar oral or inhalation bioavailability across species. We believe this method represents a useful default approach until more compound-specific information is available.