How pulse disturbances shape size‐abundance pyramids

Ecological pyramids represent the distribution of abundance and biomass of living organisms across body‐sizes. Our understanding of their expected shape relies on the assumption of invariant steady‐state conditions. However, most of the world’s ecosystems experience disturbances that keep them far from such a steady state. Here, using the allometric scaling between population growth rate and body‐size, we predict the response of size‐abundance pyramids within a trophic guild to any combination of disturbance frequency and intensity affecting all species in a similar way. We show that disturbances narrow the base of size‐abundance pyramids, lower their height and decrease total community biomass in a nonlinear way. An experimental test using microbial communities demonstrates that the model captures well the effect of disturbances on empirical pyramids. Overall, we demonstrate both theoretically and experimentally how disturbances that are not size‐selective can nonetheless have disproportionate impacts on large species.     

Fitting statistical models in bivariate allometry

Several attempts have been made in recent years to formulate a general explanation for what appear to be recurring patterns of allometric variation in morphology, physiology, and ecology of both plants and animals (e.g. the Metabolic Theory of Ecology, the Allometric Cascade, the Metabolic‐Level Boundaries hypothesis). However, published estimates for parameters in allometric equations often are inaccurate, owing to undetected bias introduced by the traditional method for fitting lines to empirical data. The traditional method entails fitting a straight line to logarithmic transformations of the original data and then back‐transforming the resulting equation to the arithmetic scale. Because of fundamental changes in distributions attending transformation of predictor and response variables, the traditional practice may cause influential outliers to go undetected, and it may result in an underparameterized model being fitted to the data. Also, substantial bias may be introduced by the insidious rotational distortion that accompanies regression analyses performed on logarithms. Consequently, the aforementioned patterns of allometric variation may be illusions, and the theoretical explanations may be wide of the mark. Problems attending the traditional procedure can be largely avoided in future research simply by performing preliminary analyses on arithmetic values and by validating fitted equations in the arithmetic domain. The goal of most allometric research is to characterize relationships between biological variables and body size, and this is done most effectively with data expressed in the units of measurement. Back‐transforming from a straight line fitted to logarithms is not a generally reliable way to estimate an allometric equation in the original scale.     

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.     

Single Cell Analysis Linking Ribosomal (r)DNA and rRNA Copy Numbers to Cell Size and Growth Rate Provides Insights into Molecular Protistan Ecology

Ribosomal (r)RNA and rDNA have been golden molecular markers in microbial ecology. However, it remains poorly understood how ribotype copy number (CN)‐based characteristics are linked with diversity, abundance, and activity of protist populations and communities observed at organismal levels. Here, we applied a single‐cell approach to quantify ribotype CNs in two ciliate species reared at different temperatures. We found that in actively growing cells, the per‐cell rDNA and rRNA CNs scaled with cell volume (CV) to 0.44 and 0.58 powers, respectively. The modeled rDNA and rRNA concentrations thus appear to be much higher in smaller than in larger cells. The observed rRNA:rDNA ratio scaled with CV^0.14. The maximum growth rate could be well predicted by a combination of per‐cell ribotype CN and temperature. Our empirical data and modeling on single‐cell ribotype scaling are in agreement with both the metabolic theory of ecology and the growth rate hypothesis, providing a quantitative framework for linking cellular rDNA and rRNA CNs with body size, growth (activity), and biomass stoichiometry. This study also demonstrates that the expression rate of rRNA genes is constrained by cell size, and favors biomass rather than abundance‐based interpretation of quantitative ribotype data in population and community ecology of protists.     

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.     

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.     

Aspects of line-fitting in bivariate allometric analyses

One of the fundamental problems involved in analyses of the scaling effects of body size (allometric analysis is the choice of an appropriate best-fit line in bivariate logarithmic plots. Following a discussion of some basic aspects of allometric analysis, the tow mai procedures for the determination of a best-fit line - the least-squares regression and the major axis - are examined with respect to their different properties and underlying models. It is important to distinguish intraspecific from interspecific scaling and to recognize the distinction between use of a best-fit line to define a relationship and use of the line for prediction. An alternative model to the bivariate normal distribution, referred to as the 'extruded normal distribution', is presented and its implications are examined with respect to two test cases (scaling of basal metabolic rate in human males; scaling of population density in mammals).     

Taxonomic versus allometric constraints on non‐linear interaction strengths

Recently, the importance of body mass and allometric scaling for the structure and dynamics of ecological networks has been highlighted in several ground‐breaking studies. However, advances in the understanding of generalities across ecosystem types are impeded to a considerable extent by a methodological dichotomy contrasting a considerable portion of marine ecology on the one hand opposite to traditional community ecology on the other hand. Many marine ecologists are bound to the taxonomy‐neglecting size spectrum approach when describing and analysing community patterns. In contrast, the mindset of the other school is focused on taxonomies according to the Linnean system at the cost of obscuring information due to applying species or population averages of body masses and other traits. Following other pioneering studies, we addressed this lingering gap, and studied non‐linear interaction strengths (i.e. functional responses) between two taxonomically‐distinct terrestrial arthropod predators (centipedes and spiders) of varying individual body masses and their prey. We fitted three non‐linear functional response models to the data: (1) a taxonomic model not accounting for variance in body masses amongst predator individuals, (2) an allometric model ignoring taxonomic differences between predator individuals, and (3) a combined model including body mass and taxonomic effects. Ranked according to their AICs, the combined model performs better than the allometric model, which provides a superior fit to the data than the taxonomic model. These results strongly indicate that the body masses of predator and prey individuals were responsible for most of the variation in non‐linear interaction strengths. Taxonomy explained some specific patterns in allometric exponents between groups and revealed mechanistic insights in predation efficiencies. Reconciling quantitative allometric models as employed by the marine size‐spectrum approach with taxonomic information may thus yield quantitative results that are generalized across ecosystem types and taxonomic groups. Using these quantitative models as novel null models should also strengthen subsequent taxonomic analyses.     

How allometric scaling relates to soil abiotics

For most species, the logarithm of their average body mass is negatively related to the logarithm of their relative population density, i.e. the numerical abundance. In this way, the allometric scaling (both mass–abundance regressions and body–size spectra) becomes useful in ecological theory to build and explain food webs. Using empirical evidence derived from 145 Dutch sites, a hypothesis is formulated to explain how soil microbivores, detritivores and predators react to increasing resource availability. Shifts in size distribution, and subsequently changes in soil food‐web structure, are further discussed in the perspective of Holling's sequential interactions between basic system functions. We show that the allometric scaling and the averages of the (log‐transformed) prey:predator body‐mass ratios are reliable predictors for assessing faunal responses to nutrient availability. We view this work as a first attempt toward an extensive comparison of ecological processes in different soil systems.     

Ecological scaling laws link individual body size variation to population abundance fluctuation

Scaling research has seen remarkable progress in the past several decades. Many scaling relationships were discovered within and across individual and population levels, such as species–abundance relationship, Taylor's law, and density mass allometry. However none of these established patterns incorporate individual variation in the formulation. Individual body size variation is a key evolutionary phenomenon and closely related to ecological diversity and species adaptation. Using a macroecological approach, I test 57 Long‐Term Ecological Research data sets and show that a power‐law and a generalized power‐law function describe well the mean‐variance scaling of individual body mass. This relationship connects Taylor's law and density mass allometry, and leads to a new scaling pattern between the individual body size variation and population abundance fluctuation, which is confirmed using freshwater fish and forest tree data. Underlying mechanisms and implications of the proposed scaling relationships are discussed. This synthesis shows that integration and extension of existing ecological laws can lead to the discovery of new scaling patterns and complete our understanding of the relation between individual trait and population abundance. Synthesis Scaling relationships are useful for community ecology as they reveal ubiquitous patterns across different levels of biological organizations. This work extends and integrates two existing scaling laws: Taylor's law and density‐mass allometry, and derives a new variance allometry between individual body mass and population abundance. The result shows that diverse individual body size is associated with stable population fluctuation, reflecting the effect of individual traits on population characteristics. Confirmed by several empirical data sets, these scaling relationships suggest new ways to study the underlying mechanisms of Taylor's law and have profound implications for fisheries and other applied sciences.     

Individual size variation reduces spatial variation in abundance of tree community assemblage,not of tree populations

Research on individual trait variation has gained much attention because of its implication for ecosystem functions and community ecology. The effect of individual variation on population and community abundance (number of individuals) variation remains scarcely tested. Using two established ecological scaling laws (Taylor's law and abundance–size relationship), we derived a new scaling relationship between the individual size variation and spatial variation of abundance. Tested against multi‐plot tree data from Diaoluo Mountain tropical forest in Hainan, China, the new scaling relationship showed that individual size variation reduced the spatial variation of community assemblage abundance, but not of taxon‐specific population abundance. The different responses of community and population to individual variation were reflected by the validity of the abundance–size relationship. We tested and confirmed this scaling framework using two measures of individual tree size: aboveground biomass and diameter at breast height. Using delta method and height‐diameter allometry, we derived the analytic relation of scaling exponents estimated under different individual size measures. In addition, we used multiple regression models to analyze the effect of taxon richness on the relationship between individual size variation and spatial variation of population or community abundance, for taxon‐specific and taxon‐mixed data, respectively. This work offers empirical evidence and a scaling framework for the negative effect of individual trait variation on spatial variation of plant community. It has implications for forest ecosystem and management where the role of individual variation in regulating population or community spatial variation is important but understudied.     

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.     

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.     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

Temperature‐dependent body size effects determine population responses to climate warming

Current understanding of animal population responses to rising temperatures is based on the assumption that biological rates such as metabolism, which governs fundamental ecological processes, scale independently with body size and temperature, despite empirical evidence for interactive effects. Here, we investigate the consequences of interactive temperature‐ and size scaling of vital rates for the dynamics of populations experiencing warming using a stage‐structured consumer‐resource model. We show that interactive scaling alters population and stage‐specific responses to rising temperatures, such that warming can induce shifts in population regulation and stage‐structure, influence community structure and govern population responses to mortality. Analysing experimental data for 20 fish species, we found size–temperature interactions in intraspecific scaling of metabolic rate to be common. Given the evidence for size–temperature interactions and the ubiquity of size structure in animal populations, we argue that accounting for size‐specific temperature effects is pivotal for understanding how warming affects animal populations and communities.     

Improved approximations to scaling relationships for species, populations, and ecosystems across latitudinal and elevational gradients

Historically, allometric equations relate organismal traits, such as metabolic rate, individual growth rate, and lifespan, to body mass. Similarly, Boltzmann or Q(10) factors are used to relate many organismal traits to body temperature. Allometric equations and Boltzmann factors are being applied increasingly to higher levels of biological organization in an attempt to describe aggregate properties of populations and ecosystems. They have been used previously for studies that analyse scaling relationships between populations and across latitudinal gradients. For these kinds of applications, it is crucial to be aware of the "fallacy of the averages", and it is often problematic or incorrect to simply substitute the average body mass or temperature for an entire population or ecosystem into allometric equations. We derive improved approximations to allometric equations and Boltzmann factors in terms of the central moments of body size and temperature, and we provide tests for the accuracy of these approximations. This framework is necessary for interpreting the predictions of scaling theories for large-scale systems and grants insight into which characteristics of a given distribution are important. These approximations and tests are applied to data for body size for several taxonomic groups, including groups with multiple species, and to data for temperature at locations of varying latitude, corresponding to ectothermic body temperatures. Based on these results, the accuracy and utility of these approximations as applied to biological systems are assessed. We conclude that approximations to allometric equations at the species level are extremely accurate. However, for systems with a large range in body size, evaluating the skewness and kurtosis is often necessary, so it may be advantageous to calculate the exact form for the averaged scaling relationships instead. Moreover, the improved approximation for the Boltzmann factor, which uses the average and standard deviation of temperature, is quite accurate and represents a significant improvement over previous approximations.     

Is non‐loglinear allometry a statistical artifact?

The allometric equation, y = ax^b, is commonly fitted to data indirectly by transforming predictor (x) and response (y) variables to logarithms, fitting a straight line to the transformations, and then back‐transforming (exponentiating) the resulting equation to the original arithmetic scale. Sometimes, however, transformation fails to linearize the observations, thereby giving rise to what has come to be known as non‐loglinear allometry. A smooth curve for observations displayed on a log–log plot is usually interpreted to mean that the scaling exponent in the allometric equation is a continuously changing function of body size, whereas a breakpoint between two (or more) linear segments on a log–log plot is typically taken to mean that the exponent changes abruptly, coincident with some important milestone in development. I applied simple graphical and statistical procedures in re‐analyses of three well‐known examples of non‐loglinear allometry, and showed in every instance that the relationship between predictor and response can be described in the original scale by simple functions with constant values for the exponent b. In no instance does the allometric exponent change during the course of development. Transformation of data to logarithms created new distributions that actually obscured the relationships between predictor and response variables in these investigations, and led to erroneous perceptions of growth. Such confounding effects of transformation are not limited to non‐loglinear allometry but are common to all applications of the allometric method. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

Many ways to be small: different environmental regulators of size generate distinct scaling relationships in Drosophila melanogaster

Static allometries, the scaling relationship between body and trait size, describe the shape of animals in a population or species, and are generated in response to variation in genetic or environmental regulators of size. In principle, allometries may vary with the different size regulators that generate them, which can be problematic since allometric differences are also used to infer patterns of selection on morphology. We test this hypothesis by examining the patterns of scaling in Drosophila melanogaster subjected to variation in three environmental regulators of size: nutrition, temperature and rearing density. Our data indicate that different environmental regulators of size do indeed generate different patterns of scaling. Consequently, flies that are ostensibly the same size may have very different body proportions. These data indicate that trait size is not simply a read-out of body size, but that different environmental factors may regulate body and trait size, and the relationship between the two, through different developmental mechanisms. It may therefore be difficult to infer selective pressures that shape scaling relationships in a wild population without first elucidating the environmental and genetic factors that generate size variation among members of the population.     

Sizing up allometric scaling theory

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks-the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets.