Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals

In this review I show that the '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy-using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional) and ultimate (evolutionary) causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b<1); and Type IV: nonlinear, ontogenetic shift from positively allometric (b>1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e. growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)-specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body-size range, and activity level. A 'metabolic-level boundaries hypothesis' focusing on two major constraints (surface-area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species. Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico-chemical and ecological constraints.     

Dichotomy of eutherian reproduction and metabolism

How anatomical, physiological and ecological (life history) features scale with body mass is a fundamental question in biology. There is an ongoing debate in the scientific literature whether allometric scaling follows a universal pattern that can be described in a single model, or differs between groups. However, recently some analyses were published demonstrating a change in scaling across the body mass range: brain‐size allometry of mammals indicates that scaling follows a curvilinear pattern in double‐logarithmic space, and a quadratic pattern in double‐logarithmic space was found in one of the largest physiological datasets, on basal metabolic rate (MR) in mammals. Here, we analysed a variety of independent datasets on anatomical, physiological and ecological characteristics in mammals, birds and reptiles to answer the question whether the quadratic scaling is a universal biological law, or a pattern unique to mammals. The pattern was present in mammalian basal and field MR, brain size, and reproduction parameters, but neither in other organ allometries in mammals, nor in the scaling of MR in birds and reptiles. However, the curvature was better explained by separate allometric scaling of three different mammalian reproduction strategies: marsupials, and eutherian mammals with one and with many offspring. The two latter strategies are distributed unequally over the body mass range in eutherian mammals. Our findings show that a quadratic model, as well as a traditional allometric model with a universal scaling exponent (such as 0.67 or 0.75), may be inappropriate in mammals as they are a result of different scalings within these three reproductive groups. We propose that the observed distribution pattern is the result of the eutherian mammal clade's uniquely pronounced dichotomy of reproductive strategies.     

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.     

Unifying elemental stoichiometry and metabolic theory in predicting species abundances

While metabolic theory predicts variance in population density within communities depending on population average body masses, the ecological stoichiometry concept relates density variation across communities to varying resource stoichiometry. Using a data set including biomass densities of 4959 populations of soil invertebrates across 48 forest sites we combined these two frameworks. We analyzed how the scaling of biomass densities with population‐averaged body masses systematically interacts with stoichiometric variables. Simplified analyses employing either only body masses or only resource stoichiometry are highly context sensitive and yield variable and often misleading results. Our findings provide strong evidence that analyses of ecological state variables should integrate allometric and stoichiometric variables to explain deviations from predicted allometric scaling and avoid erroneous conclusions. In consequence, our study provides an important step towards unifying two prominent ecological theories, metabolic theory and ecological stoichiometry.     

Spatial scaling of population synchrony in marine fish depends on their life history

The synchrony of population dynamics in space has important implications for ecological processes, for example affecting the spread of diseases, spatial distributions and risk of extinction. Here, we studied the relationship between spatial scaling in population dynamics and species position along the slow‐fast continuum of life history variation. Specifically, we explored how generation time, growth rate and mortality rate predicted the spatial scaling of abundance and yearly changes in abundance of eight marine fish species. Our results show that population dynamics of species' with ‘slow’ life histories are synchronised over greater distances than those of species with ‘fast’ life histories. These findings provide evidence for a relationship between the position of the species along the life history continuum and population dynamics in space, showing that the spatial distribution of abundance may be related to life history characteristics.     

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.     

Metabolic scaling in insects supports the predictions of the WBE model

The functional association between body size and metabolic rate (BS-MR) is one of the most intriguing issues in ecological physiology. An average scaling exponent of 3/4 is broadly observed across animal and plant taxa. The numerical value of 3/4 is theoretically predicted under the optimized version of West, Brown, and Enquist's vascular resource supply network model. Insects, however, have recently been proposed to express a numerically different scaling exponent and thus application of the WBE network model to insects has been rejected. Here, we re-analyze whether such variation is indeed supported by a global deviation across all insect taxa at the order and family levels to assess if specific taxa influence insect metabolic scaling. We show that a previous reported deviation is largely due to the effect of a single insect family (Termitidae). We conclude that the BS-MR relationship in insects broadly supports the core predictions of the WBE model. We suggest that the deviation observed within the termites warrants further investigation and may be due to either difficulty in accurately measuring termite metabolism and/or particularities of their life history. Future work on allometric scaling should assess the nature of variation around the central tendencies in scaling exponents in order to test if this variation is consistent with core assumptions and predictions of the WBE model that stem by relaxing its secondary optimizing assumptions that lead to the 3/4 exponent.     

The leaf size-twig size spectrum of temperate woody species along an altitudinal gradient: an invariant allometric scaling relationship

BACKGROUND AND AIMS: The leaf size-twig size spectrum is one of the leading dimensions of plant ecological variation, and now it is under development. The purpose of this study was to test whether the relationship between leaf size and twig size is isometric or allometric, and to examine the relationship between plant allometric growth and life history strategies in the spectrum. METHODS: Leaf and stem characters-including leaf and stem mass, total leaf area, individual leaf area, stem cross-sectional area, leaf number and stem length-at the twig level for 59 woody species were investigated along an altitudinal gradient on Changbaishan Mountain in the temperate zone of China. The environmental gradient ranges from temperate broad-leaved mixed forest at low altitude, to conifer forest at middle altitude, and to sub-alpine birch forest at high altitude. The scaling relationships between stem cross-sectional area and stem mass, stem mass and leaf mass, and leaf mass and leaf area at the twig level were simultaneously determined. KEY RESULTS: Twig cross-sectional area was found to have invariant allometric scaling relationships with the stem mass, leaf mass, total leaf area and individual leaf area, all with common slopes being significantly larger than 1, for three altitudinal-zoned vegetation types under investigation. However, leaf mass was found to be isometrically related to stem mass and leaf area along the environmental gradient. Based on the predictions of previous models, the exponent value of the relationship between twig cross-sectional area and total leaf area can be inferred to be 1.5, which falls between the confidence intervals of the relationship at each altitude, and between the confidence intervals of the common slope value (1.17-1.56) of this study. This invariant scaling relationship is assumed to result from the fractural network and/or developmental constraints of plants. The allometric constants (y-intercepts) of the relationships between the stem cross-sectional area and leaf area (both total leaf area and individual leaf area) were found to decrease significantly along the altitudinal gradient. This suggests that the species would support less leaf area at a given twig cross-sectional area with increasing environmental stress. CONCLUSIONS: This study demonstrated that plants respond to the environmental gradient by changing the y-intercepts of the relationship between leaf size-twig size, while keeping the exponent value of the allometric relationship as an invariant constant. The allometric growth in the twig size-leaf size spectrum is related to many other components of plant life history strategy, including the well established life history trade-off between efficiency and safety in the hydraulic transport of water.     

Tree height–diameter allometry across the United States

The relationship between tree height and diameter is fundamental in determining community and ecosystem structure as well as estimates of biomass and carbon storage. Yet our understanding of how tree allometry relates to climate and whole organismal function is limited. We used the Forest Inventory and Analysis National Program database to determine height–diameter allometries of 2,976,937 individuals of 293 tree species across the United States. The shape of the allometric relationship was determined by comparing linear and nonlinear functional forms. Mixed‐effects models were used to test for allometric differences due to climate and floristic (between angiosperms and gymnosperms) and functional groups (leaf habit and shade tolerance). Tree allometry significantly differed across the United States largely because of climate. Temperature, and to some extent precipitation, in part explained tree allometric variation. The magnitude of allometric variation due to climate, however, had a phylogenetic signal. Specifically, angiosperm allometry was more sensitive to differences in temperature compared to gymnosperms. Most notably, angiosperm height was more negatively influenced by increasing temperature variability, whereas gymnosperm height was negatively influenced by decreasing precipitation and increasing altitude. There was little evidence to suggest that shade tolerance influenced tree allometry except for very shade‐intolerant trees which were taller for any given diameter. Tree allometry is plastic rather than fixed and scaling parameters vary around predicted central tendencies. This allometric variation provides insight into life‐history strategies, phylogenetic history, and environmental limitations at biogeographical scales.     

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.     

Allometric growth, life-history invariants and population energetics

Population and community level processes must be at least partially determined by variation in the body sizes of constituent individuals, implying quantitative scaling relations can be extended to account for variation in those processes. Here we integrate allometric growth and life‐history invariant theories, and use this approach to develop theory describing the energetics of stationary populations. Our predictions approximate, with no free parameters, the scaling of production/biomass and assimilation/biomass ratios in mammalian populations and work partially for fish populations. This approach appears to be a promising direction and suggests the need for further development of the growth and life‐history models, and extensions of those theories.     

Intra-specific variation and taxa- sampling affects the home range — body mass relationship

The relationship between home range size and body mass is a frequently studied allometric relationship. However, the results of various studies differ greatly, leading to much debate about the nature of the relationship. We argue that this confusion is not surprising, due to intra-specific variation in home range size caused by ecological variability rather than by body mass. By random resampling of different studies from within 16 Carnivora species, we show that the scaling exponent ranged from 0.30–1.54 depending on the particular studies included for each species. Of these exponents, 10% did not contain 0.75 within their confidence limits, and 5.5% did not contain 1.00. Furthermore, by randomly sub-sampling 16 species from a total sample of 58 species, we found that the scaling exponent varied between 0.18 and 2.76. Of these exponents, 42.2% did not contain 0.75 within their confidence limits, whereas 16.8% did not contain 1.00. Therefore, we strongly recommend that greater consideration be paid to intra-specific ecological variability and taxa selection when dealing with both allometry and cross-species life history studies.     

Plant allometry, stoichiometry and the temperature-dependence of primary productivity

Aim While physical constraints influence terrestrial primary productivity, the extent to which geographical variation in productivity is influenced by physiological adaptations and changes in vegetation structure is unclear. Further, quantifying the effect of variability in species traits on ecosystems remains a critical research challenge. Here, we take a macroecological approach and ask if variation in the stoichiometric traits (C: N: P ratios) of plants and primary productivity across global‐scale temperature gradients is consistent with a scaling model that integrates recent insights from the theories of metabolic scaling and ecological stoichiometry. Location This study is global in scope, encompassing a wide variety of terrestrial plant communities. Methods We first develop a scaling model that incorporates potentially adaptive variation in leaf and whole‐plant nutrient content, kinetic aspects of photosynthesis and plant respiration, and the allometry of biomass partitioning and allocation. We then examine extensive data sets concerning the stoichiometry and productivity of diverse plant communities in light of the model. Results Across diverse ecosystems, both foliar stoichiometry (N : P) and ‘nitrogen productivity’ (which depends on both community size structure and plant nutrient content) vary systematically across global scale temperature gradients. Primary productivity shows no relationship to temperature. Main conclusions The model predicts that the observed patterns of variation in plant stoichiometry and nutrient productivity may offset the temperature dependence of primary production expected from the kinetics of photosynthesis alone. Our approach provides a quantitative framework for treating potentially adaptive functional variation across communities as a continuum and may thus inform studies of global change. More generally, our approach represents one of the first explicit combinations of ecological stoichiometry and metabolic scaling theories in the analysis of macroecological patterns.     

Pitfalls and challenges of estimating population growth rate from empirical data: consequences for allometric scaling relations

The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age‐dependent mortality and density‐dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non‐interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log₁₀(population growth rate) should scale as ?0.25 power of log₁₀(body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.     

Life‐history evolution under fluctuating density‐dependent selection and the adaptive alignment of pace‐of‐life syndromes

We present a novel perspective on life‐history evolution that combines recent theoretical advances in fluctuating density‐dependent selection with the notion of pace‐of‐life syndromes (POLSs) in behavioural ecology. These ideas posit phenotypic co‐variation in life‐history, physiological, morphological and behavioural traits as a continuum from the highly fecund, short‐lived, bold, aggressive and highly dispersive ‘fast’ types at one end of the POLS to the less fecund, long‐lived, cautious, shy, plastic and socially responsive ‘slow’ types at the other. We propose that such variation in life histories and the associated individual differences in behaviour can be explained through their eco‐evolutionary dynamics with population density – a single and ubiquitous selective factor that is present in all biological systems. Contrasting regimes of environmental stochasticity are expected to affect population density in time and space and create differing patterns of fluctuating density‐dependent selection, which generates variation in fast versus slow life histories within and among populations. We therefore predict that a major axis of phenotypic co‐variation in life‐history, physiological, morphological and behavioural traits (i.e. the POLS) should align with these stochastic fluctuations in the multivariate fitness landscape created by variation in density‐dependent selection. Phenotypic plasticity and/or genetic (co‐)variation oriented along this major POLS axis are thus expected to facilitate rapid and adaptively integrated changes in various aspects of life histories within and among populations and/or species. The fluctuating density‐dependent selection POLS framework presented here therefore provides a series of clear testable predictions, the investigation of which should further our fundamental understanding of life‐history evolution and thus our ability to predict natural population dynamics.     

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.     

Body condition helps to explain metabolic rate variation in wolf spiders

1. Metabolism is the fundamental process that powers life. Understanding what drives metabolism is therefore critical to our understanding of the ecology and behaviour of organisms in nature. 2. Metabolic rate generally scales with body size according to a power law. However, considerable unexplained variation in metabolic rate remains after accounting for body mass with scaling functions. 3. We measured resting metabolic rates (oxygen consumption) of 227 field‐caught wolf spiders. Then, we tested for effects of body mass, species, and body condition on metabolic rate. 4. Metabolic rate scales with body mass to the 0.85 power in these wolf spiders, and there are metabolic rate differences between species. After accounting for these factors, residual variation in metabolic rate is related to spider body condition (abdomen:cephalothorax ratio). Spiders with better body condition consume more oxygen. 5. These results indicate that recent foraging history is an important determinant of metabolic rate, suggesting that although body mass and taxonomic identity are important, other factors can provide helpful insights into metabolic rate variation in ecological communities.     

Population changes in Czech passerines are predicted by their life‐history and ecological traits

A species’ susceptibility to environmental change might be predicted by its ecological and life‐history traits. However, the effects of such traits on long‐term bird population trends have not yet been assessed using a comprehensive set of explanatory variables. Moreover, the extent to which phylogeny affects patterns in the interspecific variability of population changes is unclear. Our study focuses on the interspecific variability in long‐term population trends and annual population fluctuations of 68 passerine species in the Czech Republic, assessing the effects of eight life‐history and five ecological traits. Ordination of life‐history traits of 68 species revealed a life‐history gradient, from ‘r‐selected’ (e.g. small body mass, short lifespan, high fecundity, large clutch size) to ‘K‐selected’ species. r‐selected species had more negative population trends than K‐selected species, and seed‐eaters declined compared with insectivores. We suggest that the r‐selected species probably suffer from widespread environmental changes, and the seed‐eaters from current changes in agriculture and land use. Populations of residents fluctuated more than populations of short‐distance migrants, probably due to the effect of winter climatic variability. Variance partitioning at three taxonomic levels showed that whereas population trends, population fluctuations and habitat specialization expressed the highest variability at the species level, most life‐history traits were more variable at higher taxonomic levels. These results explain the loss of statistical power in the relationship between life histories and population trends after controlling for phylogeny. However, we argue that a lack of significance after controlling for phylogeny should not reduce the value of such results for conservation purposes.     

Do insect metabolic rates at rest and during flight scale with body mass?

Energetically costly behaviours, such as flight, push physiological systems to their limits requiring metabolic rates (MR) that are highly elevated above the resting MR (RMR). Both RMR and MR during exercise (e.g. flight or running) in birds and mammals scale allometrically, although there is little consensus about the underlying mechanisms or the scaling relationships themselves. Even less is known about the allometric scaling of RMR and MR during exercise in insects. We analysed data on the resting and flight MR (FMR) of over 50 insect species that fly to determine whether RMR and FMR scale allometrically. RMR scaled with body mass to the power of 0.66 (M0.66), whereas FMR scaled with M1.10. Further analysis suggested that FMR scaled with two separate relationships; insects weighing less than 10mg had fourfold lower FMR than predicted from the scaling of FMR in insects weighing more than 10mg, although both groups scaled with M0.86. The scaling exponents of RMR and FMR in insects were not significantly different from those of birds and mammals, suggesting that they might be determined by similar factors. We argue that low FMR in small insects suggests these insects may be making considerable energy savings during flight, which could be extremely important for the physiology and evolution of insect flight.     

Allometric scaling in animals and plants

In this paper we give a derivation for the allometric scaling relation between the metabolic rate and the mass of animals and plants. We show that the characteristic scaling exponent of 3/4 occurring in this relation is a result of the distribution of sources and sinks within the living organism. We further introduce a principle of least mass and discuss the kind of flows that arise from it.