Rediscovering and Reviving Old Observations and Explanations of Metabolic Scaling in Living Systems

Metabolic ecology in aquatic ecosystems: Viewed from trophic compartments and communities in food webs

A different perspective in metabolic ecology is presented using food web data, based on trophic compartments and communities in aquatic ecosystems (coastal areas, shelves and estuaries in marine ecosystems, and lake ecosystems), including primary producers (phytoplankton and aquatic plants). The relationships among the metabolic traits (biomass, respiration and production) in aquatic communities are expressed through power laws, hence, the value of one of the three metabolic traits provides the values of the other two. Noteworthily, these metabolic traits (biomass, respiration, production) are related to those of primary producers according to various power laws. That is: the metabolic traits of communities can be estimated from those of primary producers alone. These power laws appear to be universal in marine ecosystems but vary among different lake ecosystems.

A new mechanistic model for individual growth applied to insects under ad libitum conditions

Metabolic theories in ecology interpret ecological patterns at different levels through the lens of metabolism, typically applying allometric power scaling laws to describe rates of energy use. This requires a sound theory for metabolism at the individual level. Commonly used mechanistic growth models lack some potentially important aspects and fail to accurately capture a growth pattern often observed in insects. Recently, a new model (MGM-the Maintenance-Growth Model) was developed for ontogenetic and post-mature growth, based on an energy balance that expresses growth as the net result of assimilation and metabolic costs for maintenance and feeding. The most important contributions of MGM are: 1) the division of maintenance costs into a non-negotiable and a negotiable part, potentially resulting in maintenance costs that increase faster than linearly with mass and are regulated in response to food restriction; 2) differentiated energy allocation strategies between sexes and 3) explicit description of costs for finding and processing food. MGM may also account for effects of body composition and type of growth at the cellular level. The model was here calibrated and evaluated using empirical data from an experiment on house crickets growing under ad libitum conditions. The procedure involved parameter estimations from the literature and collected data, using statistical models to account for individual variation in parameter values. It was found that ingestion rate cannot be generally described by a simple allometry, here requiring a more complex description after maturity. Neither could feeding costs be related to ingestion rate in a simplistic manner. By the unusual feature of maintenance costs increasing faster than linearly with body mass, MGM could well capture the differentiated growth patterns of male and female crickets. Some other mechanistic growth models have been able to provide good predictions of insect growth during early ontogeny, but MGM may accurately describe the trajectory until terminated growth.

Interactive effects of intrinsic and extrinsic factors on metabolic rate

Metabolism energizes all biological processes, and its tempo may importantly influence the ecological success and evolutionary fitness of organisms. Therefore, understanding the broad variation in metabolic rate that exists across the living world is a fundamental challenge in biology. To further the development of a more reliable and holistic picture of the causes of this variation, we review several examples of how various intrinsic (biological) and extrinsic (environmental) factors (including body size, cell size, activity level, temperature, predation and other diverse genetic, cellular, morphological, physiological, behavioural and ecological influences) can interactively affect metabolic rate in synergistic or antagonistic ways. Most of the interactive effects that have been documented involve body size, temperature or both, but future research may reveal additional 'hub factors'. Our review highlights the complex, intimate inter-relationships between physiology and ecology, knowledge of which can shed light on various problems in both disciplines, including variation in physiological adaptations, life histories, ecological niches and various organism-environment interactions in ecosystems. We also discuss theoretical and practical implications of interactive effects on metabolic rate and provide suggestions for future research, including holistic system analyses at various hierarchical levels of organization that focus on interactive proximate (functional) and ultimate (evolutionary) causal networks. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

How and Why Does Metabolism Scale with Body Mass?

Most explanations for the relationship between body size and metabolism invoke physical constraints; such explanations are evolutionarily inert, limiting their predictive capacity. Contemporary approaches to metabolic rate and life history lack the pluralism of foundational work. Here, we call for reforging of the lost links between optimization approaches and physiology.

The Relevance of Time in Biological Scaling

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

Declining metabolic scaling parallels an ontogenetic change from elongate to deep-bodied shapes in juvenile Brown trout

Body shape and metabolic rate can be important determinants of animal performance, yet often their effects on influential traits are evaluated in a non-integrated way. This creates an important gap because the integration between shape and metabolism may be crucial to evaluate metabolic scaling theories. Here, we measured standard metabolic rate in 1- and 2-years old juvenile brown trout Salmo trutta, and used a geometric morphometrics approach to extricate the effects of ontogeny and size on the link between shape and metabolic scaling. We evidenced near-isometric ontogenetic scaling of metabolic rate with size, but also a biphasic pattern driven by a significant change in metabolic scaling, from positive to negative allometry. Moreover, the change in metabolic allometry parallels an ontogenetic change from elongate to deep-bodied shapes. This is consistent with the dynamic energy budget (DEB) and surface area (SA) theories, but not with the resource transport network theory which predicts increasing allometric exponents for trends towards more robust, three-dimensional bodies. In addition, we found a relationship between body shape and size independent metabolic rate, with a positive correlation between robustness and metabolic rate, which fits well within the view of Pace-of-Life Syndromes (POLS). Finally, our results align with previous studies that question the universality of metabolic scaling exponents and propose other mechanistic models explaining the diversity of metabolic scaling relationships or emphasizing the potential contribution of ecological factors.

Ontogenetic changes in root and shoot respiration, fresh mass and surface area of Fagus crenata

BACKGROUND AND AIMS

To date, studies on terrestrial plant ecology and evolution have focused primarily on the trade-off patterns in the allocation of metabolic production to roots and shoots in individual plants and the scaling of whole-plant respiration. However, few empirical studies have investigated the root : shoot ratio by considering scaling whole-plant respiration at various sizes throughout ontogeny.

METHODS

Here, using a whole-plant chamber system, we measured the respiration rates, fresh mass and surface area of entire roots and shoots from 377 Fagus crenata individuals, from germinating seeds to mature trees, collected from five different Japanese provenances. Non-linear regression analysis was performed for scaling of root and shoot respiration, fresh mass and surface area with body size.

KEY RESULTS

Whole-plant respiration increased rapidly in germinating seeds. In the seedling to mature tree size range, the scaling of whole-plant respiration to whole-plant fresh mass was expressed as a linear trend on the log-log coordinates (exponent slightly greater than 0.75). In the same body size range, root and shoot respiration vs. whole-plant fresh mass were modelled by upward-convex (exponent decreased from 2.35 to 0.638) and downward-convex trends (exponent increased from -0.918 to 0.864), respectively. The root fraction in whole-plant respiration, fresh mass and surface area shifted continuously throughout ontogeny, increasing in smaller seedlings during early growth stages and decreasing in larger trees.

CONCLUSIONS

Our results suggest a gradual shift in allocation priorities of metabolic energy from roots in seedlings to shoots in mature trees, providing insights into how roots contribute to shoot and whole-plant growth during ontogeny. The models of root : shoot ratio in relation to whole-plant physiology could be applied in tree growth modelling, and in linking the different levels of ecological phenomena, from individuals to ecosystems.

The added costs of winter ocean warming for metabolism, arm regeneration and survival in the brittle star Ophionereis schayeri

As the climate continues to change, it is not just the magnitude of these changes that is important - equally critical is the timing of these events. Conditions that may be well tolerated at one time can become detrimental if experienced at another, as a result of seasonal acclimation. Temperature is the most critical variable as it affects most aspects of an organism's physiology. To address this, we quantified arm regeneration and respiration in the Australian brittle star Ophionereis schayeri for 10 weeks in response to a +3°C warming (18.5°C, simulating a winter heatwave) compared with ambient winter temperature (15.5°C). The metabolic scaling rate (b=0.635 at 15.5°C and 0.746 at 18.5°C) with respect to size was similar to that of other echinoderms and was not affected by temperature. Elevated temperature resulted in up to a 3-fold increase in respiration and a doubling of regeneration growth; however, mortality was greater (up to 44.2% at 18.5°C), especially in the regenerating brittle stars. Metabolic rate of the brittle stars held at 18.5°C was much higher than expected (Q10≈23) and similar to that of O. schayeri tested in summer, which was near their estimated thermotolerance limits. The additional costs associated with the elevated metabolism and regeneration rates incurred by the unseasonably warm winter temperatures may lead to increased mortality and predation risk.

Evolutionary scaling of maximum growth rate with organism size

Data from nearly 1000 species reveal the upper bound to rates of biomass production achievable by natural selection across the Tree of Life. For heterotrophs, maximum growth rates scale positively with organism size in bacteria but negatively in eukaryotes, whereas for phototrophs, the scaling is negligible for cyanobacteria and weakly negative for eukaryotes. These results have significant implications for understanding the bioenergetic consequences of the transition from prokaryotes to eukaryotes, and of the expansion of some groups of the latter into multicellularity. The magnitudes of the scaling coefficients for eukaryotes are significantly lower than expected under any proposed physical-constraint model. Supported by genomic, bioenergetic, and population-genetic data and theory, an alternative hypothesis for the observed negative scaling in eukaryotes postulates that growth-diminishing mutations with small effects passively accumulate with increasing organism size as a consequence of associated increases in the power of random genetic drift. In contrast, conditional on the structural and functional features of ribosomes, natural selection has been able to promote bacteria with the fastest possible growth rates, implying minimal conflicts with both bioenergetic constraints and random genetic drift. If this extension of the drift-barrier hypothesis is correct, the interpretations of comparative studies of biological traits that have traditionally ignored differences in population-genetic environments will require revisiting.

Variable metabolic scaling breaks the law: from 'Newtonian' to 'Darwinian' approaches

Life's size and tempo are intimately linked. The rate of metabolism varies with body mass in remarkably regular ways that can often be described by a simple power function, where the scaling exponent (b, slope in a log-linear plot) is typically less than 1. Traditional theory based on physical constraints has assumed that b is 2/3 or 3/4, following natural law, but hundreds of studies have documented extensive, systematic variation in b. This overwhelming, law-breaking, empirical evidence is causing a paradigm shift in metabolic scaling theory and methodology from ‘Newtonian’ to ‘Darwinian’ approaches. A new wave of studies focuses on the adaptable regulation and evolution of metabolic scaling, as influenced by diverse intrinsic and extrinsic factors, according to multiple context-dependent mechanisms, and within boundary limits set by physical constraints.

Metabolic size scaling reflects growth performance effects on age-size relationships in mussels (Mytilus galloprovincialis)

Body-size scaling of metabolic rate in animals is typically allometric, with mass exponents that vary to reflect differences in the physiological status of organisms of both endogenous and environmental origin. Regarding the intraspecific analysis of this relationship in bivalve molluscs, one important source of metabolic variation comes from the large inter-individual differences in growth performance characteristic of this group. In the present study, we aimed to address the association of growth rate differences recorded among individual mussels (Mytilus galloprovincialis) with variable levels of the standard metabolic rate (SMR) resulting in growth-dependent shift in size scaling relationships. SMR was measured in mussels of different sizes and allometric functions fitting SMR vs. body-mass relationships were compared both inter- and intra-individually. The results revealed a metabolic component (the overhead of growth) attributable to the differential costs of maintenance of feeding and digestion structures between fast and slow growers; these costs were estimated to amount to a 3% increase in SMR per unit of increment in the weight specific growth rate. Scaling exponents computed for intraindividual SMR vs body-mass relationships had a common value b = 0.79 (~ ¾); however, when metabolic effects caused by differential growth were discounted, this value declined to 0.67 (= ⅔), characteristic of surface dependent processes. This last value of the scaling exponent was also recorded for the interindividual relationships of both standard and routine metabolic rates (SMR and RMR) after long-lasting maintenance of mussels under optimal uniform conditions in the laboratory. The above results were interpreted based on the metabolic level boundaries (MLB) hypothesis.

White Paper: An Integrated Perspective on the Causes of Hypometric Metabolic Scaling in Animals

Larger animals studied during ontogeny, across populations, or across species, usually have lower mass-specific metabolic rates than smaller animals (hypometric scaling). This pattern is usually observed regardless of physiological state (e.g. basal, resting, field, maximally-active). The scaling of metabolism is usually highly correlated with the scaling of many life history traits, behaviors, physiological variables, and cellular/molecular properties, making determination of the causation of this pattern challenging. For across-species comparisons of resting and locomoting animals (but less so for across populations or during ontogeny), the mechanisms at the physiological and cellular level are becoming clear. Lower mass-specific metabolic rates of larger species at rest are due to a) lower contents of expensive tissues (brains, liver, kidneys), and b) slower ion leak across membranes at least partially due to membrane composition, with lower ion pump ATPase activities. Lower mass-specific costs of larger species during locomotion are due to lower costs for lower-frequency muscle activity, with slower myosin and Ca++ ATPase activities, and likely more elastic energy storage. The evolutionary explanation(s) for hypometric scaling remain(s) highly controversial. One subset of evolutionary hypotheses relies on constraints on larger animals due to changes in geometry with size; for example, lower surface-to-volume ratios of exchange surfaces may constrain nutrient or heat exchange, or lower cross-sectional areas of muscles and tendons relative to body mass ratios would make larger animals more fragile without compensation. Another subset of hypotheses suggests that hypometric scaling arises from biotic interactions and correlated selection, with larger animals experiencing less selection for mass-specific growth or neurolocomotor performance. A additional third type of explanation comes from population genetics. Larger animals with their lower effective population sizes and subsequent less effective selection relative to drift may have more deleterious mutations, reducing maximal performance and metabolic rates. Resolving the evolutionary explanation for the hypometric scaling of metabolism and associated variables is a major challenge for organismal and evolutionary biology. To aid progress, we identify some variation in terminology use that has impeded cross-field conversations on scaling. We also suggest that promising directions for the field to move forward include: 1) studies examining the linkages between ontogenetic, population-level, and cross-species allometries, 2) studies linking scaling to ecological or phylogenetic context, 3) studies that consider multiple, possibly interacting hypotheses, and 4) obtaining better field data for metabolic rates and the life history correlates of metabolic rate such as lifespan, growth rate and reproduction.

Tolerance of an acute warming challenge declines with body mass in Nile tilapia: evidence of a link to capacity for oxygen uptake

It has been proposed that larger individuals within fish species may be more sensitive to global warming, due to limitations in their capacity to provide oxygen for aerobic metabolic activities. This could affect size distributions of populations in a warmer world but evidence is lacking. In Nile tilapia Oreochromis niloticus (n=18, mass range 21 - 313g), capacity to provide oxygen for aerobic activities (aerobic scope) was independent of mass at an acclimation temperature of 26 °C. Tolerance of acute warming, however, declined significantly with mass when evaluated as the critical temperature for fatigue from aerobic swimming (CTSmax). The CTSmax protocol challenges a fish to meet the oxygen demands of constant aerobic exercise while their demands for basal metabolism are accelerated by incremental warming, culminating in fatigue. CTSmax elicited pronounced increases in oxygen uptake in the tilapia but the maximum rates achieved prior to fatigue declined very significantly with mass. Mass-related variation in CTSmax and maximum oxygen uptake rates were positively correlated, which may indicate a causal relationship. When fish populations are faced with acute thermal stress, larger individuals may become constrained in their ability to perform aerobic activities at lower temperatures than smaller conspecifics. This could affect survival and fitness of larger fish in a future world with more frequent and extreme heatwaves, with consequences for population productivity.

How Metabolic Rate Relates to Cell Size

Metabolic rate and its covariation with body mass vary substantially within and among species in little understood ways. Here, I critically review explanations (and supporting data) concerning how cell size and number and their establishment by cell expansion and multiplication may affect metabolic rate and its scaling with body mass. Cell size and growth may affect size-specific metabolic rate, as well as the vertical elevation (metabolic level) and slope (exponent) of metabolic scaling relationships. Mechanistic causes of negative correlations between cell size and metabolic rate may involve reduced resource supply and/or demand in larger cells, related to decreased surface area per volume, larger intracellular resource-transport distances, lower metabolic costs of ionic regulation, slower cell multiplication and somatic growth, and larger intracellular deposits of metabolically inert materials in some tissues. A cell-size perspective helps to explain some (but not all) variation in metabolic rate and its body-mass scaling and thus should be included in any multi-mechanistic theory attempting to explain the full diversity of metabolic scaling. A cell-size approach may also help conceptually integrate studies of the biological regulation of cellular growth and metabolism with those concerning major transitions in ontogenetic development and associated shifts in metabolic scaling.

Metabolic Scaling in Birds and Mammals: How Taxon Divergence Time, Phylogeny, and Metabolic Rate Affect the Relationship between Scaling Exponents and Intercepts

Simple Summary

This study is based on a large dataset and re-evaluates data on the metabolic rate, providing new insights into the similarities and differences across different groups of birds and mammals. We compared six taxonomic groups of mammals and birds according to their energetic characteristics and the geological time of evolutionary origin. The overall metabolic rate of a taxonomic group increases with the geological time of evolutionary origin. The terrestrial mammals and flightless birds have almost equal metabolic levels. The higher the metabolic rate in a group, the less it increases within increasing body size in this group.

Abstract

Analysis of metabolic scaling in currently living endothermic animal species allowed us to show how the relationship between body mass and the basal metabolic rate (BMR) has evolved in the history of endothermic vertebrates. We compared six taxonomic groups according to their energetic characteristics and the time of evolutionary divergence. We transformed the slope of the regression lines to the common value and analyzed three criteria for comparing BMR of different taxa regardless of body size. Correlation between average field metabolic rate (FMR) of the group and its average BMR was shown. We evaluated the efficiency of self-maintenance in ordinary life (defined BMR/FMR) in six main groups of endotherms. Our study has shown that metabolic scaling in the main groups of endothermic animals correlates with their evolutionary age: the younger the group, the higher the metabolic rate, but the rate increases more slowly with increasing body weight. We found negative linear relationship for scaling exponents and the allometric coefficient in five groups of endotherms: in units of mL O₂/h per g, in relative units of allometric coefficients, and also in level or scaling elevation. Mammals that diverged from the main vertebrate stem earlier have a higher “b” exponent than later divergent birds. A new approach using three criteria for comparing BMR of different taxa regardless of body mass will be useful for many biological size-scaling relationships that follow the power function.

The Evolution of Offspring Size: a Metabolic Scaling Perspective

Size at the start of life reflects the initial per offspring parental investment - including both the embryo and the nutrients supplied to it. Initial offspring size can vary substantially both within and among species. Within species, increasing offspring size can enhance growth, reproduction, competitive ability, and reduce susceptibility to predation and starvation later in life, that can ultimately increase fitness. Previous work has suggested that the fitness benefits of larger offspring size may be driven by energy expenditure during development - or how offspring metabolic rate scales with offspring size. Despite the importance of early life energy expenditure in shaping later life fitness trajectories, consideration of among-species scaling of metabolic rate at the time of birth as a potential source of general metabolic scaling patterns has been overlooked by theory. Here we review the patterns and processes of energy expenditure at the start of life when mortality is often greatest. We compile existing data on metabolic rate and offspring size for 191 ectotherm species spanning eight phyla and use phylogenetically-controlled methods to quantify among-species scaling patterns. Across a 109-fold mass range, we find that offspring metabolic rate scales hypometrically with size, with an overall scaling exponent of 0.66. This exponent varies across ontogenetic stage and feeding activity, but is consistently hypometric, including across environmental temperatures. Despite differences in parental investment, life history and habitat, large-offspring species use relatively less energy as a proportion of size, compared with small-offspring species. Greater residual energy can be used to fuel the next stages of life, particularly in low resource environments. Based on available evidence, we conclude that, while large knowledge gaps remain, the evolution of offspring size is likely shaped by context-dependent selection acting on correlated traits, including metabolic rates maintaining hypometric scaling, that operates within broader physical constraints.

Growth and Mortality as Causes of Variation in Metabolic Scaling Among Taxa and Taxonomic Levels

Metabolic rate (MR) usually changes (scales) out of proportion to body mass (BM) as MR = aBMb, where a is a normalisation constant and b is the scaling exponent that reflects how steep this change is. This scaling relationship is fundamental to biology, but over a century of research has provided little consensus on the value of b, and why it appears to vary among taxa and taxonomic levels. By analysing published data on fish and taking an individual-based approach to metabolic scaling, I show that variation in growth of fish under naturally restricted food availability can explain variation in within-individual (ontogenetic) b for standard (maintenance) metabolic rate (SMR) of brown trout (Salmo trutta), with the fastest growers having the steepest metabolic scaling (b ≈ 1). Moreover, I show that within-individual b can vary much more widely than previously assumed from work on different individuals or different species, from -1 to 1 for SMR among individual brown trout. The negative scaling of SMR for some individuals was caused by reductions in metabolic rate in a food limited environment, likely to maintain positive growth. This resulted in a mean within-individual b for SMR that was significantly lower than the across-individual ("static") b, a difference that also existed for another species, cunner (Tautogolabrus adspersus). Interestingly, the wide variation in ontogenetic b for SMR among individual brown trout did not exist for maximum (active) metabolic rate (MMR) of the same fish, showing that these two key metabolic traits (SMR and MMR) can scale independently of one another. I also show that across-species ("evolutionary") b for SMR of 134 fishes is significantly steeper (b approaching 1) than the mean ontogenetic b for the brown trout and cunner. Based on these interesting findings, I hypothesise that evolutionary and static metabolic scaling can be systematically different from ontogenetic scaling, and that the steeper evolutionary than ontogenetic scaling for fishes arises as a by-product of natural selection for fast-growing individuals with steep metabolic scaling (b ≈ 1) early in life, where size-selective mortality is high for fishes. I support this by showing that b for SMR tends to increase with natural mortality rates of fish larvae within taxa.

A quantitative genetics perspective on the body-mass scaling of metabolic rate

Widely observed allometric scaling (log-log slope<1) of metabolic rate (MR) with body mass (BM) in animals has been frequently explained using functional mechanisms, but rarely studied from the perspective of multivariate quantitative genetics. This is unfortunate, given that the additive genetic slope (bA) of the MR-BM relationship represents the orientation of the 'line of least genetic resistance' along which MR and BM may most likely evolve. Here, we calculated bA in eight species. Although most bA values were within the range of metabolic scaling exponents reported in the literature, uncertainty of each bA estimate was large (only one bA was significantly lower than 3/4 and none were significantly different from 2/3). Overall, the weighted average for bA (0.667±0.098 95% CI) is consistent with the frequent observation that metabolic scaling exponents are negatively allometric in animals (b<1). Although bA was significantly positively correlated with the phenotypic scaling exponent (bP) across the sampled species, bP was usually lower than bA, as reflected in a (non-significantly) lower weighted average for bP (0.596±0.100). This apparent discrepancy between bA and bP resulted from relatively shallow MR-BM scaling of the residuals [weighted average residual scaling exponent (be)=0.503±0.128], suggesting regression dilution (owing to measurement error and within-individual variance) causing a downward bias in bP. Our study shows how the quantification of the genetic scaling exponent informs us about potential constraints on the correlated evolution of MR and BM, and by doing so has the potential to bridge the gap between micro- and macro-evolutionary studies of scaling allometry.

Evolution of metabolic scaling among the tetrapod: Effect of phylogeny, the geologic time of class formation and uniformity of species within a class

The metabolic scaling in the animal has been discussed for over 90 years, but no consensus has been reached. Our analysis of 2,126 species of vertebrates reveals a significant allometric exponent heterogeneity. We show that classes of terrestrial vertebrates exhibit the evolution of metabolic scaling. Both the allometric coefficient "a" and the allometric exponent "b" change naturally, but differently depending on the geological time of group formation. The allometric coefficient "a" shows the measure of the evolutionary development of systems that forms resting metabolism in animals. Endothermic classes, such as birds and mammals, have a metabolic rate that is in an order of magnitude higher than that in ectothermic classes, including amphibians and reptiles. In the terrestrial vertebrate phylogeny, we find that the metabolic scaling is characterized by three main allometric exponent values: b = 3/4 (mammals), b > 3/4 (ectotherms, such as amphibians and reptiles), and b < 3/4 (birds). The heterogeneity of the allometric exponent is a natural phenomenon associated with the general evolution of vertebrates. The scaling factor decreases depending on both the external design and the size (birds vs mammals) of the animal. The metabolic rate and uniformity of species within a class increase as the geological start date of formation of the class approaches the present time. The higher the mass-specific standard metabolic rate in the class, the slower metabolic rate grows with increasing body size in this class. Our results lay the groundwork for further exploration of the evolutionary and ecological aspects of the development of metabolic scaling in animals. This article is protected by copyright. All rights reserved.

Consistent scaling of whole-shoot respiration between Moso bamboo (Phyllostachys pubescens) and trees

Both Moso bamboo (Phyllostachys pubescens) and tree forests have a large biomass; they are considered to play an important role in ecosystem carbon budgets. The scaling relationship between individual whole-shoot (i.e., aboveground parts) respiration and whole-shoot mass provides a clue for comparing the carbon budgets of Moso bamboo and tree forests. However, nobody has empirically demonstrated whether there is a difference between these forest types in the whole-shoot scaling relationship. We developed whole-shoot chambers and measured the shoot respiration of 58 individual mature bamboo shoots from the smallest to the largest in a Moso bamboo forest, and then compared them with that of 254 tree shoots previously measured. For 30 bamboo shoots, we measured the respiration rate of leaves, branches, and culms. We found that the scaling exponent of whole-shoot respiration of bamboo fitted by a simple power function on a log-log scale was 0.843 (95 % CI 0.797-0.885), which was consistent with that of trees, 0.826 (95 % CI 0.799-0.851), but higher than 3/4, the value typifying the Kleiber's rule. The respiration rates of leaves, branches, and culms at the whole-shoot level were proportional to their mass, revealing a constant mean mass-specific respiration of 1.19, 0.224, and 0.0978 µmol CO2 kg- 1 s- 1, respectively. These constant values suggest common traits of organs among physiologically integrated ramets within a genet. Additionally, the larger the shoots, the smaller the allocation of organ mass to the metabolically active leaves, and the larger the allocation to the metabolically inactive culms. Therefore, these shifts in shoot-mass partitioning to leaves and culms caused a negative metabolic scaling of Moso bamboo shoots. The observed convergent metabolic scaling of Moso bamboo and trees may facilitate comparisons of the ecosystem carbon budgets of Moso bamboo and tree forests.

Biological scaling analyses are more than statistical line fitting

The magnitude of many biological traits relates strongly and regularly to body size. Consequently, a major goal of comparative biology is to understand and apply these 'size-scaling' relationships, traditionally quantified by using linear regression analyses based on log-transformed data. However, recently some investigators have questioned this traditional method, arguing that linear or non-linear regression based on untransformed arithmetic data may provide better statistical fits than log-linear analyses. Furthermore, they advocate the replacement of the traditional method by alternative specific methods on a case-by-case basis, based simply on best-fit criteria. Here, I argue that the use of logarithms in scaling analyses presents multiple valuable advantages, both statistical and conceptual. Most importantly, log-transformation allows biologically meaningful, properly scaled (scale-independent) comparisons of organisms of different size, whereas non-scaled (scale-dependent) analyses based on untransformed arithmetic data do not. Additionally, log-based analyses can readily reveal biologically and theoretically relevant discontinuities in scale invariance during developmental or evolutionary increases in body size that are not shown by linear or non-linear arithmetic analyses. In this way, log-transformation advances our understanding of biological scaling conceptually, not just statistically. I hope that my Commentary helps students, non-specialists and other interested readers to understand the general benefits of using log-transformed data in size-scaling analyses, and stimulates advocates of arithmetic analyses to show how they may improve our understanding of scaling conceptually, not just statistically.

Genome size influences adaptive plasticity of water loss, but not metabolic rates, in lungless salamanders

Many expressions of phenotype, such as physiological performance, integrate multiple underlying traits to function. Linking component traits to adaptive physiology thus gives insight into mechanisms of selection acting on performance. Genome size (C-value) is a trait that influences physiology in multiple taxa by exerting a nucleotypic effect, constraining cell size and cellular physiology such that whole-organism mass-specific metabolism is reduced with increasing C-value. We tested for this mechanism of C-value function acting in lungless salamanders, plus an unexplored potential mechanism of C-value effects constraining water transport across the body surface to influence cutaneous water loss rates. We found no evidence for a nucleotypic effect on metabolic rates, but we demonstrate a relationship between C-value and water loss physiology. Under warmer experimental conditions, C-value was inversely correlated with water loss and positively correlated with resistance to water loss, which demonstrated adaptive plasticity at higher temperatures. We hypothesize that this pattern results from differences in cell size constraining diffusion and evaporation of water from the skin under warm conditions when cutaneous perfusion is reduced. Testing this hypothesis may confirm a previously unappreciated adaptive role for C-value variation in this group, and reveals the possibility that genome size influences physiological exchange across transport barriers more broadly.

Comparison of metabolic scaling between triploid and diploid common carp

Ploidy level affects both the cell size and metabolic rate (MR) of organisms. The present study aimed to examine whether ploidy levels cause differences in cell surface area (SA), MR and metabolic scaling. The resting MR (RMR), red blood cell SA (SA_RBC), red blood cell count (RBCC), gill SA (GSA), and ventilation frequency (VF) were measured in diploid and triploid common carp with different body masses (M). The results showed that both M and ploidy level affected the RMR, GSA, VF, and SA_RBC, with interactions between M and ploidy level. The triploids had larger SA_RBC but lower RBCC than those of the diploids. The SA_RBC increased weakly but significantly with increasing M, by an exponent of 0.043, in the triploids but did not increase in the diploids. The RMR of the triploids and diploids scaled with M, by exponents of 0.696 and 1.007, respectively. The RMR was higher in the triploids than the diploids. The GSA scaled with M, with an exponent of 0.906 in the triploids and an exponent of 1.043 in the diploids. The VF scaled with M by an exponent of - 0.305 in the triploids but showed no correlation with M in the diploids. The larger SA_RBC and RMR and smaller scaling exponents of both the GSA and VF of the triploids were consistent with the finding that the b_R was smaller in the triploids than in the diploids. This suggests that the ploidy-induced changes of SA and SA scaling affect the metabolic scaling of fish.

Can shifts in metabolic scaling predict coevolution between diet quality and body size?

Larger species tend to feed on abundant resources, which nonetheless have lower quality or degradability, the so-called Jarman-Bell principle. The "eat more" hypothesis posits that larger animals compensate for lower quality diets through higher consumption rates. If so, evolutionary shifts in metabolic scaling should affect the scope for this compensation, but whether this has happened is unknown. Here, we investigated this issue using termites, major tropical detritivores that feed along a humification gradient ranging from dead plant tissue to mineral soil. Metabolic scaling is shallower in termites with pounding mandibles adapted to soil-like substrates than in termites with grinding mandibles adapted to fibrous plant tissue. Accordingly, we predicted that only larger species of the former group should have more humified, lower quality diets, given their higher scope to compensate for such a diet. Using literature data on 65 termite species, we show that diet humification does increase with body size in termites with pounding mandibles, but is weakly related to size in termites with grinding mandibles. Our findings suggest that evolution of metabolic scaling may shape the strength of the Jarman-Bell principle.

Temperature effects on metabolic scaling of a keystone freshwater crustacean depend on fish-predation regime

According to the metabolic theory of ecology, metabolic rate, an important indicator of the pace of life, varies with body mass and temperature as a result of internal physical constraints. However, various ecological factors may also affect metabolic rate and its scaling with body mass. Although reports of such effects on metabolic scaling usually focus on single factors, the possibility of significant interactive effects between multiple factors requires further study. In this study, we show that the effect of temperature on the ontogenetic scaling of resting metabolic rate of the freshwater amphipod Gammarus minus depends critically on habitat differences in predation regime. Increasing temperature tends to cause decreases in the metabolic scaling exponent (slope) in population samples from springs with fish predators, but increases in population samples from springs without fish. Accordingly, the temperature sensitivity of metabolic rate is not only size-specific, but also its relationship to body size shifts dramatically in response to fish predators. We hypothesize that the dampened effect of temperature on the metabolic rate of large adults in springs with fish, and of small juveniles in springs without fish are adaptive evolutionary responses to differences in the relative mortality risk of adults and juveniles in springs with versus without fish predators. Our results demonstrate a complex interaction among metabolic rate, body mass, temperature and predation regime. The intraspecific scaling of metabolic rate with body mass and temperature is not merely the result of physical constraints related to internal body design and biochemical kinetics, but rather is ecologically sensitive and evolutionarily malleable.

Coevolution of body size and metabolic rate in vertebrates: a life-history perspective

Despite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non-linearity of the relationship between MR and body mass. This 'statistical' view must be replaced with the life-history perspective that 'allows' organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation 'decisions' that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those 'decisions' form a wealth of life-history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single-cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life-history evolution is the best way forward.

Tracheal branching in ants is area-decreasing, violating a central assumption of network transport models

The structure of tubular transport networks is thought to underlie much of biological regularity, from individuals to ecosystems. A core assumption of transport network models is either area-preserving or area-increasing branching, such that the summed cross-sectional area of all child branches is equal to or greater than the cross-sectional area of their respective parent branch. For insects, the most diverse group of animals, the assumption of area-preserving branching of tracheae is, however, based on measurements of a single individual and an assumption of gas exchange by diffusion. Here we show that ants exhibit neither area-preserving nor area-increasing branching in their abdominal tracheal systems. We find for 20 species of ants that the sum of child tracheal cross-sectional areas is typically less than that of the parent branch (area-decreasing). The radius, rather than the area, of the parent branch is conserved across the sum of child branches. Interpretation of the tracheal system as one optimized for the release of carbon dioxide, while readily catering to oxygen demand, explains the branching pattern. Our results, together with widespread demonstration that gas exchange in insects includes, and is often dominated by, convection, indicate that for generality, network transport models must include consideration of systems with different architectures.

A fundamental assumption of models of the transport of substances through networks of tubes, such as circulatory systems in animals and vascular systems in plants, is that the total cross-sectional area of the tubes remains constant irrespective of the branching level, or that it increases slightly in the direction from the largest to the smallest tubes. One large tube should have the same or a slightly smaller area than the sum of the next two tubes after a branching. The assumption of such a pattern underpins one of biology’s most influential ideas–the metabolic theory of ecology. Surprisingly, the assumption has never been systematically examined for insects–the planet’s most diverse group of animals which deliver oxygen to and remove carbon dioxide from their bodies using a network of tubes known as tracheae. Until recently, it has been technologically very challenging to do so. Here, we use x-ray synchrotron tomography to overcome this challenge. We show that tracheal branching in 20 species of ants does not follow this pattern. Rather, cross-sectional area reduces in an inwards direction. We then use modelling to show that such a pattern facilitates outward CO₂ release, a process more challenging for insects than moving oxygen inwards. Our work suggests that much still needs to be done to understand the fundamental assumptions underlying network transport models and how they apply more generally across life–especially in the context of why metabolic rate scales with body size.

A Perspective on Body Size and Abundance Relationships across Ecological Communities

Recently, several studies have reported relationships between the abundance of organisms in an ecological community and their mean body size (called cross-community scaling relationships: CCSRs) that can be described by simple power functions. A primary focus of these studies has been on the scaling exponent (slope) and whether it approximates -3/4, as predicted by Damuth's rule and the metabolic theory in ecology. However, some CCSR studies have reported scaling exponents significantly different from the theoretical value of -3/4. Why this variation occurs is still largely unknown. The purpose of our commentary is to show the value of examining both the slopes and elevations of CCSRs and how various ecological factors may affect them. As a heuristic exercise, we reanalyzed three published data sets based on phytoplankton, rodent, and macroinvertebrate assemblages that we subdivided according to three distinctly different ecological factors (i.e., climate zone, season, and trophic level). Our analyses reveal significant variation in either or both the CCSR slopes and elevations for marine phytoplankton communities across climate zones, a desert rodent community across seasons, and saltwater lagoon macroinvertebrate communities across trophic levels. We conclude that achieving a comprehensive understanding of abundance-size relationships at the community level will require consideration of both slopes and elevations of these relationships and their possible variation in different ecological contexts.

Effects of Fish Predators on the Mass-Related Energetics of a Keystone Freshwater Crustacean

Little is known about how predators or their cues affect the acquisition and allocation of energy throughout the ontogeny of prey organisms. To address this question, we have been comparing the ontogenetic body-mass scaling of various traits related to energy intake and use between populations of a keystone amphipod crustacean inhabiting freshwater springs, with versus without fish predators. In this progress report, we analyze new and previously reported data to develop a synthetic picture of how the presence/absence of fish predators affects the scaling of food assimilation, fat content, metabolism, growth and reproduction in populations of Gammarus minus located in central Pennsylvania (USA). Our analysis reveals two major clusters of ‘symmorphic allometry’ (parallel scaling relationships) for traits related to somatic versus reproductive investment. In the presence of fish predators, the scaling exponents for somatic traits tend to decrease, whereas those for reproductive traits tend to increase. This divergence of scaling exponents reflects an intensified trade-off between somatic and reproductive investments resulting from low adult survival in the face of size-selective predation. Our results indicate the value of an integrated view of the ontogenetic size-specific energetics of organisms and its response to both top-down (predation) and bottom-up (resource supply) effects.

The euryhaline pygmy mussel, Xenostrobus securis, is a useful biomonitor of key metal contamination in the highly urbanised Sydney Estuary, Australia

This study critically evaluated the native pygmy mussel (Xenostrobus securis) as a biomonitor of the key metal contaminants in the highly urbanised Sydney Estuary, south-eastern Australia. Five metals (Cd, Cr, Cu, Pb and Zn) were identified as key contaminants, based on their enrichment factors (EFs) in the whole soft tissue of X. securis at 24 sampling sites, relative to baseline values from near-pristine reference sites in the adjacent Hawkesbury Estuary. Inverse relationships established between mussel size (dry tissue weight) and tissue concentrations of each metal were used to reduce variance (by 4-fold) among individuals; gender and reproductive status had no significant (p > 0.05) effect on tissue metal concentrations in X. securis. Metal concentrations in three environmental matrices - filtered (<0.2 μm) surface water (operationally defined as the dissolved/colloidal phase), suspended particulate matter (SPM; >0.2 μm) and surface sediment (<2 mm particle size), which are most relevant to a suspension-feeding estuarine bivalve, were also determined at each sampling site. For each of the five metals, highly significant (p < 0.01) positive linear regressions were established between metal EFs for mussel tissue and each environmental matrix. Metals in surface sediment and SPM explained 80-91% and 81-90%, respectively, of the variability in metal concentrations in mussel tissue, with filtered surface water explaining 74-86%. Cumulative mussel tissue EFs of all five metals, when regressed against each environmental matrix, showed that surface sediment concentrations explained 93% of their variability between sites, SPM 94% and filtered surface water 87-90%. Hence, X. securis very closely reflects the metal concentrations in its aquatic environment. The study provides a quality-assured benchmark of key metal contamination in the Sydney Estuary, and an appropriate methodology that may be used to discern any changes in metal contaminant status using X. securis.

Ecological pressures and the contrasting scaling of metabolism and body shape in coexisting taxa: cephalopods versus teleost fish

Metabolic rates are fundamental to many biological processes, and commonly scale with body size with an exponent ( b_R) between 2/3 and 1 for reasons still debated. According to the 'metabolic-level boundaries hypothesis', b_R depends on the metabolic level ( L_R). We test this prediction and show that across cephalopod species intraspecific b_R correlates positively with not only L_R but also the scaling of body surface area with body mass. Cephalopod species with high L_R maintain near constant mass-specific metabolic rates, growth and probably inner-mantle surface area for exchange of respiratory gases or wastes throughout their lives. By contrast, teleost fish show a negative correlation between b_R and L_R. We hypothesize that this striking taxonomic difference arises because both resource supply and demand scale differently in fish and cephalopods, as a result of contrasting mortality and energetic pressures, likely related to different locomotion costs and predation pressure. Cephalopods with high L_R exhibit relatively steep scaling of growth, locomotion, and resource-exchange surface area, made possible by body-shape shifting. We suggest that differences in lifestyle, growth and body shape with changing water depth may be useful for predicting contrasting metabolic scaling for coexisting animals of similar sizes. This article is part of the theme issue 'Physiological diversity, biodiversity patterns and global climate change: testing key hypotheses involving temperature and oxygen'.

Interspecific scaling of blood flow rates and arterial sizes in mammals

This meta-study investigated the relationships between blood flow rate (Q̇; cm³ s^-1), wall shear stress (τ_w; dyn cm^-2) and lumen radius (r _i; cm) in 20 named systemic arteries of nine species of mammals, ranging in mass from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varied between 3.7 µm in a cremaster artery of a rat and 11.2 mm in the aorta of a human. The 92 logged data points of [Formula: see text] and r _i are described by a single second-order polynomial curve with the equation: [Formula: see text] The slope of the curve increased from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci's rule ([Formula: see text]) applies to the main arteries and Murray's law ([Formula: see text]) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which [Formula: see text] is fairly constant, yielded the allometric power equation: [Formula: see text] These empirical equations allow calculation of resting perfusion rates from arterial lumen size alone, without reliance on theoretical models or assumptions on the scaling of wall shear stress in relation to body mass. As expected, [Formula: see text] of individual named arteries is strongly affected by body mass; however, [Formula: see text] of the common carotid artery from six species (mouse to horse) is also sensitive to differences in whole-body basal metabolic rate, independent of the effect of body mass.

Approaches for testing hypotheses for the hypometric scaling of aerobic metabolic rate in animals

Hypometric scaling of aerobic metabolism [larger organisms have lower mass-specific metabolic rates (MR/g)] is nearly universal for interspecific comparisons among animals, yet we lack an agreed upon explanation for this pattern. If physiological constraints on the function of larger animals occur and limit MR/g, these should be observable as direct constraints on animals of extant species and/or as evolved responses to compensate for the proposed constraint. There is evidence for direct constraints and compensatory responses to O2 supply constraint in skin-breathing animals, but not in vertebrates with gas-exchange organs. The duration of food retention in the gut is longer for larger birds and mammals, consistent with a direct constraint on nutrient uptake across the gut wall, but there is little evidence for evolving compensatory responses to gut transport constraints in larger animals. Larger placental mammals (but not marsupials or birds) show evidence of greater challenges with heat dissipation, but there is little evidence for compensatory adaptations to enhance heat loss in larger endotherms, suggesting that metabolic rate (MR) more generally balances heat loss for thermoregulation in endotherms. Size-dependent patterns in many molecular, physiological, and morphological properties are consistent with size-dependent natural selection, such as stronger selection for neurolocomotor performance and growth rate in smaller animals and stronger selection for safety and longevity in larger animals. Hypometric scaling of MR very likely arises from different mechanisms in different taxa and conditions, consistent with the diversity of scaling slopes for MR.