Metabolic scaling as an emergent outcome of variation in metabolic rate

The allometric scaling of metabolic rate and what drives it are major questions in biology with a long history. Since the metabolic rate at any level of biological organization is an emergent property of its lower-level constituents, it is an outcome of the intrinsic heterogeneity among these units and the interactions among them. However, the influence of lower-level heterogeneity on system-level metabolic rate is difficult to investigate, given the tightly integrated body plan of unitary organisms. In this context, social insects such as honeybees can serve as important model systems because unlike unitary organisms, these superorganisms can be taken apart and reassembled in different configurations to study metabolic rate and its various drivers at different levels of organization. This commentary discusses the background of such an approach and how combining it with artificial selection to generate heterogeneity in metabolic rate with an analytical framework to parse out the different mechanisms that contribute to the effects of heterogeneity can contribute to the various models of metabolic scaling. Finally, the absence of the typical allometric scaling relationship among different species of honeybees is discussed as an important prospect for deciphering the role of top-down ecological factors on metabolic scaling. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

Temperature effects on metabolism and energy requirement during the fast growth phase in the red-footed tortoise, Chelonoidis carbonaria

Early life is a challenging phase because of the high rates of morphophysiological development and growth. Changes in ambient temperature, which directly affect energy metabolism and digestive functions in ectotherms, may be of great impact during this phase. We addressed this issue in red-footed tortoise (Chelonoidis carbonaria) hatchlings kept in captivity. To this end, we investigated the effect of temperature (28 °C and 18 °C) on mass-specific gross energy intake (GEIm), daily body mass gain (MG), daily intake of gross energy (GEI), digestible energy (DEI), resting metabolic rate (RMR), and specific dynamic action (SDA) components during different seasons in the first 13 months after hatching. Greater GEIm and MG were observed in spring (381.7 ± 84.9 J.g-0.86.day-1 and 0.9 ± 0.4 g.day-1) and summer (356.9 ± 58.9 J.g-0.86.day-1 and 1.0 ± 0.4 g.day-1). The highest and lowest RMRs at 28 °C were observed in spring (36.4 ± 5.1 kJ.kg-1.day-1) and winter (22.4 ± 6.2 kJ.kg-1.day-1), respectively. Regardless season, hatchlings showed greater GEI and DEI, O2 consumption, CO2 production, RMR, maximum metabolic rate after feeding (FMRMAX), and heat increment (FMRMAX- RMR) at 28 °C compared to 18 °C. In addition, the significant body mass influence showed allometric exponents of 0.62 at 28 °C and 0.92 at 18 °C for RMR. Our results indicate an important effect of environmental temperature on energy requirements and utilization in C. carbonaria hatchlings, which is seasonally influenced even in this early phase of life.

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.

Physiological variables in machine learning QSARs allow for both cross-chemical and cross-species predictions

A major challenge in ecological risk assessment is estimating chemical-induced effects across taxa without species-specific testing. Where ecotoxicological data may be more challenging to gather, information on species physiology is more available for a broad range of taxa. Physiology is known to drive species sensitivity but understanding about the relative contribution of specific underlying processes is still elusive. Consequently, there remains a need to understand which physiological processes lead to differences in species sensitivity. The objective of our study was to utilize existing knowledge about organismal physiology to both understand and predict differences in species sensitivity. Machine learning models were trained to predict chemical- and species-specific endpoints as a function of both chemical fingerprints/descriptors and physiological properties represented by dynamic energy budget (DEB) parameters. We found that random forest models were able to predict chemical- and species-specific endpoints, and that DEB parameters were relatively important in the models, particularly for invertebrates. Our approach illuminates how physiological properties may drive species sensitivity, which will allow more realistic predictions of effects across species without the need for additional animal testing.

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.

Metabolic rates in the squareback marsh crab Armases cinereum

Metabolic rate is a basic individual metric that extends beyond the individual to link the ecology of populations, communities, and ecosystems via its role as a central component of energy budgets. Metabolic rates are often measured indirectly by quantifying respiration under simplified, standard laboratory conditions. This approach limits the application of these measurements to a small range of conditions that commonly do not reflect natural field conditions. We measured metabolic rates of the squareback marsh crab Armases cinereum under field conditions. Previous work highlights that movement of individual A. cinereum, especially females, provides a potential spatial subsidy of energy, as individuals consume foods in salt marshes and then transfer the resulting energy to upland forest ecosystems. We show that metabolic rate increases with size for both males and females and that metabolic rates are influenced by temperature and by whether females are vitellogenic. The metabolic rates that we measured more closely approximate field metabolic rates than standard metabolic rates and demonstrate that individual crabs experience high energy expenditures, reducing the amount of energy that may be transferred as a subsidy between marsh and forest as a result of the daily movements of individual crabs. Our measurements are therefore also a key component for the construction of an energy budget for this species.

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.

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.

Ontogeny of the Respiratory Area in Relation to Body Mass with Reference to Resting Metabolism in the Japanese Flounder, Paralichthys olivaceus (Temminck & Schlegel, 1846)

Metabolism is the fundamental process dictating material and energy fluxes through organisms. Several studies have suggested that resting metabolic scaling in various aquatic invertebrates is positively correlated with changes in body shape and the scaling of body surface area, which agrees with the surface area theory, but contradicts the negative correlations predicted by the resource–transport network theory. However, the relationship between resting metabolic scaling and respiration area, particularly in asymmetric fish that have undergone dramatically rapid metamorphosis, remains unclear. In this morphometric study in an asymmetric fish species (Paralichthys olivaceus), I compared my results with previous reports on resting metabolic scaling. I measured the respiratory area of P. olivaceus specimens aged 11–94 days (body weight, 0.00095–1.30000 g, respectively) to determine whether and how the resting metabolic scaling is associated with changes in body shape and respiratory area. Resting metabolic scaling might be more closely related to body surface area, because their slopes exactly corresponded with each other, than to respiratory area. Furthermore, confirming the surface area theory, it was linked to changes in body shape, but not from the resource–transport network theory. These findings provide new insights into the scaling mechanisms of area in relation to metabolism in asymmetric fish.

Energetic dissociation of individual and species ranges

The use of energy is universal to all life forms and all levels of biological organization, potentially linking processes operating at variable scales. Individual and species ranges might be energetically constrained, yet divergent metabolic limitations at both scales can disassociate these individual and species traits. We analysed comparative energetic and range data to unravel the mechanistic basis of the dissociation between individual and species range sizes observed among mammalian species. Our results demonstrate that basal, or maintenance, metabolism negatively correlates with individual ranges, but, at the same time, it positively correlates with species ranges. High aerobic capacity, i.e. maximum metabolic rate, positively correlates with individual ranges, but it is weakly related to species range size. These antagonistic energetic constraints on both ranges could lead to a disassociation between individual and species traits and to a low covariation between home and species range sizes. We show that important organismal functions, such as basal and maximum metabolic rates, have the potential to unravel mechanisms operating at different levels of biological organization and to expose links between energy-dependent processes at different scales.

Universal rules of life: metabolic rates, biological times and the equal fitness paradigm

Here we review and extend the equal fitness paradigm (EFP) as an important step in developing and testing a synthetic theory of ecology and evolution based on energy and metabolism. The EFP states that all organisms are equally fit at steady state, because they allocate the same quantity of energy, ~ 22.4 kJ/g/generation to the production of offspring. On the one hand, the EFP may seem tautological, because equal fitness is necessary for the origin and persistence of biodiversity. On the other hand, the EFP reflects universal laws of life: how biological metabolism - the uptake, transformation and allocation of energy - links ecological and evolutionary patterns and processes across levels of organisation from: (1) structure and function of individual organisms, (2) life history and dynamics of populations, and (3) interactions and coevolution of species in ecosystems. The physics and biology of metabolism have facilitated the evolution of millions of species with idiosyncratic anatomy, physiology, behaviour and ecology but also with many shared traits and tradeoffs that reflect the single origin and universal rules of life.

Temperature dependence of population responses to competition and metabolic stress: An agent-based model to inform ecological risk assessment in a changing climate

Understanding the interactions among multiple stressors is a crucial issue for ecological risk assessment and ecosystem management. However, it is often impractical, or impossible, to collect empirical data concerning all the interactions at any scale because the type of interaction differs across species and levels of biological organization. We applied an agent-based model to simulate the effects of a hypothetical chemical stressor and inter-specific competition (both alone and together) on greenback cutthroat trout (GCT), a listed species under the US Endangered Species Act, in two temperature scenarios. The trout life cycle is modeled using the Dynamic Energy Budget theory. The chemical stressor is represented by a reduction in ingestion efficiency, and competition is implemented by introducing a population of brown trout. Results show that chemical exposure is the major stressor in the colder temperature scenario, whereas competition mostly affected the GCT population in the warmer environment. Moreover, the effects of the stressors at the individual level were not predictive of the type of interactions between stressors (additive, antagonistic, synergistic) at the population level, which differed between the two-temperature scenarios. We conclude that mechanistic models can help to identify generalities about interactions among environmental and stressor properties, create in-silico experiments to provide different scenarios for conservation purposes, and explore multiple-exposure consequences at higher levels of biological organization. In this way they can provide useful tools for improving ecological risk assessment and informing management decisions.

Oxygen limitation may affect the temperature and size dependence of metabolism in aquatic ectotherms

Organismal responses to climate change are mediated through its effects on physiology and metabolism. In aquatic environments, both water temperature and oxygen availability may modulate these responses by altering the aerobic metabolism fueling physiological performance. However, ecological models aimed at predicting how environmental factors shape aerobic metabolism disregard the role of oxygen supply. Here, we expand on these models by explicitly incorporating oxygen supply. Our results show that warmer water increases oxygen demand relative to supply, and the resulting reduction in aerobic scope appears to be stronger in larger individuals. Smaller aerobic scopes in warming water imply that climate change will reduce energy budgets needed to support the activities of aquatic animals and their physiological performance in the future.

Both oxygen and temperature are fundamental factors determining metabolic performance, fitness, ecological niches, and responses of many aquatic organisms to climate change. Despite the importance of physical and physiological constraints on oxygen supply affecting aerobic metabolism of aquatic ectotherms, ecological theories such as the metabolic theory of ecology have focused on the effects of temperature rather than oxygen. This gap currently impedes mechanistic models from accurately predicting metabolic rates (i.e., oxygen consumption rates) of aquatic organisms and restricts predictions to resting metabolism, which is less affected by oxygen limitation. Here, we expand on models of metabolic scaling by accounting for the role of oxygen availability and temperature on both resting and active metabolic rates. Our model predicts that oxygen limitation is more likely to constrain metabolism in larger, warmer, and active fish. Consequently, active metabolic rates are less responsive to temperature than are resting metabolic rates, and metabolism scales to body size with a smaller exponent whenever temperatures or activity levels are higher. Results from a metaanalysis of fish metabolic rates are consistent with our model predictions. The observed interactive effects of temperature, oxygen availability, and body size predict that global warming will limit the aerobic scope of aquatic ectotherms and may place a greater metabolic burden on larger individuals, impairing their physiological performance in the future. Our model reconciles the metabolic theory with empirical observations of oxygen limitation and provides a formal, quantitative framework for predicting both resting and active metabolic rate and hence aerobic scope of aquatic ectotherms.

What is the status of metabolic theory one century after Pütter invented the von Bertalanffy growth curve?

Metabolic theory aims to tackle ecological and evolutionary problems by explicitly including physical principles of energy and mass exchange, thereby increasing generality and deductive power. Individual growth models (IGMs) are the fundamental basis of metabolic theory because they represent the organisational level at which energy and mass exchange processes are most tightly integrated and from which scaling patterns emerge. Unfortunately, IGMs remain a topic of great confusion and controversy about the origins of the ideas, their domain and breadth of application, their logical consistency and whether they can sufficiently capture reality. It is now 100 years since the first theoretical model of individual growth was put forward by Pütter. His insights were deep, but his model ended up being attributed to von Bertalanffy and his ideas largely forgotten. Here I review Pütter's ideas and trace their influence on existing theoretical models for growth and other aspects of metabolism, including those of von Bertalanffy, the Dynamic Energy Budget (DEB) theory, the Gill-Oxygen Limitation Theory (GOLT) and the Ontogenetic Growth Model (OGM). I show that the von Bertalanffy and GOLT models are minor modifications of Pütter's original model. I then synthesise, compare and critique the ideas of the two most-developed theories, DEB theory and the OGM, in relation to Pütter's original ideas. I formulate the Pütter, DEB and OGM models in the same structure and with the same notation to illustrate the major similarities and differences among them. I trace the confusion and controversy regarding these theories to the notions of anabolism, catabolism, assimilation and maintenance, the connections to respiration rate, and the number of parameters and state variables their models require. The OGM model has significant inconsistencies that stem from the interpretation of growth as the difference between anabolism and maintenance, and these issues seriously challenge its ability to incorporate development, reproduction and assimilation. The DEB theory is a direct extension of Pütter's ideas but with growth being the difference between assimilation and maintenance rather than anabolism and catabolism. The DEB theory makes the dynamics of Pütter's 'nutritive material' explicit as well as extending the scheme to include reproduction and development. I discuss how these three major theories for individual growth have been used to explain 'macrometabolic' patterns including the scaling of respiration, the temperature-size rule (first modelled by Pütter), and the connection to life history. Future research on the connections between theory and data in these macrometabolic topics have the greatest potential to advance the status of metabolic theory and its value for pure and applied problems in ecology and evolution.

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.

Conspecific chemical cues drive density-dependent metabolic suppression independently of resource intake

Within species, individuals of the same size can vary substantially in their metabolic rate. One source of variation in metabolism is conspecific density - individuals in denser populations may have lower metabolism than those in sparser populations. However, the mechanisms through which conspecifics drive metabolic suppression remain unclear. Although food competition is a potential driver, other density-mediated factors could act independently or in combination to drive metabolic suppression, but these drivers have rarely been investigated. We used sessile marine invertebrates to test how food availability interacts with oxygen availability, water flow and chemical cues to affect metabolism. We show that conspecific chemical cues induce metabolic suppression independently of food and this metabolic reduction is associated with the downregulation of physiological processes rather than feeding activity. Conspecific cues should be considered when predicting metabolic variation and competitive outcomes as they are an important, but underexplored, source of variation in metabolic traits.

The responses of metabolic rate and neuropeptides to food deprivation in striped hamsters (Cricetulus barabensis) with different basal metabolic rate

High basal metabolic rate (BMR) is related to a powerful metabolic engine even under food shortage, which can lead to high levels of daily energy expenditure and requires more energy for maintenance in small mammals. To test the hypothesis that animals with different BMR levels respond differently to food shortage, we compared the changes in metabolism, morphology, and gene expression in response to food deprivation (FD) in male-striped hamsters (Cricetulus barabensis) with low (L)- or high (H)-BMR levels. After 36 hr of FD, energy expenditure, metabolic rate (MR), mass of body composition, and leptin and agouti-related peptide gene expressions in the white adipose tissues and the hypothalamus, respectively, decreased significantly in hamsters. The energy expenditure of H-BMR hamsters was reduced more than that of L-BMR hamsters after 36 hr of FD. Furthermore, MR was significantly reduced by FD, and that of the H-BMR group decreased more than that of the L-BMR group during the daytime. Therefore, our data suggest that striped hamsters with different BMR display different responses to variations in food availability. During FD, MR in H-BMR hamsters was more flexible than that in L-BMR animals and L-BMR hamsters could not reduce their MR any lower.

Evolution of size-dependent intraspecific competition predicts body size scaling of metabolic rate

Growth in body size is accompanied by changes in foraging capacity and metabolic costs, which lead to changes in competitive ability during ontogeny. The resulting size-dependent competitive asymmetry influences population dynamics and community structure, but it is not clear whether natural selection leads to asymmetry in intraspecific competition.We address this question by using a size-structured consumer-resource model, in which the strength and direction of competitive asymmetry between different consumer individuals depends on the scaling of maximum ingestion and maintenance metabolism with consumer body size. We use adaptive dynamics to study selection on the scaling exponents of these processes.Selection leads to an identical scaling of maximum ingestion and maintenance metabolism with consumer body size. Equal scaling exponents neutralize strong competitive differences within the consumer population, because all consumer individuals require the same amount of resources to cover maintenance requirements. Furthermore, the scaling exponents respond adaptively to changes in mortality such that biomass production through growth or reproduction increases in the life stage that is subject to increased mortality. Also, decreasing size at birth leads to increased investment in juvenile growth, while increasing maximum size leads to increased investment in post-maturation growth and reproduction.These results provide an explanation for observed variation in the ontogenetic scaling of metabolic rate with body size. Data of teleost fish are presented that support these predictions. However, selection towards equal scaling exponents is contradicted by empirical findings, which suggests that additional ecological complexity beyond this basic consumer-resource interaction is required to understand the evolution of size-dependent asymmetry in intraspecific competition. A plain language summary is available for this article.

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.

Response to formal comment on Myhrvold (2016) submitted by Griebeler and Werner (2017)

Griebeler and Werner offer a formal comment on Myhrvold, 2016 defending the conclusions of Werner and Griebeler, 2014. Although the comment criticizes several aspects of methodology in Myhrvold, 2016, all three papers concur on a key conclusion: the metabolism of extant endotherms and ectotherms cannot be reliably classified using growth-rate allometry, because the growth rates of extant endotherms and ectotherms overlap. A key point of disagreement is that the 2014 paper concluded that despite this general case, one can nevertheless classify dinosaurs as ectotherms from their growth rate allometry. The 2014 conclusion is based on two factors: the assertion (made without any supporting arguments) that the comparison with dinosaurs must be restricted only to extant sauropsids, ignoring other vertebrate groups, and that extant sauropsid endotherm and ectotherm growth rates in a data set studied in the 2014 work do not overlap. The Griebeler and Werner formal comment presents their first arguments in support of the restriction proposition. In this response I show that this restriction is unsupported by established principles of phylogenetic comparison. In addition, I show that the data set studied in their 2014 work does show overlap, and that this is visible in one of its figures. I explain how either point effectively invalidates the conclusion of their 2014 paper. I also address the other methodological criticisms of Myhrvold 2016, and find them unsupported.

Differentiating causality and correlation in allometric scaling: ant colony size drives metabolic hypometry

Metabolic rates of individual animals and social insect colonies generally scale hypometrically, with mass-specific metabolic rates decreasing with increasing size. Although this allometry has wide ranging effects on social behaviour, ecology and evolution, its causes remain controversial. Because it is difficult to experimentally manipulate body size of organisms, most studies of metabolic scaling depend on correlative data, limiting their ability to determine causation. To overcome this limitation, we experimentally reduced the size of harvester ant colonies (Pogonomyrmex californicus) and quantified the consequent increase in mass-specific metabolic rates. Our results clearly demonstrate a causal relationship between colony size and hypometric changes in metabolic rate that could not be explained by changes in physical density. These findings provide evidence against prominent models arguing that the hypometric scaling of metabolic rate is primarily driven by constraints on resource delivery or surface area/volume ratios, because colonies were provided with excess food and colony size does not affect individual oxygen or nutrient transport. We found that larger colonies had lower median walking speeds and relatively more stationary ants and including walking speed as a variable in the mass-scaling allometry greatly reduced the amount of residual variation in the model, reinforcing the role of behaviour in metabolic allometry. Following the experimental size reduction, however, the proportion of stationary ants increased, demonstrating that variation in locomotory activity cannot solely explain hypometric scaling of metabolic rates in these colonies. Based on prior studies of this species, the increase in metabolic rate in size-reduced colonies could be due to increased anabolic processes associated with brood care and colony growth.

Birth mass is the key to understanding the negative correlation between lifespan and body size in dogs

Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why the lifespan of dogs scales negatively with body size. The model also predicts that the difference in mass-specific lifetime metabolic energy usage between dog breeds is proportional to the difference in birth/adult mass ratio. Empirical data on lifespan, body mass, and metabolic scaling law of dogs strongly supports this prediction.

Do Performance-Safety Tradeoffs Cause Hypometric Metabolic Scaling in Animals?

Hypometric scaling of aerobic metabolism in animals has been widely attributed to constraints on oxygen (O₂) supply in larger animals, but recent findings demonstrate that O₂ supply balances with need regardless of size. Larger animals also do not exhibit evidence of compensation for O₂ supply limitation. Because declining metabolic rates (MRs) are tightly linked to fitness, this provides significant evidence against the hypothesis that constraints on supply drive hypometric scaling. As an alternative, ATP demand might decline in larger animals because of performance-safety tradeoffs. Larger animals, which typically reproduce later, exhibit risk-reducing strategies that lower MR. Conversely, smaller animals are more strongly selected for growth and costly neurolocomotory performance, elevating metabolism.

Physics of metabolic organization

We review the most comprehensive metabolic theory of life existing to date. A special focus is given to the thermodynamic roots of this theory and to implications that the laws of physics-such as the conservation of mass and energy-have on all life. Both the theoretical foundations and biological applications are covered. Hitherto, the foundations were more accessible to physicists or mathematicians, and the applications to biologists, causing a dichotomy in what always should have been a single body of work. To bridge the gap between the two aspects of the same theory, we (i) adhere to the theoretical formalism, (ii) try to minimize the amount of information that a reader needs to process, but also (iii) invoke examples from biology to motivate the introduction of new concepts and to justify the assumptions made, and (iv) show how the careful formalism of the general theory enables modular, self-consistent extensions that capture important features of the species and the problem in question. Perhaps the most difficult among the introduced concepts, the utilization (or mobilization) energy flow, is given particular attention in the form of an original and considerably simplified derivation. Specific examples illustrate a range of possible applications-from energy budgets of individual organisms, to population dynamics, to ecotoxicology.

A metabolic perspective of Peto's paradox and cancer

The frequency of cancer is postulated to be proportional to the number of cells an animal possesses, as each cell is similarly exposed to mutagens with every cell division. Larger animals result from more cell divisions with more mutagenic exposure, and hence are expected to have higher frequencies of cancer. Yet, as stipulated by Peto's paradox, larger animals do not have the higher rates of cancers seen in smaller animals despite the significant differences in cell numbers and a longer lifetime that would expose larger animals to more mutagens. The rates of cancer appear to be inversely proportional to animal body size, which scales inversely with specific metabolic rates of mammals. Studies over the past 20 years have linked oncogenes and tumour suppressors to alterations in cancer metabolism, and conversely, mutations in metabolic genes have been documented to trigger tumorigenesis. The by-products and intermediates of metabolism, such as reactive oxygen species, oxoglutarate, citrate and acetate, all have the potential to mutate and alter the genome or epigenome. On the basis of these general observations, it is proposed that metabolic rates correlate with mutagenic rates, which are higher in small animals and give the mechanistic basis for Peto's paradox. The observations discussed in this overview collectively indicate that specific metabolic rate varies inversely with body size, which seems to support the hypothesis that metabolism drives tumorigenesis and accounts for Peto's paradox.

Shape shifting predicts ontogenetic changes in metabolic scaling in diverse aquatic invertebrates

Metabolism fuels all biological activities, and thus understanding its variation is fundamentally important. Much of this variation is related to body size, which is commonly believed to follow a 3/4-power scaling law. However, during ontogeny, many kinds of animals and plants show marked shifts in metabolic scaling that deviate from 3/4-power scaling predicted by general models. Here, we show that in diverse aquatic invertebrates, ontogenetic shifts in the scaling of routine metabolic rate from near isometry (bR = scaling exponent approx. 1) to negative allometry (bR < 1), or the reverse, are associated with significant changes in body shape (indexed by bL = the scaling exponent of the relationship between body mass and body length). The observed inverse correlations between bR and bL are predicted by metabolic scaling theory that emphasizes resource/waste fluxes across external body surfaces, but contradict theory that emphasizes resource transport through internal networks. Geometric estimates of the scaling of surface area (SA) with body mass (bA) further show that ontogenetic shifts in bR and bA are positively correlated. These results support new metabolic scaling theory based on SA influences that may be applied to ontogenetic shifts in bR shown by many kinds of animals and plants.

Metabolic allometric scaling model. Combining cellular transportation and heat dissipation constraints

Living organisms need energy to be "alive". Energy is produced by biochemical processing of nutrients. The rate of energy production is called metabolic rate. Metabolism is very important from evolutionary, ecological perspectives, and for organisms' development and functioning. It depends on different parameters, of which organisms' mass is considered as one of the most important. Simple relationships between the mass of organisms and their metabolic rates were empirically discovered a while ago. Such dependence is described by a power function, whose exponent is called allometric scaling coefficient. With the increase of mass the metabolic rate usually increases slower; if mass increases by two times, the metabolic rate increases less than two times. This fact has far reaching implications for organization of life. The fundamental biological and biophysical mechanisms underlying this phenomenon are still not well understood. Here, we show that one of such primary mechanisms relates to transportation of substances, like nutrients and waste, at a cellular level. We show how variations in cell size and associated cellular transportation costs explain the known variance of allometric exponent. The introduced model also includes heat dissipation constraints. The model agrees with experimental observations and reconciles experimental results across different taxa. It ties metabolic scaling to organismal and environmental characteristics; helps defining perspective directions of future researches; allows predicting allometric exponents based on characteristics of organisms and environments they live in.

Progressive hypoxia decouples activity and aerobic performance of skate embryos

Although fish population size is strongly affected by survival during embryonic stages, our understanding of physiological responses to environmental stressors is based primarily on studies of post-hatch fishes. Embryonic responses to acute exposure to changes in abiotic conditions, including increase in hypoxia, could be particularly important in species exhibiting long developmental time, as embryos are unable to select a different environment behaviourally. Given that oxygen is key to metabolic processes in fishes and aquatic hypoxia is becoming more severe and frequent worldwide, organisms are expected to reduce their aerobic performance. Here, we examined the metabolic and behavioural responses of embryos of a benthic elasmobranch fish, the little skate (Leucoraja erinacea), to acute progressive hypoxia, by measuring oxygen consumption and movement (tail-beat) rates inside the egg case. Oxygen consumption rates were not significantly affected by ambient oxygen levels until reaching 45% air saturation (critical oxygen saturation, S crit). Below S crit, oxygen consumption rates declined rapidly, revealing an oxygen conformity response. Surprisingly, we observed a decoupling of aerobic performance and activity, as tail-beat rates increased, rather than matching the declining metabolic rates, at air saturation levels of 55% and below. These results suggest a significantly divergent response at the physiological and behavioural levels. While skate embryos depressed their metabolic rates in response to progressive hypoxia, they increased water circulation inside the egg case, presumably to restore normoxic conditions, until activity ceased abruptly around 9.8% air saturation.

Measuring maximum and standard metabolic rates using intermittent-flow respirometry: a student laboratory investigation of aerobic metabolic scope and environmental hypoxia in aquatic breathers

Metabolic rate is one of the most widely measured physiological traits in animals and may be influenced by both endogenous (e.g. body mass) and exogenous factors (e.g. oxygen availability and temperature). Standard metabolic rate (SMR) and maximum metabolic rate (MMR) are two fundamental physiological variables providing the floor and ceiling in aerobic energy metabolism. The total amount of energy available between these two variables constitutes the aerobic metabolic scope (AMS). A laboratory exercise aimed at an undergraduate level physiology class, which details the appropriate data acquisition methods and calculations to measure oxygen consumption rates in rainbow trout Oncorhynchus mykiss, is presented here. Specifically, the teaching exercise employs intermittent flow respirometry to measure SMR and MMR, derives AMS from the measurements and demonstrates how AMS is affected by environmental oxygen. Students' results typically reveal a decline in AMS in response to environmental hypoxia. The same techniques can be applied to investigate the influence of other key factors on metabolic rate (e.g. temperature and body mass). Discussion of the results develops students' understanding of the mechanisms underlying these fundamental physiological traits and the influence of exogenous factors. More generally, the teaching exercise outlines essential laboratory concepts in addition to metabolic rate calculations, data acquisition and unit conversions that enhance competency in quantitative analysis and reasoning. Finally, the described procedures are generally applicable to other fish species or aquatic breathers such as crustaceans (e.g. crayfish) and provide an alternative to using higher (or more derived) animals to investigate questions related to metabolic physiology.

High temperature slows down growth in tobacco hornworms (Manduca sexta larvae) under food restriction

When fed ad libitum (AL), ectothermic animals usually grow faster and have higher metabolic rate at higher ambient temperature. However, if food supply is limited, there is an energy tradeoff between growth and metabolism. Here we hypothesize that for ectothermic animals under food restriction (FR), high temperature will lead to a high metabolic rate, but growth will slow down to compensate for the high metabolism. We measure the rates of growth and metabolism of 4 cohorts of 5th instar hornworms (Manduca sexta larvae) reared at 2 levels of food supply (AL and FR) and 2 temperatures (20 and 30 °C). Our results show that, compared to the cohorts reared at 20 °C, the ones reared at 30 °C have high metabolic rates under both AL and FR conditions, but a high growth rate under AL and a low growth rate under FR, supporting this hypothesis.

Metabolic scaling in animals: methods, empirical results, and theoretical explanations

Life on earth spans a size range of around 21 orders of magnitude across species and can span a range of more than 6 orders of magnitude within species of animal. The effect of size on physiology is, therefore, enormous and is typically expressed by how physiological phenomena scale with mass(b). When b ≠ 1 a trait does not vary in direct proportion to mass and is said to scale allometrically. The study of allometric scaling goes back to at least the time of Galileo Galilei, and published scaling relationships are now available for hundreds of traits. Here, the methods of scaling analysis are reviewed, using examples for a range of traits with an emphasis on those related to metabolism in animals. Where necessary, new relationships have been generated from published data using modern phylogenetically informed techniques. During recent decades one of the most controversial scaling relationships has been that between metabolic rate and body mass and a number of explanations have been proposed for the scaling of this trait. Examples of these mechanistic explanations for metabolic scaling are reviewed, and suggestions made for comparing between them. Finally, the conceptual links between metabolic scaling and ecological patterns are examined, emphasizing the distinction between (1) the hypothesis that size- and temperature-dependent variation among species and individuals in metabolic rate influences ecological processes at levels of organization from individuals to the biosphere and (2) mechanistic explanations for metabolic rate that may explain the size- and temperature-dependence of this trait.

Critical PO2 is size-independent in insects: implications for the metabolic theory of ecology

Insects, and all animals, exhibit hypometric scaling of metabolic rate, with larger species having lower mass-specific metabolic rates. The metabolic theory of ecology (MTE) is based on models ascribing hypometric scaling of metabolic rate to constrained O₂ supply systems in larger animals. We compiled critical PO₂ of metabolic and growth rates for more than 40 insect species with a size range spanning four orders of magnitude. Critical PO₂ values vary from far below 21kPa for resting animals to near 21kPa for growing or flying animals and are size-independent, demonstrating that supply capacity matches oxygen demand. These data suggest that hypometric scaling of resting metabolic rate in insects is not driven by constraints on oxygen availability.

Body shape shifting during growth permits tests that distinguish between competing geometric theories of metabolic scaling

Metabolism fuels all of life's activities, from biochemical reactions to ecological interactions. According to two intensely debated theories, body size affects metabolism via geometrical influences on the transport of resources and wastes. However, these theories differ crucially in whether the size dependence of metabolism is derived from material transport across external surfaces, or through internal resource-transport networks. We show that when body shape changes during growth, these models make opposing predictions. These models are tested using pelagic invertebrates, because these animals exhibit highly variable intraspecific scaling relationships for metabolic rate and body shape. Metabolic scaling slopes of diverse integument-breathing species were significantly positively correlated with degree of body flattening or elongation during ontogeny, as expected from surface area theory, but contradicting the negative correlations predicted by resource-transport network models. This finding explains strong deviations from predictions of widely adopted theory, and underpins a new explanation for mass-invariant metabolic scaling during ontogeny in animals and plants.