A Sceptics View: “Kleiber’s Law” or the “3/4 Rule” is neither a Law nor a Rule but Rather an Empirical Approximation

Does death drive the scaling of life?

The magnitude of many kinds of biological structures and processes scale with organismal size, often in regular ways that can be described by power functions. Traditionally, many of these "biological scaling" relationships have been explained based on internal geometric, physical, and energetic constraints according to universal natural laws, such as the "surface law" and "3/4-power law". However, during the last three decades it has become increasingly apparent that biological scaling relationships vary greatly in response to various external (environmental) factors. In this review, I propose and provide several lines of evidence supporting a new ecological perspective that I call the "mortality theory of ecology" (MorTE). According to this viewpoint, mortality imposes time limits on the growth, development, and reproduction of organisms. Accordingly, small, vulnerable organisms subject to high mortality due to predation and other environmental hazards have evolved faster, shorter lives than larger, more protected organisms. A MorTE also includes various corollary, size-related internal and external causative factors (e.g. intraspecific resource competition, geometric surface area to volume effects on resource supply/transport and the protection of internal tissues from environmental hazards, internal homeostatic regulatory systems, incidence of pathogens and parasites, etc.) that impact the scaling of life. A mortality-centred approach successfully predicts the ranges of body-mass scaling slopes observed for many kinds of biological and ecological traits. Furthermore, I argue that mortality rate should be considered the ultimate (evolutionary) driver of the scaling of life, that is expressed in the context of other proximate (functional) drivers such as information-based biological regulation and spatial (geometric) and energetic (metabolic) constraints.

Exploring the Evolution-Coupling Hypothesis: Do Enzymes' Performance Gains Correlate with Increased Dissipation?

The research literature presents divergent opinions regarding the role of dissipation in living systems, with views ranging from it being useless to it being essential for driving life. The implications of universal thermodynamic evolution are often overlooked or considered controversial. A higher rate of entropy production indicates faster thermodynamic evolution. We calculated enzyme-associated dissipation under steady-state conditions using minimalistic models of enzyme kinetics when all microscopic rate constants are known. We found that dissipation is roughly proportional to the turnover number, and a log-log power-law relationship exists between dissipation and the catalytic efficiency of enzymes. "Perfect" specialized enzymes exhibit the highest dissipation levels and represent the pinnacle of biological evolution. The examples that we analyzed suggested two key points: (a) more evolved enzymes excel in free-energy dissipation, and (b) the proposed evolutionary trajectory from generalist to specialized enzymes should involve increased dissipation for the latter. Introducing stochastic noise in the kinetics of individual enzymes may lead to optimal performance parameters that exceed the observed values. Our findings indicate that biological evolution has opened new channels for dissipation through specialized enzymes. We also discuss the implications of our results concerning scaling laws and the seamless coupling between thermodynamic and biological evolution in living systems immersed in out-of-equilibrium environments.

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.

An improved dynamic metabolic model for application to biota

Any major nuclear facility must ensure the conservation of biodiversity regarding radiation protection of biota. A special concern is for tritium (3H) and radiocarbon (14C) transfer in wild mammals, birds and reptiles. Hydrogen and carbon are the main components of biological tissues and enter the life cycle. The present study improves the scientific bases of a previous model, analyses the uncertainty of input parameters and tests the model for a larger range of mammals and birds. The biological and metabolic half-times for organically bound tritium (OBT) and 14C are linked with energy metabolism and recent results are revised in relation with metabolic scaling. A large data base regarding basal metabolic rate (BMR), field metabolic rate (FMR), and organ mass is used for input information of the present model, which considers brain as a separate compartment. Metabolic energy partition in organs of active animal is defined and the factors affecting the metabolic rate are analysed. Body and ambient temperature, diet and habitat, and phylogeny are important factors considered in animal adaptation to environment. The available experimental data for carbon turnover rates in animals are analysed and it is observed that the experimental conditions are not appropriate for wild animals. The link between 13,14C and 134,137Cs turnover rate is analysed and the present metabolic approach is successfully tested for mammals and reptiles. Considering animal adaptation and the large data base for 134,137Cs, the radiological impact of accidental releases of 3H and 14C on biota can be pursued in the future research.

How Hot is too Hot? Metabolic Responses to Temperature Across Life Stages of a Small Ectotherm

To understand how global warming will impact biodiversity, we need to pay attention to those species with higher vulnerability. However, to assess vulnerability, we also need to consider the thermoregulatory mechanisms, body size, and thermal tolerance of species. Studies addressing thermal tolerance on small ectotherms have mostly focused on insects, while other arthropods, such as arachnids remain understudied. Here, we quantified the physiological thermal sensitivity of the pseudoscorpion Dactylochelifer silvestris using a respirometry setup with a ramping temperature increase. Overall, we found that D. silvestris has a much lower metabolic rate than other organisms of similar size. As expected, metabolic rate increased with body size, with adults having larger metabolic rates, but the overall metabolic scaling exponent was low. Both the temperature at which metabolism peaked and the critical thermal maxima were high (>44°C) and comparable to those of other arachnids. The activation energy, which characterizes the rising portion of the thermal sensitivity curve, was 0.66 eV, consistent with predictions for insects and other taxa in general. Heat tolerances and activation energy did not differ across life stages. We conclude that D. silvestris has low metabolic rates and a high thermal tolerance, which would likely influence how all stages and sexes of this species could endure climate change.

Multi-scaling allometry in human development, mammalian morphology, and tree growth

Various animal and plant species exhibit allometric relationships among their respective traits, wherein one trait undergoes expansion as a power-law function of another due to constraints acting on growth processes. For instance, the acknowledged consensus posits that tree height scales with the two-thirds power of stem diameter. In the context of human development, it is posited that body weight scales with the second power of height. This prevalent allometric relationship derives its nomenclature from fitting two variables linearly within a logarithmic framework, thus giving rise to the term "power-law relationship." Here, we challenge the conventional assumption that a singular power-law equation adequately encapsulates the allometric relationship between any two traits. We strategically leverage quantile regression analysis to demonstrate that the scaling exponent characterizing this power-law relationship is contingent upon the centile within these traits' distributions. This observation fundamentally underscores the proposition that individuals occupying disparate segments of the distribution may employ distinct growth strategies, as indicated by distinct power-law exponents. We introduce the innovative concept of "multi-scale allometry" to encapsulate this newfound insight. Through a comprehensive reevaluation of (i) the height-weight relationship within a cohort comprising 7, 863, 520 Japanese children aged 5-17 years for which the age, sex, height, and weight were recorded as part of a national study, (ii) the stem-diameter-height and crown-radius-height relationships within an expansive sample of 498, 838 georeferenced and taxonomically standardized records of individual trees spanning diverse geographical locations, and (iii) the brain-size-body-size relationship within an extensive dataset encompassing 1, 552 mammalian species, we resolutely substantiate the viability of multi-scale allometric analysis. This empirical substantiation advocates a paradigm shift from uni-scaling to multi-scaling allometric modeling, thereby affording greater prominence to the inherent growth processes that underlie the morphological diversity evident throughout the living world.

Genome and life-history evolution link bird diversification to the end-Cretaceous mass extinction

Complex patterns of genome evolution associated with the end-Cretaceous [Cretaceous-Paleogene (K-Pg)] mass extinction limit our understanding of the early evolutionary history of modern birds. Here, we analyzed patterns of avian molecular evolution and identified distinct macroevolutionary regimes across exons, introns, untranslated regions, and mitochondrial genomes. Bird clades originating near the K-Pg boundary exhibited numerous shifts in the mode of molecular evolution, suggesting a burst of genomic heterogeneity at this point in Earth's history. These inferred shifts in substitution patterns were closely related to evolutionary shifts in developmental mode, adult body mass, and patterns of metabolic scaling. Our results suggest that the end-Cretaceous mass extinction triggered integrated patterns of evolution across avian genomes, physiology, and life history near the dawn of the modern bird radiation.

Allometric multi-scaling of weight-for-height relation in children and adolescents: Revisiting the theoretical basis of body mass index of thinness and obesity assessment

The body mass index (BMI), defined as weight in kilograms divided by height in meters squared, has been widely used to assess thinness and obesity in all age groups, including children and adolescents. However, the validity and utility of BMI as a reliable measure of nutritional health have been questioned. This study discusses the mathematical conditions that support the validity of BMI based on population statistics. Here, we propose a condition defined as allometric uni-scaling to ensure the validity of BMI as an objective height-adjusted measure. Any given centile curve, including the median curve, in a weight-for-height distribution should be approximated using power-law functions with the same scaling exponent. In contrast, when the scaling exponent varies depending on the position of the centile curve, it is called allometric multi-scaling. By introducing a method for testing these scaling properties using quantile regression, we analyzed a large-scale Japanese database that included 7,863,520 children aged 5-17 years. We demonstrated the remarkable multi-scaling properties at ages 5-13 years for males and 5-11 years for females, and the convergence to uni-scaling with a scaling exponent close to 2 as they approached 17 years of age for both sexes. We confirmed that conventional BMI is appropriate as an objective height-adjusted mass measure at least 17 years of age, close to adulthood, for both males and females. However, the validity of BMI could not be confirmed in younger age groups. Our findings indicate that the growth of children's weight-for-height relation is much more complex than previously assumed. Therefore, a single BMI-type formula cannot be used to assess thinness and obesity in children and adolescents.

Allometric-kinetic model predictions of concentration ratios for anthropogenic radionuclides across animal classes and food selection

Protection of the environment from radiation fundamentally relies on dose assessments for non-human biota. Many of these dose assessments use measured or predicted concentrations of radionuclides in soil or water combined with Concentration Ratios (CRs) to estimate whole body concentrations in animals and plants, yet there is a paucity of CR data relative to the vast number of potential taxa and radioactive contaminants in the environment and their taxon-specific ecosystems. Because there are many taxa each having very different behaviors and biology, and there are many possible bioavailable radionuclides, CRs have the potential to vary by orders-of-magnitude, as often seen in published data. Given the diversity of taxa, the International Commission on Radiological Protection (ICRP) has selected 12 non-human biota as reference animals and plants (RAPs), while the U.S. Department of Energy (DOE) uses the non-taxon specific categories of terrestrial, riparian, and aquatic animals. The question we examine here, in part, is: are these RAPs and categorizations sufficient to adequately protect all species given the broad diversity of animals in a region? To explore this question, we utilize an Allometric-Kinetic (A-K) model to calculate radionuclide-specific CRs for common animal classes, which are then further subcategorized into herbivores, omnivores, carnivores, and invertebrate detritivores. Comparisons in CRs among animal classes exhibited only small differences, but there was order of magnitude differences between herbivores, carnivores, and especially detritivores, for many radionuclides of interest. These findings suggest that the ICRP RAPs and the DOE categories are reasonable, but their accuracy could be improved by including sub-categories related to animal dietary ecology and biology. Finally, comparisons of A-K model predicted CR values to published CRs show order-of-magnitude variations, providing justification for additional studies of animal assimilation across radionuclides, environmental conditions, and animal classes.

Allometric-kinetic model predictions of radionuclide dynamics across turtle taxa

Chelonians (turtles, tortoises, and sea turtles; hereafter, turtles) inhabit a wide variety of ecosystems that are currently, or have the potential in the future to become, radioactively contaminated. Because they are long-lived, turtles may uniquely accumulate significant amounts of the radionuclides, especially those with long half-lives and are less environmentally mobile. Further, turtle shells are covered by scutes made of keratin. For many turtle taxa, each year, keratin grows sequentially creating annual growth rings or layers. Theoretically, analysis of these scute layers for radionuclides could provide a history of the radioactivity levels in the environment, yet there are few previously published studies focused on the dynamics of radionuclide intake in turtles. Using established biochemical and ecological principles, we developed an allometric-kinetic model to establish relationships between the radionuclide concentrations in turtles and the environment they inhabit. Specifically, we calculated Concentration Ratios (CRs - ratio of radionuclide concentration in the turtle divided by the concentration in the soil, sediment, or water) for long-lived radionuclides of uranium and plutonium for freshwater turtles, tortoises, and sea turtles. These CRs allowed prediction of environmental concentrations based on measured concentrations within turtles or vice-versa. We validated model-calculated CR values through comparison with published CR values for representative organisms, and the uncertainty in each of the model parameters was propagated through the CR calculation using Monte Carlo techniques. Results show an accuracy within a factor of three for most CR comparisons though the difference for plutonium was larger with a CR ratio of about 200 times for sea turtles, driven largely by the uncertainty of the solubility of plutonium in sea water.

Challenging obesity and sex based differences in resting energy expenditure using allometric modeling, a sub-study of the DIETFITS clinical trial

BACKGROUND & AIMS

Resting energy expenditure (REE) is a major component of energy balance. While REE is usually indexed to total body weight (BW), this may introduce biases when assessing REE in obesity or during weight loss intervention. The main objective of the study was to quantify the bias introduced by ratiometric scaling of REE using BW both at baseline and following weight loss intervention.

DESIGN

Participants in the DIETFITS Study (Diet Intervention Examining The Factors Interacting with Treatment Success) who completed indirect calorimetry and dual-energy X-ray absorptiometry (DXA) were included in the study. Data were available in 438 participants at baseline, 340 at 6 months and 323 at 12 months. We used multiplicative allometric modeling based on lean body mass (LBM) and fat mass (FM) to derive body size independent scaling of REE. Longitudinal changes in indexed REE were then assessed following weight loss intervention.

RESULTS

A multiplicative model including LBM, FM, age, Black race and the double product (DP) of systolic blood pressure and heart rate explained 79% of variance in REE. REE indexed to [LBM^0.66 × FM^0.066] was body size and sex independent (p = 0.91 and p = 0.73, respectively) in contrast to BW based indexing which showed a significant inverse relationship to BW (r = -0.47 for female and r = -0.44 for male, both p < 0.001). When indexed to BW, significant baseline differences in REE were observed between male and female (p < 0.001) and between individuals who are overweight and obese (p < 0.001) while no significant differences were observed when indexed to REE/[LBM^0.66 × FM^0.066], p > 0.05). Percentage predicted REE adjusted for LBM, FM and DP remained stable following weight loss intervention (p = 0.614).

CONCLUSION

Allometric scaling of REE based on LBM and FM removes body composition-associated biases and should be considered in obesity and weight-based intervention studies.

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 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.

On the rules of life and Kleiber's law: the macroscopic relationship between materials and energy

Efforts to accommodate the growth in global energy consumption within a fragile biosphere are primarily focused on managing the transition towards a low-carbon energy mix. We show evidence that a more fundamental problem exists through a scaling relation, akin to Kleiber's Law, between society's energy consumption and material stocks. Humanity's energy consumption scales at 0.78 of its material stocks, which implies predictable environmental pressure regardless of the energy mix. If true, future global energy scenarios imply vast amounts of materials and corresponding environmental degradation, which have not been adequately acknowledged. Thus, limits to energy consumption are needed regardless of the energy mix to stabilize human intervention in the biosphere.

Oxygen Deficient (OD) Combustion and Metabolism: Allometric Laws of Organs and Kleiber’s Law from OD Metabolism?

The biology literature presents allometric relations for the specific metabolic rate (SMRk) of an organ k of mass mk within the body of mass mB: SMRk ∝ mBfk (body mass allometry, BMA). Wang et al. used BMA, summed-up energy from all organs and validated Kleiber’s law of the whole body: SMRM ∝ mBb’, b’ = −0.25. The issues raised in biology are: (i) why fk and b’ < 0, (ii) how do the organs adjust fk to yield b’? The current paper presents a “system” approach involving the field of oxygen deficient combustion (ODC) of a cloud of carbon particles and oxygen deficient metabolism (ODM), and provides partial answers by treating each vital organ as a cell cloud. The methodology yields the following: (i) a dimensionless “group” number GOD to indicate extent of ODM, (ii) SMRk of an organ in terms of the effectiveness factor; (iii) curve fitting of the effectiveness factor to yield the allometric exponents for the organ mass-based allometric laws (OMA); (iv) validation of the results with data from 111 biological species (BS) with mB ranging from 0.0075 to 6500 kg. The “hypoxic” condition at organ level, particularly for COVID-19 patients, and the onset of cancer and virus multiplication are interpreted in terms of ODM and glycolysis.

Diversity begets diversity in mammal species and human cultures

Across the planet the biogeographic distribution of human cultural diversity tends to correlate positively with biodiversity. In this paper we focus on the biogeographic distribution of mammal species and human cultural diversity. We show that not only are these forms of diversity similarly distributed in space, but they both scale superlinearly with environmental production. We develop theory that explains that as environmental productivity increases the ecological kinetics of diversity increases faster than expected because more complex environments are also more interactive. Using biogeographic databases of the global distributions of mammal species and human cultures we test a series of hypotheses derived from this theory and find support for each. For both mammals and cultures, we show that (1) both forms of diversity increase exponentially with ecological kinetics; (2) the kinetics of diversity is faster than the kinetics of productivity; (3) diversity scales superlinearly with environmental productivity; and (4) the kinetics of diversity is faster in increasingly productive environments. This biogeographic convergence is particularly striking because while the dynamics of biological and cultural evolution may be similar in principle the underlying mechanisms and time scales are very different. However, a common currency underlying all forms of diversity is ecological kinetics; the temperature-dependent fluxes of energy and biotic interactions that sustain all forms of life at all levels of organization. Diversity begets diversity in mammal species and human cultures because ecological kinetics drives superlinear scaling with environmental productivity.

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.

Mitochondrial performance of a continually growing marine bivalve, Mytilus edulis, depends on body size

Allometric decline of mass-specific metabolic rate with increasing body size in organisms is a well-documented phenomenon. Despite a long history of research, the mechanistic causes of metabolic scaling with body size remain under debate. Some hypotheses suggest that intrinsic factors such as allometry of cellular and mitochondrial metabolism may contribute to the organismal-level metabolic scaling. The aim of our present study was to determine the metabolic allometry at the mitochondrial level using a continually growing marine ectotherm, the mussel Mytilus edulis, as a model. Mussels from a single cohort that considerably differed in body size were selected, implying faster growth in the larger specimens. We determined the body mass-dependent scaling of the mitochondrial proton leak respiration, respiration in the presence of ADP indicative of the oxidative phosphorylation (OXPHOS), and maximum activity of the mitochondrial electron transport system (ETS) and cytochrome c oxidase (COX). Respiration was measured at normal (15°C), and elevated (27°C) temperatures. The results demonstrated a pronounced allometric increase in both proton leak respiration and OXPHOS activity of mussel mitochondria. Mussels with faster growth (larger body size) showed an increase in OXPHOS rate, proton leak respiration rate, and ETS and COX activity (indicating an overall improved mitochondrial performance) and higher respiratory control ratio (indicating better mitochondrial coupling and potentially lower costs of mitochondrial maintenance at the same OXPHOS capacity) compared with slower growing (smaller) individuals. Our data show that the metabolic allometry at the organismal level cannot be directly explained by mitochondrial functioning.

Physiological essay on Gulliver's Travels: a correction after three centuries

Gulliver's Travels by Jonathan Swift, published in 1726, was analyzed from the viewpoint of scaling in comparative physiology. According to the original text, the foods of 1724 Lilliputians, tiny human creatures, are needed for Gulliver, but the author found that those of 42 Lilliputians and of 1/42 Brobdingnagians (gigantic human creatures) are enough to support the energy of Gulliver. The author further estimated their heartbeats, respiration rates, life spans and blood pressure. These calculations were made by the use of three equations, i.e., body mass index (BMI = W/H2) and quarter-power laws (E∝W3/4 and T∝W1/4), where W, H, E, and T denote body weight, height, energy and time, respectively. Their blood pressures were estimated with reference to that of the giraffe and barosaurus, a long-neck dinosaur. Based on the above findings, the food requirement of Gulliver in the original text should be corrected after almost three centuries.

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.

Effects of fat and exoskeletal mass on the mass scaling of metabolism in Carabidae beetles

The rate at which organisms metabolize resources and consume oxygen is tightly linked to body mass. Typically, there is a sub-linear allometric relationship between metabolic rates and body mass (mass-scaling exponent b < 1). The origin of this pattern remains one of the most intriguing and hotly debated topics in evolutionary physiology. A decrease in mass-specific metabolic rates in larger organisms might reflect disproportionate increases in body components with low metabolic activity, such as storage and skeletal tissues. Addressing this hypothesis, we studied standard metabolic rates, body mass, and fat and exoskeletal mass in males and females from 15 species of Carabidae beetles. There was a sub-linear allometric relationship of metabolic rate with body mass: b = 0.72 (phylogeny not considered), b = 0.54 (phylogeny considered). The latter exponent was significantly lower than 0.75, which is sometimes regarded as a universal exponent value in the mass scaling of metabolic rates. Contrary to our hypothesis, the relative contribution of fat and the exoskeleton to body mass decreased, rather than increased with body mass, as indicated by the sub-linear allometric mass scaling of both components (b < 1). Supporting the role of metabolically inert body components in shaping metabolic scaling, the exponents (b) for metabolism became slightly smaller (b = 0.70, phylogeny not considered; 0.52, phylogeny considered) when we removed lipids and the exoskeleton from body mass calculations and considered only the lean mass of soft tissue in the mass scaling. Overall, our results indicate that, in beetles, the relative content of metabolically inert components changes across species according to species-specific body mass. Nevertheless, we did not find evidence that this changing contribution plays a central role in the origin of interspecific metabolic scaling in carabids. Our findings stress the need for finding alternative explanations, at least in carabids, for the origin of the mass scaling of metabolic rates.

On the thermodynamic origin of metabolic scaling

The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organism to maintain its metabolism. This balance tunes the shape of an additive model from which different effective scalings can be recovered as particular cases, thereby reconciling previously inconsistent empirical evidence in mammals, birds, insects and even plants under a unified framework. This model is biologically motivated, fits remarkably well the data, and also explains additional features such as the relation between energy lost as heat and mass, the role and influence of different climatic environments or the difference found between endotherms and ectotherms.

Was endothermy in amniotes induced by an early stop in growth during ontogeny?

Endothermy and its evolution are still an unresolved issue. Here, we present a model which transforms an ectothermic amniote (ancestor) into a derived amniote (descendant) showing many characteristics seen in extant endothermic birds and mammals. Consistent with the fossil record within the ancestral lineages of birds and mammals, the model assumes that mutations in genes which get active during ontogeny and affect body growth resulted in a reduced asymptotic body size and an early growth stop of the descendant. We show that such a postulated early growth stop in the descendant simultaneously increases the growth rate and metabolic rate, and also changes six life history traits (offspring mass, annual clutch/litter mass, number of offspring per year, age and mass at which sexual maturity is reached, age at which the individual is fully grown) of the descendant compared to a similar-sized ancestor. All these changes coincide with known differences between recent ectothermic and endothermic amniotes. We also elaborate many other differences and similarities in biological characteristics supporting the early growth stop. An early stop in growth during ontogeny thus could have played a key role in the evolution of endothermy within the reptilia and therapsids. It generated variability in characteristics of ancestral ectotherms, which was subject to natural selection in the past and resulted in many adaptations linked to endothermy in today's birds and mammals.

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.

Ecology of ontogenetic body-mass scaling of gill surface area in a freshwater crustacean

Several studies have documented ecological effects on intraspecific and interspecific body-size scaling of metabolic rate. However, little is known about how various ecological factors may affect the scaling of respiratory structures supporting oxygen uptake for metabolism. To our knowledge, our study is the first to provide evidence for ecological effects on the scaling of a respiratory structure among conspecific populations of any animal. We compared the body-mass scaling of gill surface area (SA) among eight spring-dwelling populations of the amphipod crustacean Gammarus minus Although gill SA scaling was not related to water temperature, conductivity or G. minus population density, it was significantly related to predation regime (and secondarily to pH). Body-mass scaling slopes for gill SA were significantly lower in four populations inhabiting springs with fish predators than for four populations in springs without fish (based on comparing means of the population slopes, or slopes calculated from pooled raw data for each comparison group). As a result, gill SA was proportionately smaller in adult amphipods from springs with versus without fish. This scaling difference paralleled similar differences in the scaling exponents for the rates of growth and resting metabolic rate. We hypothesized that gill SA scaling is shallower in fish-containing versus fishless spring populations of G. minus because of effects of size-selective predation on size-specific growth and activity that in turn affect the scaling of oxygen demand and concomitantly the gill capacity (SA) for oxygen uptake. Although influential theory claims that metabolic scaling is constrained by internal body design, our study builds on previous work to show that the scaling of both metabolism and the respiratory structures supporting it may be ecologically sensitive and evolutionarily malleable.

Mass scaling of metabolic rates in carabid beetles (Carabidae) – the importance of phylogeny, regression models and gas exchange patterns

The origin of the allometric relationship between standard metabolic rate (MR) and body mass (M), often described as MR=aMb, remains puzzling and interpretation of the mass-scaling exponent, b may depend on the methodological approach, shapes of residuals, coefficient of determination (r2) and sample size. We investigated the mass scaling of MRs within and between species of Carabidae beetles. We used ordinary least squares (OLS) regression, phylogenetically generalized least squares (PGLS) regression and standardized major axis (SMA) regression to explore the effects of different model-fitting methods and data clustering caused by phylogenetic clades (grade shift) and gas exchange patterns (discontinuous, cyclic and continuous). At the interspecific level, the relationship between MR and M was either negatively allometric (b&lt;1) or isometric (b=1), depending on the fitting method. At the intraspecific level, the relationship either did not exist or was isometric or positively allometric (b&gt;1), and the fit was significantly improved after the analysed dataset was split according to gas exchange patterns. The studied species originated from two distinct phylogenetic clades that had different intercepts but a common scaling exponent (OLS, 0.61) that was much shallower than the scaling exponent for the combined dataset for all species (OLS, 0.71). The best scaling exponent estimates were obtained by applying OLS while accounting for grade shifts or by applying PGLS. Overall, we show that allometry of MR in insects can depend heavily on the model fitting method, the structure of phylogenetic non-independence and ecological factors that elicit different modes of gas exchange.

Mass, phylogeny, and temperature are sufficient to explain differences in metabolic scaling across mammalian orders?

Whether basal metabolic rate-body mass scaling relationships have a single exponent is highly discussed, and also the correct statistical model to establish relationships. Here, we aimed (1) to identify statistically best scaling models for 17 mammalian orders, Marsupialia, Eutheria and all mammals, and (2) thereby to prove whether correcting for differences in species' body temperature and their shared evolutionary history improves models and their biological interpretability. We used the large dataset from Sieg et al. (The American Naturalist174, 2009, 720) providing species' body mass (BM), basal metabolic rate (BMR) and body temperature (T). We applied different statistical approaches to identify the best scaling model for each taxon: ordinary least squares regression analysis (OLS) and phylogenetically informed analysis (PGLS), both without and with controlling for T. Under each approach, we tested linear equations (log-log-transformed data) estimating scaling exponents and normalization constants, and such with a variable normalization constant and a fixed exponent of either ⅔ or ¾, and also a curvature. Only under temperature correction, an additional variable coefficient modeled the influence of T on BMR. Except for Pholidata and Carnivora, in all taxa studied linear models were clearly supported over a curvature by AICc. They indicated no single exponent at the level of orders or at higher taxonomic levels. The majority of all best models corrected for phylogeny, whereas only half of them included T. When correcting for T, the mathematically expected correlation between the exponent (b) and the normalization constant (a) in the standard scaling model y = a x^b was removed, but the normalization constant and temperature coefficient still correlated strongly. In six taxa, T and BM correlated positively or negatively. All this hampers a disentangling of the effect of BM, T and other factors on BMR, and an interpretation of linear BMR-BM scaling relationships in the mammalian taxa studied.

The Biokinetic Spectrum for Temperature

We identify and describe the distribution of temperature-dependent specific growth rates for life on Earth, which we term the biokinetic spectrum for temperature. The spectrum has the potential to provide for more robust modeling in thermal ecology since any conclusions derived from it will be based on observed data rather than using theoretical assumptions. It may also provide constraints for systems biology model predictions and provide insights in physiology. The spectrum has a Δ-shape with a sharp peak at around 42°C. At higher temperatures up to 60°C there was a gap of attenuated growth rates. We found another peak at 67°C and a steady decline in maximum rates thereafter. By using Bayesian quantile regression to summarise and explore the data we were able to conclude that the gap represented an actual biological transition between mesophiles and thermophiles that we term the Mesophile-Thermophile Gap (MTG). We have not identified any organism that grows above the maximum rate of the spectrum. We used a thermodynamic model to recover the Δ-shape, suggesting that the growth rate limits arise from a trade-off between activity and stability of proteins. The spectrum provides underpinning principles that will find utility in models concerned with the thermal responses of biological processes.

Indexing cardiovascular and respiratory variables: allometric scaling principles

OBJECTIVES

To describe the allometric scaling principles underlying appropriate indexing of cardiovascular and respiratory measurements obtained in adult mammals, and to propose guidelines for indexing experimental cardiovascular and respiratory data.

DATABASE USED

PubMed, using the terms 'allometry', 'allometric', 'indexing', 'cardiovascular' and 'respiratory'.

CONCLUSIONS

Indexing of cardiopulmonary variables is commonly used in attempts to account for the effects of body size on measurements and to standardize them. Some cardiopulmonary variables have been indexed using various functions of body mass in a process that often ignores the underlying relationship between the variable of interest and body size, as described in the allometry literature. This can result in a failure to ideally reduce the effect of body size on measurements in a manner that highlights differences. We review how commonly measured cardiopulmonary variables are related to body mass in mammalian species according to the allometry literature, and offer suggestions on how this information can be used to appropriately index cardiopulmonary variables in a simple and informative manner.

Kleiber's Law: How the Fire of Life ignited debate, fueled theory, and neglected plants as model organisms

Size is a key feature of any organism since it influences the rate at which resources are consumed and thus affects metabolic rates. In the 1930s, size-dependent relationships were codified as "allometry" and it was shown that most of these could be quantified using the slopes of log-log plots of any 2 variables of interest. During the decades that followed, physiologists explored how animal respiration rates varied as a function of body size across taxa. The expectation was that rates would scale as the 2/3 power of body size as a reflection of the Euclidean relationship between surface area and volume. However, the work of Max Kleiber (1893-1976) and others revealed that animal respiration rates apparently scale more closely as the 3/4 power of body size. This phenomenology, which is called "Kleiber's Law," has been described for a broad range of organisms, including some algae and plants. It has also been severely criticized on theoretical and empirical grounds. Here, we review the history of the analysis of metabolism, which originated with the works of Antoine L. Lavoisier (1743-1794) and Julius Sachs (1832-1897), and culminated in Kleiber's book The Fire of Life (1961; 2. ed. 1975). We then evaluate some of the criticisms that have been leveled against Kleiber's Law and some examples of the theories that have tried to explain it. We revive the speculation that intracellular exo- and endocytotic processes are resource delivery-systems, analogous to the supercellular systems in multicellular organisms. Finally, we present data that cast doubt on the existence of a single scaling relationship between growth and body size in plants.