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

Divergent evolution of colony-level metabolic scaling in ants

Metabolic scaling-the relationship between organismal metabolic rate (R) and body mass (M)-is an important property of life. In general, this relationship has been summarized by the scaling function, R = aMb. Both the scaling elevation (a) and the scaling exponent (b) have been shown to diverge among taxa and ecological groups. However, it is unclear whether this ecological divergence observed in unitary organisms also occurs at higher levels of biological organization, such as eusocial colonies. We used the published literature to assemble the estimates of the metabolic rate of active colonies and their mass for 51 species of ants, along with three ecologically important traits with available data: trophic level (herbivorous to predaceous), foraging coordination level (solitary to trunk trail) and caste polymorphism (polymorphic vs. monomorphic). Interspecific colony metabolic scaling was steeper (higher b) in species occupying higher trophic levels and in species with polymorphic versus monomorphic workers. Species occupying higher trophic levels also had a higher metabolic level (higher a). These findings are consistent with divergent selection on colony-level metabolic scaling. We conclude that the ecological dependence of metabolic scaling has evolved across levels of biological organization and should be explicitly considered by both metabolic and social evolution theories.

Simplicity within biological complexity

Motivation

Heterogeneous, interconnected, systems-level, molecular (multi-omic) data have become increasingly available and key in precision medicine. We need to utilize them to better stratify patients into risk groups, discover new biomarkers and targets, repurpose known and discover new drugs to personalize medical treatment. Existing methodologies are limited and a paradigm shift is needed to achieve quantitative and qualitative breakthroughs.

Results

In this perspective paper, we survey the literature and argue for the development of a comprehensive, general framework for embedding of multi-scale molecular network data that would enable their explainable exploitation in precision medicine in linear time. Network embedding methods (also called graph representation learning) map nodes to points in low-dimensional space, so that proximity in the learned space reflects the network's topology-function relationships. They have recently achieved unprecedented performance on hard problems of utilizing few omic data in various biomedical applications. However, research thus far has been limited to special variants of the problems and data, with the performance depending on the underlying topology-function network biology hypotheses, the biomedical applications, and evaluation metrics. The availability of multi-omic data, modern graph embedding paradigms and compute power call for a creation and training of efficient, explainable and controllable models, having no potentially dangerous, unexpected behaviour, that make a qualitative breakthrough. We propose to develop a general, comprehensive embedding framework for multi-omic network data, from models to efficient and scalable software implementation, and to apply it to biomedical informatics, focusing on precision medicine and personalized drug discovery. It will lead to a paradigm shift in the computational and biomedical understanding of data and diseases that will open up ways to solve some of the major bottlenecks in precision medicine and other domains.

All You Need to Know About Allometric Scaling: An Integrative Review on the Theoretical Basis, Empirical Evidence, and Application in Human Pharmacology

Scaling approaches are used to describe or predict clearance for paediatric or obese populations from normal-weight adult values. Theoretical allometry assumes the existence of a universal bodyweight-based scaling relationship. Although theoretical allometry is highly disputed, it is commonly applied in pharmacological data analyses and clinical practice. The aim of the current review is to (1) increase pharmacologists' understanding of theoretical allometry to better understand the (implicit) assumptions and (dis)advantages and (2) highlight important methodological considerations with the application of this methodology. Theoretical allometry originated in an empirical, and later debated, observation by Kleiber of a scaling exponent of 0.75 between basal metabolic rate and body mass of mammals. The mathematical framework of West, Brown, and Enquist provides one possible explanation for this value. To date, multiple key assumptions of this framework have been disputed or disproven, and an increasing body of evidence is emerging against the existence of one universal allometric exponent. The promise of ease and universality of use that comes with theoretical approaches may be the reason they are so strongly sought after and defended. However, ecologists have suggested that the theory should move from a 'Newtonian approach', in which physical explanations are sought for a universal law and variability is of minor importance, to a 'Darwinian approach', in which variability is considered of primary importance for which evolutionary explanations can be found. No scientific support was found for the application of allometry for within-species scaling, so the application of basal metabolic rate-based scaling principles to clearance scaling remains unsubstantiated. Recent insights from physiologically based modelling approaches emphasise the interplay between drugs with different properties and physiological variables that underlie drug clearance, which drives the variability in the allometric scaling exponent in the field of pharmacology. To deal with this variability, drug-specific or patient-specific adaptations to theoretical allometric scaling are proposed, that introduce empiric elements and reduce the universality of the theory. The use of allometric scaling with an exponent of 0.75 may hold empirical merit for paediatric populations, except for the youngest individuals (aged ≤ 5 years). Nevertheless, biological interpretations and extrapolation potential attributed to models based on 0.75 allometric scaling are theoretically unfounded, and merits of the empirical application of this function should, as for all models, always be supported by appropriate model validation procedures. In this respect, it is not the value of the allometric exponent but the description and prediction of individual clearance values and drug concentrations that are of primary interest.

Dive Deep: Bioenergetic Adaptation of Deep-Sea Animals

The deep sea, which encompasses the largest habitat on Earth, presents a set of extreme and unique environmental conditions, including high hydrostatic pressure, near-freezing temperatures, and perpetual darkness. These conditions pose significant challenges to the survival and energy management of its inhabitants. Deep-sea organisms have evolved a range of bioenergetic adaptations to negotiate these harsh conditions, ensuring efficient energy acquisition and utilization. This review examines the multifaceted strategies employed by deep-sea animals, focusing on three key areas: energy input, digestive and absorptive efficiency, and energy consumption. We examine the physical environment of the deep sea, highlighting vertical profiles of temperature, salinity, and dissolved oxygen, which contrast sharply with surface conditions. Physiological adaptations of deep-sea species, such as specialized digestive systems and enzyme modifications that function optimally under high pressure, are explored in detail. Furthermore, we discuss behavioral adaptations, including diurnal vertical migration, which optimize energy intake and reduce metabolic costs. Comparative analyses with shallow-water species provide insights into the evolutionary pressures that have shaped these adaptations. This review also addresses the concept of "power budgeting", in which energy expenditures for specific dynamic actions (SDAs) must be balanced with other metabolic demands. This comprehensive examination of bioenergetic adaptation in deep-sea organisms enhances our understanding of their resilience and adaptability, offering glimpses into the complex interplay between environmental constraints and biological processes in one of the most challenging habitats on the planet.

Life History Differences Between Lepidoptera Larvae and Blattodea Nymphs Lead to Different Energy Allocation Strategies and Cellular Qualities

Different life histories result in different strategies to allocate energy in biosynthesis, including growth and reproduction, and somatic maintenance. One of the most notable life history differences between Lepidoptera and Blattodea species is that the former grow much faster than the latter, and during metamorphosis, a large amount of tissue in Lepidoptera species disintegrates. In this review, using Lepidoptera caterpillars and cockroach nymphs as examples, we show that, due to these differences in growth processes, cockroach nymphs spend 20 times more energy on synthesizing one unit of biomass (indirect cost of growth) than butterfly caterpillars. Because of the low indirect cost of growth in caterpillars, the fraction of metabolic energy allocated to growth is six times lower, and that for maintenance is seven times higher in caterpillars, compared to cockroach nymphs, despite caterpillar's higher growth rates. Moreover, due to the higher biosynthetic energy cost in cockroach nymphs, they have better cellular qualities, including higher proteasomal activity for protein quality control and higher resistance to oxidative stress. We also show that under food restriction conditions, the fraction of assimilated energy allocated to growth was reduced by 120% in cockroach nymphs, as they lost body weight under food restriction, while this reduction was only 14% in hornworms, and the body mass increased at a lower rate. Finaly, we discuss future research, especially the difference in adult lifespans associated with the energetic differences.

Metabolic scaling, energy allocation tradeoffs, and the evolution of humans' unique metabolism

All organisms use limited energy to grow, survive, and reproduce, necessitating energy allocation tradeoffs, but there is debate over how selection impacted metabolic budgets and tradeoffs in primates, including humans. Here, we develop a method to compare metabolic rates as quotients of observed relative to expected values for mammals corrected for size, body composition, environmental temperature, and phylogenetic relatedness. Contrary to previous analyses, these quotients reveal that nonhuman primates have total metabolic rates expected for similar-sized mammals in similar environments. In addition, data from several small-scale societies show that humans evolved exceptionally high resting, activity, and total metabolic rates apparently by overcoming tradeoffs between resting and active energy expenditures that constrain other primates. Enhanced metabolic rates help humans fuel expanded brains, faster reproductive rates, extended longevity, and high percentage of body fat.

Biomass competition connects individual and community scaling patterns

Both metabolism and growth scale sublinearly with body mass across species. Ecosystems show the same sublinear scaling between production and total biomass, but ecological theory cannot reconcile the existence of these nearly identical scalings at different levels of biological organization. We attempt to solve this paradox using marine phytoplankton, connecting individual and ecosystem scalings across three orders of magnitude in body size and biomass. We find that competitive interactions determined by biomass slow metabolism in a consistent fashion across species of different sizes. These effects dominate over species-specific peculiarities, explaining why community composition does not affect respiration and production patterns. The sublinear scaling of ecosystem production thus emerges from this metabolic density-dependence that operates across species, independently of the equilibrium state or resource regime. Our findings demonstrate the connection between individual and ecosystem scalings, unifying aspects of physiology and ecology to explain why growth patterns are so strikingly similar across scales.

The Promise of a Pointillist Perspective for Comparative Immunology

Most studies in comparative immunology involve investigations into the detailed mechanisms of the immune system of a nonmodel organism. Although this approach has been insightful, it has promoted a deep understanding of only a handful of species, thus inhibiting the recognition of broad taxonomic patterns. Here, we call for investigating the immune defenses of numerous species within a pointillist framework, that is, the meticulous, targeted collection of data from dozens of species and investigation of broad patterns of organismal, ecological, and evolutionary forces shaping those patterns. Without understanding basic immunological patterns across species, we are limited in our ability to extrapolate and/or translate our findings to other organisms, including humans. We illustrate this point by focusing predominantly on the biological scaling literature with some integrations of the pace of life literature, as these perspectives have been the most developed within this framework. We also highlight how the more traditional approach in comparative immunology works synergistically with a pointillist approach, with each approach feeding back into the other. We conclude that the pointillist approach promises to illuminate comprehensive theories about the immune system and enhance predictions in a wide variety of domains, including host-parasite dynamics and disease ecology.

An allometry perspective on crops

Understanding trait-trait coordination is essential for successful plant breeding and crop modeling. Notably, plant size drives variation in morphological, physiological, and performance-related traits, as described by allometric laws in ecology. Yet, as allometric relationships have been limitedly studied in crops, how they influence and possibly limit crop performance remains unknown. Here, we review how an allometry perspective on crops gains insights into the phenotypic evolution during crop domestication, the breeding of varieties adapted to novel conditions, and the prediction of crop yields. As allometry is an active field of research, modeling and manipulating crop allometric relationships can help to develop more resilient and productive agricultural systems to face future challenges.

Life, Death and Energy: What Does Nature Select?

Evolutionary biology is poised for a third major synthesis. The first presented Darwin's evidence from natural history. The second incorporated genetic mechanisms. The third will be based on energy and biophysical processes. It should include the equal fitness paradigm (EFP), which quantifies how organisms convert biomass into surviving offspring. Natural selection tends to maximise energetic fitness,E = P coh GFQ $$ E={P}_{\mathrm{coh}}\mathrm{GFQ} $$ , whereP coh $$ {P}_{\mathrm{coh}} $$ is mass-specific rate of cohort biomass production,G $$ G $$ is generation time,F $$ F $$ is fraction of cohort production that is passed to surviving offspring, andQ $$ Q $$ is energy density of biomas. At steady state, parents replace themselves with offspring of equal mass-specific energy content,E $$ E $$  ≈ 22.4 kJ/g, and biomass,M $$ M $$  ≈ 1 g/g. The EFP highlights: (i) the energetic basis of survival and reproduction; (ii) how natural selection acts directly on the parameters ofM $$ M $$ ; (iii) why there is no inherent intrinsic fitness advantage for higher metabolic power, ontogenetic or population growth rate, fecundity, longevity, or resource use efficiency; and (iv) the role of energy in animals with a variety of life histories. Underlying the spectacular diversity of living things is pervasive similarity in how energy is acquired from the environment and used to leave descendants offspring in future generations.

Reporting guidelines for terrestrial respirometry: Building openness, transparency of metabolic rate and evaporative water loss data

Respirometry is an important tool for understanding whole-animal energy and water balance in relation to the environment. Consequently, the growing number of studies using respirometry over the last decade warrants reliable reporting and data sharing for effective dissemination and research synthesis. We provide a checklist guideline on five key sections to facilitate the transparency, reproducibility, and replicability of respirometry studies: 1) materials, set up, plumbing, 2) subject conditions/maintenance, 3) measurement conditions, 4) data processing, and 5) data reporting and statistics, each with explanations and example studies. Transparency in reporting and data availability has benefits on multiple fronts. Authors can use this checklist to design and report on their study, and reviewers and editors can use the checklist to assess the reporting quality of the manuscripts they review. Improved standards for reporting will enhance the value of primary studies and will greatly facilitate the ability to carry out higher quality research syntheses to address ecological and evolutionary theories.

Body Mass Shapes Most Life History Traits and a Fast-Slow Continuum in Amphibians

Amphibians have the least studied life histories among vertebrates, although they have unique and the most diverse life histories within this group. We compiled a new dataset on adult body mass and 16 other life history traits of 2069 amphibian species across three orders (1796 frogs, 236 salamanders, 37 caecilians). These traits characterise fecundity, offspring development from egg deposition to metamorphosis and adult life. We established allometric models on traits for all amphibians and each of the three orders to assess a potential scaling of traits to body mass and then checked whether allometric slopes were consistent with two different metabolic scaling exponents. Further, we examined a possible fast-slow continuum in all amphibians, as well as in each of the two orders frogs and salamanders by applying principal component analysis (PCA) to five traits. Our allometric models indicated a positive scaling to body mass for 11 traits across all amphibians, 12 in frogs, and 10 in salamanders, and for five out of eight traits analysed in caecilians. Allometric slopes on most traits characterising offspring development were not significant. All slopes did not support a three-quarter metabolic scaling exponent, whereas slopes on age at maturity and maximum longevity were consistent with an amphibian metabolic scaling exponent of 0.88. As in fishes, reptiles, birds, and mammals, the first axes of our PCAs indicated a body mass-dependent fast-slow continuum in amphibians. Amphibian species of slow life histories have larger body masses, later sexual maturities and longer lifespans and lay more and larger eggs than species of fast life histories, a pattern also known from reptiles. The second axes indicated a trade-off between egg size and number. As this trade-off was nearly independent of body mass, we hypothesise that amphibians have occupied a broad range of ecological niches without evolutionary changes in body mass.

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

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

Ecological consequences of body size reduction under warming

Body size reduction is a universal response to warming, but its ecological consequences across biological levels, from individuals to ecosystems, remain poorly understood. Most biological processes scale with body size, and warming-induced changes in body size can therefore have important ecological consequences. To understand these consequences, we propose a unifying, hierarchical framework for the ecological impacts of intraspecific body size reductions due to thermal plasticity that explicitly builds on three key pathways: morphological constraints, bioenergetic constraints and surface-to-volume ratio. Using this framework, we synthesize key consequences of warming-induced body size reductions at multiple levels of biological organization. We outline how this trait-based framework can improve our understanding, detection and generalization of the ecological impacts of warming.

Unraveling power-law scaling through exponential cell division dynamics

A primary objective of biology is the development of universal laws that define how organic form develops and how it evolves as a function of size, both ontogenetically and across evolutionary time. Scaling theory has been essential in reaching this goal by giving a complete perspective point, particularly in illuminating the fundamental biological features produced within scaling exponents defining families of equations. Nonetheless, the theoretical basis of the allometric equation within scaling theory are inadequately explained, particularly when it comes to establishing links between micro-level processes at the cellular level and macro-level phenomena. We proposed an unlimited cell bipartition, resulting in an exponential growth in cell numbers during an individual's lifespan, to bridge this conceptual gap between cellular processes and allometric scaling. The power-law scaling between body mass and organ weight was produced by the synchronous exponential increments and the allometric exponent is rate of logarithmic cell proliferation rate. Substituting organ weight for erythrocyte weight aided in the development of a power-law scaling relationship between body mass and metabolic rate. Furthermore, it is critical to understand how cell size affects the exponent in power-law scaling. We find that a bigger exponent will result from an increase in the average weight of organ cells or a decrease in the average weight of all cells. Furthermore, cell proliferation dynamics showed a complex exponential scaling between body mass and longevity, defying the previously reported power-law scaling. We discovered a quadratic link between longevity and logarithmic body mass. Notably, all of the parameters included in these relationships are explained by indices linked to cell division and embryonic development. This research adds to our understanding of the complex interaction between cellular processes and overarching scaling phenomena in biology.

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'.

Interactive effects of intrinsic and extrinsic factors on metabolic rate

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

Eco-evolutionary emergence of macroecological scaling in plankton communities

Macroecological scaling patterns, such as between prey and predator biomass, are fundamental to our understanding of the rules of biological organization and ecosystem functioning. Although these scaling patterns are ubiquitous, how they arise is poorly understood. To explain these patterns, we used an eco-evolutionary predator-prey model parameterized using data for phytoplankton and zooplankton. We show that allometric scaling relationships at lower levels of biological organization, such as body-size scaling of nutrient uptake and predation, give rise to scaling relationships at the food web and ecosystem levels. Our predicted macroecological scaling exponents agree well with observed values across ecosystems. Our findings explicitly connect scaling relationships at different levels of biological organization to ecological and evolutionary mechanisms, yielding testable hypotheses for how observed macroecological patterns emerge.

The scaling of elemental stoichiometry and growth rate over the course of bamboo ontogeny

Stoichiometric rules may explain the allometric scaling among biological traits and body size, a fundamental law of nature. However, testing the scaling of elemental stoichiometry and growth to size over the course of plant ontogeny is challenging. Here, we used a fast-growing bamboo species to examine how the concentrations and contents of carbon (C), nitrogen (N) and phosphorus (P), relative growth rate (G), and nutrient productivity scale with whole-plant mass (M) at the culm elongation and maturation stages. The whole-plant C content vs M and N content vs P content scaled isometrically, and the N or P content vs M scaled as a general 3/4 power function across both growth stages. The scaling exponents of G vs M and N (and P) productivity in newly grown mass vs M relationships across the whole growth stages decreased as a -1 power function. These findings reveal the previously undocumented generality of stoichiometric allometries over the course of plant ontogeny and provide new insights for understanding the origin of ubiquitous quarter-power scaling laws in the biosphere.

Thermal Impact and the Relevance of Body Size and Activity on the Oxygen Consumption of a Terrestrial Snail, Theba pisana (Helicidae) at High Ambient Temperatures

Metabolism, mainly driven by oxygen consumption, plays a key role in life, as it is one of the main ways to respond to extreme temperatures through internal processes. Theba pisana, a widespread Mediterranean land snail, is exposed to a wide range of ambient temperature. In this species the oxygen consumption was tested as a response variable by multiple regression modelling on the "explanatory" variables shell-free mass, temperature, and relative humidity. Our results show that the oxygen consumption of T. pisana can be well described (73.1%) by these three parameters. In the temperature range from 23 °C to 35 °C the oxygen consumption decreased with increasing temperature. Relative humidity, in the range of 67% to 100%, had the opposite effect: if it increases, oxygen consumption will increase as well. Metabolism is proportional to an individual's mass to the power of the allometric scaling exponent α, which is between 0.62 and 0.77 in the mentioned temperature range. CT scans of shells and gravimetry revealed the shell-free mass to be calculated by multiplying the shell diameter to the third power by 0.2105. Data were compared to metabolic scaling exponents for other snails reported in the literature.

The allometry of mitochondrial efficiency is tissue dependent: a comparison between skeletal and cardiac muscles of birds

Body mass is known to be a fundamental driver of many biological traits, including metabolism. However, the effect of body mass on mitochondrial energy transduction is still poorly understood and has mainly been described in mammals. Using 13 species of birds ranging from 15 g (finches) to 160 kg (ostrich), we report here that the mitochondrial production of ATP, and the corresponding oxygen consumption, are negatively dependent on body mass in skeletal muscles but not in the heart. Results also showed that mitochondrial efficiency was positively correlated with body mass at sub-maximal phosphorylating states in the skeletal muscle, but not in the heart. This difference between muscle tissues is potentially linked to the difference in energetic demand expandability and the heavy involvement of skeletal muscle in thermoregulation.

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.

Body size and temperature affect metabolic and cardiac thermal tolerance in fish

Environmental warming is associated with reductions in ectotherm body sizes, suggesting that larger individuals may be more vulnerable to climate change. The mechanisms driving size-specific vulnerability to temperature are unknown but are required to finetune predictions of fisheries productivity and size-structure community responses to climate change. We explored the potential metabolic and cardiac mechanisms underlying these body size vulnerability trends in a eurythermal fish, barred surfperch. We acutely exposed surfperch across a large size range (5-700 g) to four ecologically relevant temperatures (16 °C, 12 °C, 20 °C, and 22 °C) and subsequently, measured their metabolic capacity (absolute and factorial aerobic scopes, maximum and resting metabolic rates; AAS, FAS, MMR, RMR). Additionally, we estimated the fish's cardiac thermal tolerance by measuring their maximum heart rates (fHmax) across acutely increasing temperatures. Barred surfperch had parallel hypoallometric scaling of MMR and RMR (exponent 0.81) and a weaker hypoallometric scaling of fHmax (exponent - 0.05) across all test temperatures. In contrast to our predictions, the fish's aerobic capacity was maintained across sizes and acute temperatures, and larger fish had greater cardiac thermal tolerance than smaller fish. These results demonstrate that thermal performance may be limited by different physiological constraints depending on the size of the animal and species of interest.

A new flexible model for maintenance and feeding expenses that improves description of individual growth in insects

Metabolic theories in ecology interpret ecological patterns at different levels through the lens of metabolism, typically applying allometric scaling to describe energy use. This requires a sound theory for individual metabolism. Common mechanistic growth models, such as 'von Bertalanffy', 'dynamic energy budgets' and the 'ontogenetic growth model' lack some potentially important aspects, especially regarding regulation of somatic maintenance. We develop a model for ontogenetic growth of animals, applicable to ad libitum and food limited conditions, based on an energy balance that expresses growth as the net result of assimilation and metabolic costs for maintenance, feeding and food processing. The most important contribution is the division of maintenance into a 'non-negotiable' and a 'negotiable' part, potentially resulting in hyperallometric scaling of maintenance and downregulated maintenance under food restriction. The model can also account for effects of body composition and type of growth at the cellular level. Common mechanistic growth models often fail to fully capture growth of insects. However, our model was able to capture empirical growth patterns observed in house crickets.

The Relevance of Time in Biological Scaling

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