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

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.

Deciphering the Hearts: Geometric Morphometrics Reveals Shape Variation in Abatus Sea Urchins across Subantarctic and Antarctic Seas

Abatus is a genus of irregular brooding sea urchins to the Southern Ocean. Among the 11 described species, three shared morphological traits and present an infaunal lifestyle in the infralittoral from the Subantarctic province; A. cavernosus in Patagonia, A. cordatus in Kerguelen, and A. agassizii in Tierra del Fuego and South Shetlands. The systematic of Abatus, based on morphological characters and incomplete phylogenies, is complex and largely unresolved. This study evaluates the shape variation among these species using geometric morphometrics analysis (GM). For this, 72 individuals from four locations; South Shetlands, Kerguelen, Patagonia, and Falklands/Malvinas were photographed, and 37 landmarks were digitized. To evaluate the shape differences among species, a principal component analysis and a Procrustes ANOVA were performed. Our results showed a marked difference between the Falklands/Malvinas and the other localities, characterized by a narrower and more elongated shape and a significant influence of location in shape but not sex. Additionally, the effect of allometry was evaluated using a permutation test and a regression between shape and size, showing significant shape changes during growth in all groups. The possibility that the Falklands/Malvinas group shows phenotypic plasticity or represents a distinct evolutionary unit is discussed. Finally, GM proved to be a powerful tool to differentiate these species, highlighting its utility in systematic studies.

Discontinuous, biphasic, ontogenetic shifts in the metabolic allometry of aquatic animals?

Several investigations in recent years have reported patterns of discontinuous, biphasic, loglinear variation in the metabolic allometry of aquatic animals. These putative shifts in pattern of allometry have been attributed to changes in the primary site for gas exchange from cutaneous to branchial as animals undergo ontogenetic changes in size, shape, and surface area. Because of the important implications of the earlier research with regard to both physiology and evolution, I re-examined data that purportedly support claims of discontinuous, biphasic allometry in oxygen consumption versus body size of American eels (Anguilla rostrata) and spiny lobsters (Sagmariasus verreauxi). I used ANCOVA to fit three different statistical models to each set of logarithmic transformations and then assessed the fits by Akaike's Information Criterion. The observations for both species were described better by a single straight line fitted to the full distribution than by a biphasic model. Eels, lobsters, and other aquatic animals undergo changes in shape and surface area as they grow, but such changes are not necessarily accompanied by changes in the pattern of metabolic allometry.

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'.

The Relevance of Time in Biological Scaling

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

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

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

Commentary: Allometric analyses of data with outlying observations: The ontogenetic shift in metabolic allometry of American eels (Anguilla rostrata)

Authors of a recent report concluded that different patterns of metabolic allometry characterize juvenile and subadult stages in the life cycle of American eels (Anguilla rostrata). This conclusion was based on a comparison of straight lines fitted to logarithmic transformations of the original observations for metabolic rate and body mass, with the line fitted to transformations for 30 juveniles having a substantially lower slope than the line describing observations for 30 subadults. However, the authors failed to account for an influential outlier in the sample of juvenile eels, and this one outlier was determinative for the outcome of the analysis. When the outlier is removed from the combined data set for juveniles and subadults, the resulting sample of 59 observations is well described by a single straight line, which implies, in turn, that untransformed observations can be described by a two-parameter power equation with lognormal error. This supposition is confirmed by a graph of the two-parameter equation against the backdrop of the untransformed data. Thus, no change in the pattern of metabolic allometry occurs during the ontogeny of American eels: the same pattern of allometric variation characterizes both juvenile and subadult animals.

Metabolic Rates of Japanese Anchovy (Engraulis japonicus) during Early Development Using a Novel Modified Respirometry Method

The allometric relationship between metabolic rate (VO2) and body mass (M) has been a subject of fascination and controversy for decades. Nevertheless, little is known about intraspecific size-scaling metabolism in marine animals such as teleost fish. The Japanese anchovy Engraulis japonicus is a planktotrophic pelagic fish with a rapid growth and metabolic rate. However, metabolic rate measurements are difficult in this species due to their extremely small body size after hatching. Herein, the metabolic rate of this species during its early developmental stage was measured for 47 individuals weighing 0.00009–0.09 g (from just after hatching to 43 days old) using the micro-semi-closed method, a newly modified method for monitoring metabolism developed specifically for this study. As a result, three distinct allometric phases were identified. During these phases, two stepwise increases in scaling constants occurred at around 0.001 and 0.01 g, although the scaling exponent constant remained unchanged in each phase (b^ = 0.683). Behavioral and morphological changes accompanied the stepwise increases in scaling constants. Although this novel modified respirometry method requires further validation, it is expected that this study will be useful for future metabolic ecology research in fish to determine metabolism and survival strategy.

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.

How Metabolic Rate Relates to Cell Size

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

The Evolution of Offspring Size: a Metabolic Scaling Perspective

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

Complications with body-size correction in comparative biology: possible solutions and an appeal for new approaches

The magnitude of many kinds of biological traits relates strongly to body size. Therefore, a first step in comparative studies frequently involves correcting for effects of body size on the variation of a phenotypic trait, so that the effects of other biological and ecological factors can be clearly distinguished. However, commonly used traditional methods for making these body-size adjustments ignore or do not completely separate the causal interactive effects of body size and other factors on trait variation. Various intrinsic and extrinsic factors may affect not only the variation of a trait, but also its covariation with body size, thus making it difficult to remove completely the effect of body size in comparative studies. These complications are illustrated by several examples of how body size interacts with diverse developmental, physiological, behavioral and ecological factors to affect variation in metabolic rate both within and across species. Such causal interactions are revealed by significant effects of these factors on the body-mass scaling slope of metabolic rate. I discuss five possible major kinds of methods for removing body-size effects that attempt to overcome these complications, at least in part, but I hope that my Review will encourage the development of other, hopefully better methods for doing so.

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.

Linking species traits and demography to explain complex temperature responses across levels of organization

Microbial communities regulate ecosystem responses to climate change. However, predicting these responses is challenging because of complex interactions among processes at multiple levels of organization. Organismal traits that determine individual performance and ecological interactions are essential for scaling up environmental responses from individuals to ecosystems. We combine protist microcosm experiments and mathematical models to show that key traits-cell size, shape, and contents-each explain different aspects of species' demographic responses to changes in temperature. These differences in species' temperature responses have complex cascading effects across levels of organization-causing nonlinear shifts in total community respiration rates across temperatures via coordinated changes in community composition, equilibrium densities, and community-mean species mass in experimental protist communities that tightly match theoretical predictions. Our results suggest that traits explain variation in population growth, and together, these two factors scale up to influence community- and ecosystem-level processes across temperatures. Connecting the multilevel microbial processes that ultimately influence climate in this way will help refine predictions about complex ecosystem-climate feedbacks and the pace of climate change itself.

Effects of temperature on metabolic scaling in silver carp

The association between temperature and metabolic scaling varies among species, which could be due to variation in the surface area and its scaling. This study aims to examine the effect of temperature on metabolic scaling and to verify the links between metabolic scaling and surface area scaling at both the whole body and the cell levels. The routine metabolic rate (RMR), gill surface area (GSA), ventilation frequency (VF), red blood cell surface area (S_RBC ), and metabolic rate (MR_RBC ) were determined in silver carp, and their mass-scaling exponents were analyzed at 10 and 25°C. These results showed that body mass and temperature independently affected the RMR, GSA, and VF, suggesting constant scaling exponents of RMR (0.772), GSA (0.912), and VF (-0.282) with changing temperature. The RMR at 25°C was 2.29 times higher than that at 10°C, suggesting increased metabolic demand at a higher temperature. The results showed that the RMR increased, while the scaling exponents of RMR, GSA, and VF remained unchanged with increasing temperature. These results support the view that the scaling of oxygen supply capacity importantly affects metabolic scaling. The S_RBC did not change with either temperature or body mass. However, the MR_RBC increased by 5.48 times from 10 to 25°C but did not change with body mass. As the scaling exponents of RMR did not change between temperatures, the results indicate that no obvious link exists between the scaling of both the cell size and cell metabolic rate and the metabolic scaling of silver carp.

Biological scaling analyses are more than statistical line fitting

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

Comparison of metabolic scaling between triploid and diploid common carp

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

Changes to benthic community structure may impact organic matter consumption on Pacific Arctic shelves

Changes in species composition and biomass of Arctic benthic communities are predicted to occur in response to environmental changes associated with oceanic warming and sea-ice loss. Such changes will likely impact ecosystem function, including flows of energy and organic material through the Arctic marine food web. Oxygen consumption rates can be used to quantify differences in metabolic demand among species and estimate the effects of shifting community structure on benthic carbon consumption. Closed-system respirometry using non-invasive oxygen optodes was conducted onboard the R/V Sikuliaq in June 2017 and 2018 on six dominant species of benthic macrofauna from the northern Bering and southern Chukchi Sea shelves, including five bivalve species (Macoma sp., Serripes groenlandicus, Astarte sp., Hiatella arctica and Nuculana pernula) and one amphipod species (Ampelisca macrocephala). Results revealed species-specific respiration rates with high metabolic demand for S. groenlandicus and A. macrocephala compared to that of the other species. For a hypothetical 0.1-g ash-free dry mass individual, the standard metabolic rate of S. groenlandicus would be 4.3 times higher than that of Astarte sp. Overall, carbon demand ranged from 8 to 475 μg C individual^-1 day^-1 for the species and sizes of individuals measured. The allometric scaling of respiration rate with biomass also varied among species. The scaling coefficient was similar for H. arctica, A. macrocephala and Astarte sp., while it was high for S. groenlandicus and low for Macoma sp. These results suggest that observed shifts in spatial distribution of the dominant macrofaunal taxa across this region will impact carbon demand of the benthic community. Hence, ecosystem models seeking to incorporate benthic system functionality may need to differentiate between communities that exhibit different oxygen demands.

Shrinking body sizes in response to warming: explanations for the temperature-size rule with special emphasis on the role of oxygen

Body size is central to ecology at levels ranging from organismal fecundity to the functioning of communities and ecosystems. Understanding temperature-induced variations in body size is therefore of fundamental and applied interest, yet thermal responses of body size remain poorly understood. Temperature-size (T-S) responses tend to be negative (e.g. smaller body size at maturity when reared under warmer conditions), which has been termed the temperature-size rule (TSR). Explanations emphasize either physiological mechanisms (e.g. limitation of oxygen or other resources and temperature-dependent resource allocation) or the adaptive value of either a large body size (e.g. to increase fecundity) or a short development time (e.g. in response to increased mortality in warm conditions). Oxygen limitation could act as a proximate factor, but we suggest it more likely constitutes a selective pressure to reduce body size in the warm: risks of oxygen limitation will be reduced as a consequence of evolution eliminating genotypes more prone to oxygen limitation. Thus, T-S responses can be explained by the 'Ghost of Oxygen-limitation Past', whereby the resulting (evolved) T-S responses safeguard sufficient oxygen provisioning under warmer conditions, reflecting the balance between oxygen supply and demands experienced by ancestors. T-S responses vary considerably across species, but some of this variation is predictable. Body-size reductions with warming are stronger in aquatic taxa than in terrestrial taxa. We discuss whether larger aquatic taxa may especially face greater risks of oxygen limitation as they grow, which may be manifested at the cellular level, the level of the gills and the whole-organism level. In contrast to aquatic species, terrestrial ectotherms may be less prone to oxygen limitation and prioritize early maturity over large size, likely because overwintering is more challenging, with concomitant stronger end-of season time constraints. Mechanisms related to time constraints and oxygen limitation are not mutually exclusive explanations for the TSR. Rather, these and other mechanisms may operate in tandem. But their relative importance may vary depending on the ecology and physiology of the species in question, explaining not only the general tendency of negative T-S responses but also variation in T-S responses among animals differing in mode of respiration (e.g. water breathers versus air breathers), genome size, voltinism and thermally associated behaviour (e.g. heliotherms).

Water content quantitatively affects metabolic rates over the course of plant ontogeny

Plant metabolism determines the structure and dynamics of ecological systems across many different scales. The metabolic theory of ecology quantitatively predicts the scaling of metabolic rate as a function of body size and temperature. However, the role of tissue water content has been neglected even though hydration significantly affects metabolism, and thus ecosystem structure and functioning. Here, we use a general model based on biochemical kinetics to quantify the combined effects of water content, body size and temperature on plant metabolic rates. The model was tested using a comprehensive dataset from 205 species across 10 orders of magnitude in body size from seeds to mature large trees. We show that water content significantly influences mass-specific metabolic rates as predicted by the model. The scaling exponents of whole-plant metabolic rate vs body size numerically converge onto 1.0 after water content is corrected regardless of body size or ontogenetic stage. The model provides novel insights into how water content together with body size and temperature quantitatively influence plant growth and metabolism, community dynamics and ecosystem energetics.

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.

Ventilation Frequency Reveals the Roles of Exchange Surface Areas in Metabolic Scaling

The surface area (SA) theory proposes that resting metabolic rate (RMR) scales with body mass, which parallels the exchange SA of organisms, and that a species with a larger scaling exponent of exchange SA has a larger scaling exponent of RMR. However, the effects of exchange SA on metabolic scaling may be eclipsed because oxygen transfer across the respiratory surface is determined not only by the exchange SA but also by ventilation. We hypothesize that the scaling of both gill surface area (GSA) and ventilation frequency (VF) positively affects the scaling of metabolic rate. In six closely related species of carp maintained under the same experimental conditions, the scaling exponents of RMR and GSA were analyzed. In the goldfish, RMR scaled with body mass by an exponent significantly lower than that of GSA but not different from the exponents of GSA in the remaining five species. The scaling exponent of RMR was positively related to those of both GSA and VF among the species. In addition, the VF-corrected metabolic scaling exponent was positively related to the scaling exponent of GSA among the species. These results suggest that variations in GSA scaling and in VF scaling among species mutually affect metabolic scaling.

Effects of temperature on metabolic scaling in black carp

The surface area (SA) of organs and cells may vary with temperature, which changes the SA exchange limitation on metabolic flows as well as the influence of temperature on metabolic scaling. The effect of SA change can intensify (when the effect is the same as that of temperature) or compensate for (when the effect is the opposite of that of temperature) the negative effects of temperature on metabolic scaling, which can result in multiple patterns of metabolic scaling with temperature among species. The present study aimed to examine whether metabolic scaling in black carp changes with temperature and to identify the link between metabolic scaling and SA at the organ and cellular levels at different temperatures. The resting metabolic rate (RMR), gill surface area (GSA) and red blood cell (RBC) size of black carp with different body masses were measured at 10 °C and 25 °C, and the scaling exponents of these parameters were compared. The results showed that both body mass and temperature independently affected the RMR, GSA and RBC size of black carp. A consistent scaling exponent of RMR (0.764, 95% CI [0.718-0.809]) was obtained for both temperatures. The RMR at 25 °C was 2.7 times higher than that at 10 °C. At both temperatures, the GSA scaled consistently with body mass by an exponent of 0.802 (95% CI [0.759-0.846]), while RBC size scaled consistently with body mass by an exponent of 0.042 (95% CI [0.010-0.075]). The constant GSA scaling can explain the constant metabolic scaling as temperature increases, as metabolism may be constrained by fluxes across surfaces. The GSA at 10 °C was 1.2 times higher than that at 25 °C, which suggests that the constraints of GSA on the metabolism of black carp is induced by the higher temperature. The RBC size at 10 °C was 1.1 times higher than that at 25 °C. The smaller RBC size (a larger surface-to-volume ratio) at higher temperature suggests an enhanced oxygen supply and a reduced surface boundary limit on b _R, which offset the negative effect of temperature on b _R.

A new framework for growth curve fitting based on the von Bertalanffy Growth Function

All organisms grow. Numerous growth functions have been applied to a wide taxonomic range of organisms, yet some of these models have poor fits to empirical data and lack of flexibility in capturing variation in growth rate. We propose a new VBGF framework that broadens the applicability and increases flexibility of fitting growth curves. This framework offers a curve-fitting procedure for five parameterisations of the VBGF: these allow for different body-size scaling exponents for anabolism (biosynthesis potential), besides the commonly assumed 2/3 power scaling, and allow for supra-exponential growth, which is at times observed. This procedure is applied to twelve species of diverse aquatic invertebrates, including both pelagic and benthic organisms. We reveal widespread variation in the body-size scaling of biosynthesis potential and consequently growth rate, ranging from isomorphic to supra-exponential growth. This curve-fitting methodology offers improved growth predictions and applies the VBGF to a wider range of taxa that exhibit variation in the scaling of biosynthesis potential. Applying this framework results in reliable growth predictions that are important for assessing individual growth, population production and ecosystem functioning, including in the assessment of sustainability of fisheries and aquaculture.

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

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

Effects of gill excision and food deprivation on metabolic scaling in the goldfish Carassius auratus

According to the metabolic-level boundaries hypothesis, metabolic level mediates the relative influence of surface area or volume-related metabolic processes on metabolic scaling in organisms. Therefore, variation in both metabolic level and surface area may affect metabolic scaling. Goldfish were used to determine the influence of both a surgical reduction in respiratory surface area and food deprivation on metabolic scaling exponents (b_R ). Gill excision did not change resting metabolic rate (RMR) or b_R (a common value of 0.895). However, ventilation frequency (VF) increased from 21.6 times min^-1 before gill excision to 52.8 times min^-1 after gill excision. This suggests that the acceleration of breathing after gill excision offsets the constraints of the respiratory surface area on RMR and results in no influence of surface area reduction on metabolic scaling. In the food deprivation experiment, RMR decreased; however, b_R (a common value of 0.872) did not increase. The VFs of the fish at weeks 1 and 2 were approximately 22% and 38% lower than that at Week 0, which may enhance exchange surface area limits and result in no increase in b_R with a decreasing RMR induced by food deprivation. The results suggest that food deprivation reduces metabolic level, but does not alter metabolic scaling exponent owing to variation in VF.

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

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

Modeling the Growth of Organisms Validates a General Relation between Metabolic Costs and Natural Selection

Metabolism and evolution are closely connected: if a mutation incurs extra energetic costs for an organism, there is a baseline selective disadvantage that may or may not be compensated for by other adaptive effects. A long-standing, but to date unproven, hypothesis is that this disadvantage is equal to the fractional cost relative to the total resting metabolic expenditure. We validate this result from physical principles through a general growth model and show it holds to excellent approximation for experimental parameters drawn from a wide range of species.

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.

A broad-scale comparison of aerobic activity levels in vertebrates: endotherms versus ectotherms

Differences in the limits and range of aerobic activity levels between endotherms and ectotherms remain poorly understood, though such differences help explain basic differences in species' lifestyles (e.g. movement patterns, feeding modes, and interaction rates). We compare the limits and range of aerobic activity in endotherms (birds and mammals) and ectotherms (fishes, reptiles, and amphibians) by evaluating the body mass-dependence of VO₂ max, aerobic scope, and heart mass in a phylogenetic context based on a newly constructed vertebrate supertree. Contrary to previous work, results show no significant differences in the body mass scaling of minimum and maximum oxygen consumption rates with body mass within endotherms or ectotherms. For a given body mass, resting rates and maximum rates were 24-fold and 30-fold lower, respectively, in ectotherms than endotherms. Factorial aerobic scope ranged from five to eight in both groups, with scope in endotherms showing a modest body mass-dependence. Finally, maximum consumption rates and aerobic scope were positively correlated with residual heart mass. Together, these results quantify similarities and differences in the potential for aerobic activity among ectotherms and endotherms from diverse environments. They provide insights into the models and mechanisms that may underlie the body mass-dependence of oxygen consumption.

Temperature-Dependent Growth and Fission Rate Plasticity Drive Seasonal and Geographic Changes in Body Size in a Clonal Sea Anemone

The temperature-size rule is a commonly observed pattern where adult body size is negatively correlated with developmental temperature. In part, this may occur as a consequence of allometric scaling, where changes in the ratio of surface area to mass limit oxygen diffusion as body size increases. As oxygen demand increases with temperature, a smaller body should be favored as temperature increases. For clonal animals, small changes in growth and/or fission rate can rapidly alter the average body size of clonal descendants. Here I test the hypothesis that the clonal sea anemone Diadumene lineata is able to track an optimal body size through seasonal temperature changes using fission rate plasticity. Individuals from three regions (Florida, Georgia, and Massachusetts) across the species' latitudinal range were grown in a year-long reciprocal common garden experiment mimicking seasonal temperature changes at three sites. Average body size was found to be smaller and fission rates higher in warmer conditions, consistent with the temperature-size rule pattern. However, seasonal size and fission patterns reflect a complex interaction between region-specific thermal reaction norms and the local temperature regime. These details provide insight into both the range of conditions required for oxygen limitation to contribute to a negative correlation between body size and temperature and the role that fission rate plasticity can play in tracking a rapidly changing optimal phenotype.

Bridging Food Webs, Ecosystem Metabolism, and Biogeochemistry Using Ecological Stoichiometry Theory

Although aquatic ecologists and biogeochemists are well aware of the crucial importance of ecosystem functions, i.e., how biota drive biogeochemical processes and vice-versa, linking these fields in conceptual models is still uncommon. Attempts to explain the variability in elemental cycling consequently miss an important biological component and thereby impede a comprehensive understanding of the underlying processes governing energy and matter flow and transformation. The fate of multiple chemical elements in ecosystems is strongly linked by biotic demand and uptake; thus, considering elemental stoichiometry is important for both biogeochemical and ecological research. Nonetheless, assessments of ecological stoichiometry (ES) often focus on the elemental content of biota rather than taking a more holistic view by examining both elemental pools and fluxes (e.g., organismal stoichiometry and ecosystem process rates). ES theory holds the promise to be a unifying concept to link across hierarchical scales of patterns and processes in ecology, but this has not been fully achieved. Therefore, we propose connecting the expertise of aquatic ecologists and biogeochemists with ES theory as a common currency to connect food webs, ecosystem metabolism, and biogeochemistry, as they are inherently concatenated by the transfer of carbon, nitrogen, and phosphorous through biotic and abiotic nutrient transformation and fluxes. Several new studies exist that demonstrate the connections between food web ecology, biogeochemistry, and ecosystem metabolism. In addition to a general introduction into the topic, this paper presents examples of how these fields can be combined with a focus on ES. In this review, a series of concepts have guided the discussion: (1) changing biogeochemistry affects trophic interactions and ecosystem processes by altering the elemental ratios of key species and assemblages; (2) changing trophic dynamics influences the transformation and fluxes of matter across environmental boundaries; (3) changing ecosystem metabolism will alter the chemical diversity of the non-living environment. Finally, we propose that using ES to link nutrient cycling, trophic dynamics, and ecosystem metabolism would allow for a more holistic understanding of ecosystem functions in a changing environment.

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.

A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees

Lognormal distributions and self-similarity are characteristics associated with a wide range of biological systems. The sequential breakage model has established a link between lognormal distributions and self-similarity and has been used to explain species abundance distributions. To date, however, there has been no similar evidence in studies of multicellular organismal forms. We tested the hypotheses that the distribution of the lengths of terminal stems of Japanese elm trees (Ulmus davidiana), the end products of a self-similar branching process, approaches a lognormal distribution. We measured the length of the stem segments of three elm branches and obtained the following results: (i) each occurrence of branching caused variations or errors in the lengths of the child stems relative to their parent stems; (ii) the branches showed statistical self-similarity; the observed error distributions were similar at all scales within each branch and (iii) the multiplicative effect of these errors generated variations of the lengths of terminal twigs that were well approximated by a lognormal distribution, although some statistically significant deviations from strict lognormality were observed for one branch. Our results provide the first empirical evidence that statistical self-similarity of an organismal form generates a lognormal distribution of organ sizes.

Testing mechanistic models of growth in insects

Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes.

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.

Urchins in a high CO2 world: partitioned effects of body-size, ocean warming and acidification on metabolic rate

Body-size and temperature are the major factors explaining metabolic rate, and the additional factor of pH is a major driver at the biochemical level. These three factors have frequently been found to interact, complicating the formulation of broad models predicting metabolic rates and hence ecological functioning. In this first study of the effects of warming and ocean acidification, and their potential interaction, on metabolic rate across a broad body-size range (two-to-three orders of magnitude difference in body mass) we addressed the impact of climate change on the sea urchin Heliocidaris erythrogramma in context with climate projections for east Australia, an ocean warming hotspot. Urchins were gradually introduced to two temperatures (18 and 23 °C) and two pH (7.5 and 8.0), and maintained for two months. That a new physiological steady-state had been reached, otherwise know as acclimation, was validated through identical experimental trials separated by several weeks. The relationship between body-size, temperature and acidification on the metabolic rate of H. erythrogramma was strikingly stable. Both stressors caused increases in metabolic rate; 20% for temperature and 19% for pH. Combined effects were additive; a 44% increase in metabolism. Body-size had a highly stable relationship with metabolic rate regardless of temperature or pH. None of these diverse drivers of metabolism interacted or modulated the effects of the others, highlighting the partitioned nature of how each influences metabolic rate, and the importance of achieving a full acclimation state. Despite these increases in energetic demand there was very limited capacity for compensatory modulating of feeding rate; food consumption increased only in the very smallest specimens, and only in response to temperature, and not pH. Our data show that warming, acidification and body-size all substantially affect metabolism and are highly consistent and partitioned in their effects, and for H. erythrogramma near-future climate change will incur a substantial energetic cost.