Energetic cost of biosynthesis is a missing link between growth and longevity in mammals

The comparative studies of aging have established a negative correlation between Gompertz postnatal growth constant and maximum lifespan across mammalian species, but the underlying physiological mechanism remains unclear. This study shows that the Gompertz growth constant can be decomposed into two energetic components, mass-specific metabolic rate and the energetic cost of biosynthesis, and that after controlling the former as a confounder, the negative correlation between growth constant and lifespan still exists due to a 100-fold variation in the latter, revealing that the energetic cost of biosynthesis is a link between growth and longevity in mammals. Previously, the energetic cost of biosynthesis has been thought to be a constant across species and therefore was not considered a contributor to the variation in any life history traits, such as growth and lifespan. This study employs a recently proposed model based on energy conservation to explain the physiological effect of the variation in this energetic cost on the aging process and illustrates its role in linking growth and lifespan. The conventional life history theory suggested a tradeoff between growth and somatic maintenance, but the findings in this study suggest that allocating more energy to biosynthesis may enhance the somatic maintenance and extend lifespan and, hence, reveal a more complex nature of the tradeoff.

Dissipative scaling of development and aging in multicellular organisms

Evolution, self-replication and ontogenesis are highly dynamic, irreversible and self-organizing processes dissipating energy. While progress has been made to decipher the role of thermodynamics in cellular fission, it is not yet clear how entropic balances shape organism growth and aging. This paper derives a general dissipation theory for the life history of organisms. It implies a self-regulated energy dissipation facilitating exponential growth within a hierarchical and entropy lowering self-organization. The theory predicts ceilings in energy expenditures imposed by geometric constrains, which promote thermal optimality during development, and a dissipative scaling across organisms consistent with ecological scaling laws combining isometric and allometric terms. The theory also illustrates how growing organisms can tolerate damage through continuous extension and production of new dissipative structures low in entropy. However, when organisms reduce their rate of cell division and reach a steady adult state, they become thermodynamically unstable, increase internal entropy by accumulating damage, and age.

Comparison of Energy Budget of Cockroach Nymph (Hemimetabolous) and Hornworm (Holometabolous) under Food Restriction

Animals with different life histories budget their intake energy differently when food availability is low. It has been shown previously that hornworm (larva of Manduca sexta), a holometabolous insect species with a short development stage, prioritizes growth at the price of metabolism under food restriction, but it is unclear how hemimetabolous insect species with a relatively long development period budget their intake energy under food scarcity. Here, we use orange head cockroaches (Eublaberus posticus) to investigate this question. We found that for both species under food restriction, rates of metabolism and growth were suppressed, but the degree of reduction was more severe in growth than that of metabolism for cockroaches. Under both free-feeding and food restriction conditions, hornworms allocated a larger fraction of assimilated energy to growth than to metabolism, and cockroaches were the opposite. More importantly, when food availability was low, the fraction of assimilated energy allocated to growth was reduced by 120% in cockroaches, and the energy from growth was channeled to compensate for the reduction in metabolism; but, the fraction of assimilated energy allocated to growth was only reduced by 14% in hornworms. These results suggest that, compared to hornworms, cockroaches prioritize metabolism over growth.

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.

Temperature and pressure dependency of oxygen consumption during long-term sustained swimming of European eels

Many aspects of the typically 5000-10,000 km spawning migration of the European eel (Anguilla anguilla) remain unknown. As part of this migration, eels undertake extensive diurnal vertical migrations to depths below 1000 m, being exposed to a wide range of temperatures and hydrostatic pressures. In this experimental study, we exposed eels to different combinations of temperature (12-20°C) and pressure (100--800 kPa) during long-term sustained swimming (32-47 days). Both temperature and pressure affected oxygen consumption rate, such that there was a significant increase of metabolic rate with temperature, whereas pressure reduced oxygen consumption, albeit only at higher temperatures. Average oxygen consumption rates ranged between 15 mg kg-1 h-1 (12°C, 100 kPa) and 30.2 mg kg-1 h-1 (20°C, 100 kPa), highlighting the remarkably high swimming efficiency of this species and, more importantly, indicating that past evaluations of the cost of transport are potentially overestimates as they are often based on experiments conducted at atmospheric pressure at higher temperatures.

Gene and protein expression and metabolic flux analysis reveals metabolic scaling in liver ex vivo and in vivo

Metabolic scaling, the inverse correlation of metabolic rates to body mass, has been appreciated for more than 80 years. Studies of metabolic scaling have largely been restricted to mathematical modeling of caloric intake and oxygen consumption, and mostly rely on computational modeling. The possibility that other metabolic processes scale with body size has not been comprehensively studied. To address this gap in knowledge, we employed a systems approach including transcriptomics, proteomics, and measurement of in vitro and in vivo metabolic fluxes. Gene expression in livers of five species spanning a 30,000-fold range in mass revealed differential expression according to body mass of genes related to cytosolic and mitochondrial metabolic processes, and to detoxication of oxidative damage. To determine whether flux through key metabolic pathways is ordered inversely to body size, we applied stable isotope tracer methodology to study multiple cellular compartments, tissues, and species. Comparing C57BL/6 J mice with Sprague-Dawley rats, we demonstrate that while ordering of metabolic fluxes is not observed in in vitro cell-autonomous settings, it is present in liver slices and in vivo. Together, these data reveal that metabolic scaling extends beyond oxygen consumption to other aspects of metabolism, and is regulated at the level of gene and protein expression, enzyme activity, and substrate supply.

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.

Link between Energy Investment in Biosynthesis and Proteostasis: Testing the Cost-Quality Hypothesis in Insects

The energy requirement for biosynthesis plays an important role in an organism's life history, as it determines growth rate, and tradeoffs with the investment in somatic maintenance. This energetic trait is different between painted lady (Vanessa cardui) and Turkestan cockroach (Blatta lateralis) due to the different life histories. Butterfly caterpillars (holometabolous) grow 30-fold faster, and the energy cost of biosynthesis is 20 times cheaper, compared to cockroach nymphs (hemimetabolous). We hypothesize that physiologically the difference in the energy cost is partially attributed to the differences in protein retention and turnover rate: Species with higher energy cost may have a lower tolerance to errors in newly synthesized protein. Newly synthesized proteins with errors are quickly unfolded and refolded, and/or degraded and resynthesized via the proteasomal system. Thus, much protein output may be given over to replacement of the degraded new proteins, so the overall energy cost on biosynthesis is high. Consequently, the species with a higher energy cost for biosyntheses has better proteostasis and cellular resistance to stress. Our study found that, compared to painted lady caterpillars, the midgut tissue of cockroach nymphs has better cellular viability under oxidative stresses, higher activities of proteasome 20S, and a higher RNA/growth ratio, supporting our hypothesis. This comparative study offers a departure point for better understanding life history tradeoffs between somatic maintenance and biosynthesis.

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.

Factors affecting gestation periods in elasmobranch fishes

Gestation periods vary greatly across elasmobranch species. Differences in body size and body temperature (i.e. major determinants of metabolic rates) might explain such variation. Although temperature effects have been demonstrated for captive animals, body size effects remain undocumented. Moreover, whether metabolic rates of mothers or those of embryos affect gestation periods remains unclear. Because biological times generally scale with mass1-β, where β is metabolic scaling exponent (0.8-0.9 in fishes), we hypothesized that elasmobranch gestation periods would scale with mass0.1-0.2. We also hypothesized that regionally endothermic species with elevated metabolic rates should have shorter gestation periods than similar-sized ectothermic species if the metabolic rates of mothers are responsible. We compiled data on gestation periods for 36 elasmobranch species to show that gestation periods scale with M0.11 and m0.17, where M and m are adult female mass and birth mass, respectively. Litter size and body temperature also affected gestation periods. Our findings suggest that the body-mass dependence of metabolic rate explains some variations in elasmobranch gestation periods. Unexpectedly, regionally endothermic sharks did not have shorter gestation periods than their ectothermic counterparts, suggesting that the metabolic rates of embryos, which are likely ectothermic in all elasmobranch species, may be responsible. This article has an associated First Person interview with the first author of the paper.

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.

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.

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

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

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

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

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

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

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.

The extremely low energy cost of biosynthesis in holometabolous insect larvae

The metabolic cost of growth, which quantifies the amount of energy required to synthesize a unit of biomass, is an important component of an animal's ontogenetic energy budget. Here we investigated this quantity as well as other energy budget variables of the larvae of a holometabolous insect species, Vanessa cardui (painted lady). We found that the high growth rate of this caterpillar cannot be explained by its metabolic rate and the percentage of the metabolic energy allocated to growth; the key to understanding its fast growth is the extremely low cost of growth, 336 Joules/gram of dry mass. The metabolic cost of growth in caterpillars is 15-65 times lower than that of the endothermic and ectothermic species investigated in previous studies. Our results suggest that the low cost cannot be attributed to its body composition, diet composition, or body size. To explain the "cheap price" of growth in caterpillars, we assumed that a high metabolic cost for biosynthesis resulted in a high "quality" of cells, which have fewer errors during biosynthesis and higher resistance to stressors. Considering the life history of the caterpillars, i.e., tissue disintegration during metamorphosis and a short developmental period and lifespan, we hypothesized that an energy budget that allocates a large amount of energy to biosynthesizing high quality cells would be selected against in this species. As a preliminary test of this hypothesis, we estimated the metabolic cost of growth in larvae of Manduca sexta (tobacco hornworm) and nymphs of Blatta lateralis (Turkestan cockroach). The preliminary data supported our hypothesis.

Toward a metabolic theory of life history

The life histories of animals reflect the allocation of metabolic energy to traits that determine fitness and the pace of living. Here, we extend metabolic theories to address how demography and mass-energy balance constrain allocation of biomass to survival, growth, and reproduction over a life cycle of one generation. We first present data for diverse kinds of animals showing empirical patterns of variation in life-history traits. These patterns are predicted by theory that highlights the effects of 2 fundamental biophysical constraints: demography on number and mortality of offspring; and mass-energy balance on allocation of energy to growth and reproduction. These constraints impose 2 fundamental trade-offs on allocation of assimilated biomass energy to production: between number and size of offspring, and between parental investment and offspring growth. Evolution has generated enormous diversity of body sizes, morphologies, physiologies, ecologies, and life histories across the millions of animal, plant, and microbe species, yet simple rules specified by general equations highlight the underlying unity of life.

Strong Evidence for an Intraspecific Metabolic Scaling Coefficient Near 0.89 in Fish

As an example of applying the evidential approach to statistical inference, we address one of the longest standing controversies in ecology, the evidence for, or against, a universal metabolic scaling relationship between metabolic rate and body mass. Using fish as our study taxa, we curated 25 studies with measurements of standard metabolic rate, temperature, and mass, with 55 independent trials and across 16 fish species and confronted this data with flexible random effects models. To quantify the body mass - metabolic rate relationship, we perform model selection using the Schwarz Information Criteria (ΔSIC), an established evidence function. Further, we formulate and justify the use of ΔSIC intervals to delineate the values of the metabolic scaling relationship that should be retained for further consideration. We found strong evidence for a metabolic scaling coefficient of 0.89 with a ΔSIC interval spanning 0.82 to 0.99, implying that mechanistically derived coefficients of 0.67, 0.75, and 1, are not supported by the data. Model selection supports the use of a random intercepts and random slopes by species, consistent with the idea that other factors, such as taxonomy or ecological or lifestyle characteristics, may be critical for discerning the underlying process giving rise to the data. The evidentialist framework applied here, allows for further refinement given additional data and more complex models.

Ecophysiological determinants of sexual size dimorphism: integrating growth trajectories, environmental conditions, and metabolic rates

Sexual size dimorphism (SSD) often results in dramatic differences in body size between females and males. Despite its ecological importance, little is known about the relationship between developmental, physiological, and energetic mechanisms underlying SSD. We take an integrative approach to understand the relationship between developmental trajectories, metabolism, and environmental conditions resulting in extreme female-biased SSD in the crab spider Mecaphesa celer (Thomisidae). We tested for sexual differences in growth trajectories, as well as in the energetics of growth, hypothesizing that female M. celer have lower metabolic rates than males or higher energy assimilation. We also hypothesized that the environment in which spiderlings develop influences the degree of SSD of a population. We tracked growth and resting metabolic rates of female and male spiderlings throughout their ontogeny and quantified the adult size of individuals raised in a combination of two diet and two temperature treatments. We show that M. celer's SSD results from differences in the shape of female and male growth trajectories. While female and male resting metabolic rates did not differ, diet, temperature, and their interaction influenced body size through an interactive effect with sex, with females being more sensitive to the environment than males. We demonstrate that the shape of the growth curve is an important but often overlooked determinant of SSD and that females may achieve larger sizes through a combination of high food ingestion and low activity levels. Our results highlight the need for new models of SSD based on ontogeny, ecology, and behavior.

Trends in embryonic and ontogenetic growth metabolisms in nonavian dinosaurs and extant birds, mammals, and crocodylians with implications for dinosaur egg incubation

The embryonic metabolism of the saurischian dinosaur Troodon formosus and the ornithischian dinosaurs Protoceratops andrewsi and Hypacrosaurus stebingeri have been determined by using a mass growth model based on conservation of energy and found to be very similar. Embryonic and ontogenetic growth metabolisms are also evaluated for extant altricial birds, precocial birds, mammals, and crocodylians to examine for trends in the different groups of animals and to provide a context for interpreting our results for nonavian dinosaurs. This analysis reveals that the embryonic metabolisms of these nonavian dinosaurs were closer to the range observed in extant crocodylians than extant birds. The embryonic metabolisms of nonavian dinosaurs were in the range observed for extant mammals of similar masses. The measured embryonic metabolic rates for these three nonavian dinosaurs are then used to calculate the incubation times for eggs of 22 nonavian dinosaurs from both Saurischia and Ornithischia. The calculated incubation times vary from about 50 days for Archaeopteryx lithographica to about 150 days for Alamosaurus sanjuanensis.

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.

Energy Flow in Growth and Production

Growth involves two flows of energy: the chemical energy in the monomers used to construct the macromolecules that comprise tissue (proteins, nucleic acids, lipid membranes), and the metabolic energy used to build those macromolecules. The metabolic costs of synthesising the macromolecules necessary to build tissue are well defined, and we have a robust estimate of the overall cost of growth for an individual ectotherm. At the population level the cost of production appears to be much greater for endotherms than ectotherms, the reasons for which are not fully understood. These uncertainties are important to resolve if we wish to accurately model the flow of energy through populations or ecosystems because simply scaling up from individual energetics may produce misleading results.

Information use during movement regulates how fragmentation and loss of habitat affect body size

An individual's body size is central to its behaviour and physiology, and tightly linked to its movement ability. The spatial arrangement of resources and a consumer's capacity to locate them are therefore expected to exert strong selection on consumer body size. We investigated the evolutionary impact of both the fragmentation and loss of habitat on consumer body size and its feedback effects on resource distribution, under varying levels of information used during habitat choice. We developed a mechanistic, individual-based, spatially explicit model, including several allometric rules for key consumer traits. Our model reveals that as resources become more fragmented and scarce, informed habitat choice selects for larger body sizes while random habitat choice promotes small sizes. Information use may thus be an overlooked explanation for the observed variation in body size responses to habitat fragmentation. Moreover, we find that resources can accumulate and aggregate if information about resource abundance is incomplete. Informed movement results in stable resource-consumer dynamics and controlled resources across space. However, habitat loss and fragmentation destabilize local dynamics and disturb resource suppression by the consumer. Considering information use during movement is thus critical to understand the eco-evolutionary dynamics underlying the functioning and structuring of consumer communities.

The energetics of fish growth and how it constrains food-web trophic structure

The allocation of metabolic energy to growth fundamentally influences all levels of biological organisation. Here we use a first-principles theoretical model to characterise the energetics of fish growth at distinct ontogenetic stages and in distinct thermal regimes. Empirically, we show that the mass scaling of growth rates follows that of metabolic rate, and is somewhat steeper at earlier ontogenetic stages. We also demonstrate that the cost of growth, E_m , varies substantially among fishes, and that it may increase with temperature, trophic level and level of activity. Theoretically, we show that E_m is a primary determinant of the efficiency of energy transfer across trophic levels, and that energy is transferred more efficiently between trophic levels if the prey are young and sedentary. Overall, our study demonstrates the importance of characterising the energetics of individual growth in order to understand constraints on the structure of food webs and ecosystems.

Dynamics of starvation and recovery predict extinction risk and both Damuth's law and Cope's rule

The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of their constituent individuals. Of particular importance is the interplay between reproduction and the dynamics of starvation and recovery. To elucidate this interplay, here we introduce a nutritional state-structured model that incorporates two classes of consumers: nutritionally replete, reproducing consumers, and undernourished, nonreproducing consumers. We obtain strong constraints on starvation and recovery rates by deriving allometric scaling relationships and find that population dynamics are typically driven to a steady state. Moreover, these rates fall within a "refuge" in parameter space, where the probability of population extinction is minimized. We also show that our model provides a natural framework to predict steady state population abundances known as Damuth's law, and maximum mammalian body size. By determining the relative stability of an otherwise homogeneous population to a competing population with altered percent body fat, this framework provides a principled mechanism for a selective driver of Cope's rule.

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

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

Human bipedalism and body-mass index

Body-mass index, abbreviated as BMI and given by M/H² with the mass M and the height H, has been widely used as a useful proxy to measure a general health status of a human individual. We generalise BMI in the form of M/H^p and pursue to answer the question of the value of p for populations of animal species including human. We compare values of p for several different datasets for human populations with the ones obtained for other animal populations of fish, whales, and land mammals. All animal populations but humans analyzed in our work are shown to have p ≈ 3 unanimously. In contrast, human populations are different: As young infants grow to become toddlers and keep growing, the sudden change of p is observed at about one year after birth. Infants younger than one year old exhibit significantly larger value of p than two, while children between one and five years old show p ≈ 2, sharply different from other animal species. The observation implies the importance of the upright posture of human individuals. We also propose a simple mechanical model for a human body and suggest that standing and walking upright should put a clear division between bipedal human (p ≈ 2) and other animals (p ≈ 3).

The evolution of bacterial cell size: the internal diffusion-constraint hypothesis

Size is one of the most important biological traits influencing organismal ecology and evolution. However, we know little about the drivers of body size evolution in unicellulars. A long-term evolution experiment (Lenski's LTEE) in which Escherichia coli adapts to a simple glucose medium has shown that not only the growth rate and the fitness of the bacterium increase over time but also its cell size. This increase in size contradicts prominent 'external diffusion' theory (EDC) predicting that cell size should have evolved toward smaller cells. Among several scenarios, we propose and test an alternative 'internal diffusion-constraint' (IDC) hypothesis for cell size evolution. A change in cell volume affects metabolite concentrations in the cytoplasm. The IDC states that a higher metabolism can be achieved by a reduction in the molecular traffic time inside of the cell, by increasing its volume. To test this hypothesis, we studied a population from the LTEE. We show that bigger cells with greater growth and CO₂ production rates and lower mass-to-volume ratio were selected over time in the LTEE. These results are consistent with the IDC hypothesis. This novel hypothesis offers a promising approach for understanding the evolutionary constraints on cell size.

Embryonic metabolism of the ornithischian dinosaurs Protoceratops andrewsi and Hypacrosaurus stebingeri and implications for calculations of dinosaur egg incubation times

The embryonic metabolisms of the ornithischian dinosaurs Protoceratops andrewsi and Hypacrosaurus stebingeri have been determined and are in the range observed in extant reptiles. The average value of the measured embryonic metabolic rates for P. andrewsi and H. stebingeri are then used to calculate the incubation times for 21 dinosaurs from both Sauischia and Ornithischia using a mass growth model based on conservation of energy. The calculated incubation times vary from about 70 days for Archaeopteryx lithographica to about 180 days for Alamosaurus sanjuanensis. Such long incubation times seem unlikely, particularly for the sauropods and large theropods. Incubation times are also predicted with the assumption that the saurischian dinosaurs had embryonic metabolisms in the range observed in extant birds.

A general model for metabolic scaling in self-similar asymmetric networks

How a particular attribute of an organism changes or scales with its body size is known as an allometry. Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. Perhaps the most central biological allometry is how metabolic rate scales with body size. A core assumption of the WBE model is that networks are symmetric with respect to their geometric properties. That is, any two given branches within the same generation in the network are assumed to have identical lengths and radii. However, biological networks are rarely if ever symmetric. An open question is: Does incorporating asymmetric branching change or influence the predictions of the WBE model? We derive a general network model that relaxes the symmetric assumption and define two classes of asymmetrically bifurcating networks. We show that asymmetric branching can be incorporated into the WBE model. This asymmetric version of the WBE model results in several theoretical predictions for the structure, physiology, and metabolism of organisms, specifically in the case for the cardiovascular system. We show how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber’s Law can still be attained within many asymmetric networks.

We present a model for incorporating geometrically asymmetric branching into biological resource distribution networks. Our work shows how space-filling and fluid flow principles constrain allowed branching morphologies within the context of our model. Simultaneously, we demonstrate that there is a wide range of asymmetrically branching network architectures that still give rise to 3/4 metabolic scaling exponents.

A model for brain life history evolution

Complex cognition and relatively large brains are distributed across various taxa, and many primarily verbal hypotheses exist to explain such diversity. Yet, mathematical approaches formalizing verbal hypotheses would help deepen the understanding of brain and cognition evolution. With this aim, we combine elements of life history and metabolic theories to formulate a metabolically explicit mathematical model for brain life history evolution. We assume that some of the brain's energetic expense is due to production (learning) and maintenance (memory) of energy-extraction skills (or cognitive abilities, knowledge, information, etc.). We also assume that individuals use such skills to extract energy from the environment, and can allocate this energy to grow and maintain the body, including brain and reproductive tissues. The model can be used to ask what fraction of growth energy should be allocated at each age, given natural selection, to growing brain and other tissues under various biological settings. We apply the model to find uninvadable allocation strategies under a baseline setting ("me vs nature"), namely when energy-extraction challenges are environmentally determined and are overcome individually but possibly with maternal help, and use modern-human data to estimate model's parameter values. The resulting uninvadable strategies yield predictions for brain and body mass throughout ontogeny and for the ages at maturity, adulthood, and brain growth arrest. We find that: (1) a me-vs-nature setting is enough to generate adult brain and body mass of ancient human scale and a sequence of childhood, adolescence, and adulthood stages; (2) large brains are favored by intermediately challenging environments, moderately effective skills, and metabolically expensive memory; and (3) adult skill is proportional to brain mass when metabolic costs of memory saturate the brain metabolic rate allocated to skills.

Does the membrane pacemaker theory of metabolism explain the size dependence of metabolic rate in marine mussels?

According to the Membrane Pacemaker Theory of metabolism (MPT) allometric scaling of metabolic rate in animals is determined by the composition of cellular and mitochondrial membranes that changes with body size in a predictable manner. MPT has been elaborated from interspecific comparisons in mammals. It projects that the degree of unsaturation of membrane phospholipids decreases in larger organisms, thereby lowering ion permeability of the membranes and making cellular and thus whole animal metabolism more efficient. Here we tested the applicability of the MPT to a marine ectotherm, the mussel Mytilus edulis at the intraspecific level. We determined effects of body mass on whole organism, tissue and cellular oxygen consumption rates, on heart rate, metabolic enzyme activities and on the lipid composition of membranes. In line with allometric patterns the organismal functions and processes such as heart rate, whole animal respiration rate and phospholipid contents showed a mass-dependent decline. However, the allometry of tissue and cellular respiration and activity of metabolic enzymes was poor; fatty acid unsaturation of membrane phospholipids of gill tissue was independent of animal size. It is thus conceivable that most of the metabolic allometry observed at the organismal level is determined by systemic functions. These whole organism patterns may be supported by energy savings associated with growing cell size but not by structural changes in membranes. Overall, the set of processes contributing to metabolic allometry in ectotherms may differ from that operative in mammals and birds, with a reduced involvement of the mechanisms proposed by the MPT.

Incubation times of dinosaur eggs via embryonic metabolism

The incubation times for the eggs of 21 dinosaurs are determined from an estimate of their embyronic metabolic rate and the mass of the hatchlings via a mass growth model based on conservation of energy. Embryos in extant birds and crocodiles are studied in order to determine the best model for embryonic metabolism and growth. These results are used to develop a theoretical model that predicts the incubation times of an egg. This model is applied to dinosaur eggs and provides a unique window into dinosaur reproduction. The dinosaurs studied come from both Saurischia and Ornithischia. The incubation times vary from about 28 days for Archaeopteryx lithographica to about 76 days for Alamosaurus sanjuanensis.

Cellular oxidative damage is more sensitive to biosynthetic rate than to metabolic rate: A test of the theoretical model on hornworms (Manduca sexta larvae)

We develop a theoretical model from an energetic viewpoint for unraveling the entangled effects of metabolic and biosynthetic rates on oxidative cellular damage accumulation during animal's growth, and test the model by experiments in hornworms. The theoretical consideration suggests that most of the cellular damages caused by the oxidative metabolism can be repaired by the efficient maintenance mechanisms, if the energy required by repair is unlimited. However, during growth a considerable amount of energy is allocated to the biosynthesis, which entails tradeoffs with the requirements of repair. Thus, the model predicts that cellular damage is more influenced by the biosynthetic rate than the metabolic rate. To test the prediction, we induced broad variations in metabolic and biosynthetic rates in hornworms, and assayed the lipid peroxidation and protein carbonyl. We found that the increase in the cellular damage was mainly caused by the increase in biosynthetic rate, and the variations in metabolic rate had negligible effect. The oxidative stress hypothesis of aging suggests that high metabolism leads to high cellular damage and short lifespan. However, some empirical studies showed that varying biosynthetic rate, rather than metabolic rate, changes animal's lifespan. The conflicts between the empirical evidence and the hypothesis are reconciled by this study.

Constrained growth flips the direction of optimal phenological responses among annual plants

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.

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

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

Fundamental insights into ontogenetic growth from theory and fish

The fundamental features of growth may be universal, because growth trajectories of most animals are very similar, but a unified mechanistic theory of growth remains elusive. Still needed is a synthetic explanation for how and why growth rates vary as body size changes, both within individuals over their ontogeny and between populations and species over their evolution. Here, we use Bertalanffy growth equations to characterize growth of ray-finned fishes in terms of two parameters, the growth rate coefficient, K, and final body mass, m∞. We derive two alternative empirically testable hypotheses and test them by analyzing data from FishBase. Across 576 species, which vary in size at maturity by almost nine orders of magnitude, K scaled as [Formula: see text]. This supports our first hypothesis that growth rate scales as [Formula: see text] as predicted by metabolic scaling theory; it implies that species that grow to larger mature sizes grow faster as juveniles. Within fish species, however, K scaled as [Formula: see text]. This supports our second hypothesis, which predicts that growth rate scales as [Formula: see text] when all juveniles grow at the same rate. The unexpected disparity between across- and within-species scaling challenges existing theoretical interpretations. We suggest that the similar ontogenetic programs of closely related populations constrain growth to [Formula: see text] scaling, but as species diverge over evolutionary time they evolve the near-optimal [Formula: see text] scaling predicted by metabolic scaling theory. Our findings have important practical implications because fish supply essential protein in human diets, and sustainable yields from wild harvests and aquaculture depend on growth rates.

Metabolism of dinosaurs as determined from their growth

A model based on cellular properties is used to analyze the mass growth curves of 20 dinosaurs. This analysis yields the first measurement of the average cellular metabolism of dinosaurs. The organismal metabolism is also determined. The cellular metabolism of dinosaurs is found to decrease with mass at a slower rate than is observed in extant animals. The organismal metabolism increases with the mass of the dinosaur. These results come from both the Saurischia and Ornithischia branches of Dinosauria, suggesting that the observed metabolic features were common to all dinosaurs. The results from dinosaurs are compared to data from extant placental and marsupial mammals, a monotreme, and altricial and precocial birds, reptiles, and fish. Dinosaurs had cellular and organismal metabolisms in the range observed in extant mesotherms.