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 (b_R = scaling exponent approx. 1) to negative allometry (b_R < 1), or the reverse, are associated with significant changes in body shape (indexed by b_L = the scaling exponent of the relationship between body mass and body length). The observed inverse correlations between b_R and b_L 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 (b_A) further show that ontogenetic shifts in b_R and b_A are positively correlated. These results support new metabolic scaling theory based on SA influences that may be applied to ontogenetic shifts in b_R shown by many kinds of animals and plants.     

Ontogenetic and interspecific scaling of consumption in insects

The uptake of resources from the environment is a basic feature of all life. Consumption rate has been found to scale with body size with an exponent close to unity across diverse organisms. However, past analyses have ignored the important distinction between ontogenetic and interspecific size comparisons. Using principles of dynamic energy budget theory, we present a mechanistic model for the body mass scaling of consumption, which separates interspecific size effects from ontogenetic size effects. Our model predicts uptake to scale with surface‐area (mass^2/3) during ontogenetic growth but more quickly (between mass^3/4 and mass¹) for interspecific comparisons. Available data for 41 insect species on consumption and assimilation during ontogeny provides strong empirical support for our theoretical predictions. Specifically, consumption rate scaled interspecifically with an exponent close to unity (0.89) but during ontogenetic growth scaled more slowly with an exponent of 0.70. Assimilation rate (consumption minus defecation) through ontogeny scaled more slowly than consumption due to a decrease in assimilation efficiency as insects grow. Our results highlight how body size imposes different constraints on metabolism depending on whether the size comparison is ontogenetic or inter‐specific. Synthesis One of the most robust patterns in biology is the effect of body size on metabolism – a relationship that underlies the rapidly emerging field of metabolic ecology. However, the precise energetic constraints imposed by body size have been notoriously difficult to entangle. Here we show that the constraints imposed on metabolism by body size are different depending on whether the size comparison is ontogenetic or interspecific. Using a single unifying theory of animal metabolism and a newly compiled data set on insect consumption and assimilation rates, we show that interspecific comparisons generally lead to the estimation of higher scaling exponents compared with ontogenetic comparisons. Our results help to explain large variation in estimated metabolic scaling exponents and will encourage future studies in metabolic ecology to make the important distinction between ontogenetic and evolutionary size changes.     

Unifying elemental stoichiometry and metabolic theory in predicting species abundances

While metabolic theory predicts variance in population density within communities depending on population average body masses, the ecological stoichiometry concept relates density variation across communities to varying resource stoichiometry. Using a data set including biomass densities of 4959 populations of soil invertebrates across 48 forest sites we combined these two frameworks. We analyzed how the scaling of biomass densities with population‐averaged body masses systematically interacts with stoichiometric variables. Simplified analyses employing either only body masses or only resource stoichiometry are highly context sensitive and yield variable and often misleading results. Our findings provide strong evidence that analyses of ecological state variables should integrate allometric and stoichiometric variables to explain deviations from predicted allometric scaling and avoid erroneous conclusions. In consequence, our study provides an important step towards unifying two prominent ecological theories, metabolic theory and ecological stoichiometry.     

An empirical assessment of tree branching networks and implications for plant allometric scaling models

Several theories predict whole‐tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self‐similar within trees. However, differences among scaling exponents calculated at node‐ and whole‐tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

Metabolic scaling in modular animals

Metabolic scaling is the relationship between organismal metabolic rate and body mass. Understanding the patterns and causes of metabolic scaling provides a powerful foundation for predicting biological processes at the level of individuals, populations, communities, and ecosystems. Despite intense interest in, and debate on, the mechanistic basis of metabolic scaling, relatively little attention has been paid to metabolic scaling in clonal animals with modular construction, such as colonial cnidarians, bryozoans, and colonial ascidians. Unlike unitary animals, modular animals are structural individuals subdivided into repeated morphological units, or modules, each able to acquire, process, and share resources. A modular design allows flexibility in organism size and shape with consequences for metabolic scaling. Furthermore, with careful consideration of the biology of modular animals, the size and shape of individual colonies can be experimentally manipulated to test competing theories pertaining to metabolic scaling. Here, we review metabolic scaling in modular animals and find that a wide range of scaling exponents, rather than a single value, has been reported for a variety of modular animals. We identify factors influencing variation in intraspecific scaling in this group that relate to the general observation that not all modules within a colony are identical. We highlight current gaps in our understanding of metabolic scaling in modular animals, and suggest future research directions, such as manipulating metabolic states and comparisons among species that differ in extent of module integration.     

Linking phytoplankton community metabolism to the individual size distribution

Quantifying variation in ecosystem metabolism is critical to predicting the impacts of environmental change on the carbon cycle. We used a metabolic scaling framework to investigate how body size and temperature influence phytoplankton community metabolism. We tested this framework using phytoplankton sampled from an outdoor mesocosm experiment, where communities had been either experimentally warmed (+ 4 °C) for 10 years or left at ambient temperature. Warmed and ambient phytoplankton communities differed substantially in their taxonomic composition and size structure. Despite this, the response of primary production and community respiration to long‐ and short‐term warming could be estimated using a model that accounted for the size‐ and temperature dependence of individual metabolism, and the community abundance‐body size distribution. This work demonstrates that the key metabolic fluxes that determine the carbon balance of planktonic ecosystems can be approximated using metabolic scaling theory, with knowledge of the individual size distribution and environmental temperature.     

Models projecting the fate of fish populations under climate change need to be based on valid physiological mechanisms

Some recent modelling papers projecting smaller fish sizes and catches in a warmer future are based on erroneous assumptions regarding (i) the scaling of gills with body mass and (ii) the energetic cost of ‘maintenance’. Assumption (i) posits that insurmountable geometric constraints prevent respiratory surface areas from growing as fast as body volume. It is argued that these constraints explain allometric scaling of energy metabolism, whereby larger fishes have relatively lower mass‐specific metabolic rates. Assumption (ii) concludes that when fishes reach a certain size, basal oxygen demands will not be met, because of assumption (i). We here demonstrate unequivocally, by applying accepted physiological principles with reference to the existing literature, that these assumptions are not valid. Gills are folded surfaces, where the scaling of surface area to volume is not constrained by spherical geometry. The gill surface area can, in fact, increase linearly in proportion to gill volume and body mass. We cite the large body of evidence demonstrating that respiratory surface areas in fishes reflect metabolic needs, not vice versa, which explains the large interspecific variation in scaling of gill surface areas. Finally, we point out that future studies basing their predictions on models should incorporate factors for scaling of metabolic rate and for temperature effects on metabolism, which agree with measured values, and should account for interspecific variation in scaling and temperature effects. It is possible that some fishes will become smaller in the future, but to make reliable predictions the underlying mechanisms need to be identified and sought elsewhere than in geometric constraints on gill surface area. Furthermore, to ensure that useful information is conveyed to the public and policymakers about the possible effects of climate change, it is necessary to improve communication and congruity between fish physiologists and fisheries scientists.     

Effetcs of ontogenetic scaling on resource exploitation and cohort size distributions

Variation in growth rates among individuals leading to the formation of broad size distributions is commonly observed in animal cohorts. Here we use laboratory derived size–scaling relationships to identify mechanisms driving changes in size distribution patterns within cohorts during early ontogeny. We introduced young‐of‐the‐year perch Perca fluviatilis cohorts with different variation in body size distributions in pond enclosures. We kept the exploitative competitive environment constant by adjusting the number of introduced fish such that metabolic requirements were constant between different treatments. Based on modelling results we theoretically derived relative growth rates of differently sized fish when only taken exploitative competitive interactions into account. In agreement with predictions we found that initial variation in body size was negatively correlated with subsequent changes in body size variation in the pond experiment. Corresponding results were obtained in a field study covering 13 studied young‐of‐the‐year perch cohorts in a small lake. Besides having a lower maximum growth capacity, initially large fish also suffered more from resource limitation in our experiment. The results suggest that exploitation competition is a major factor behind growth patterns in young fish cohorts, generally leading to size convergence. To explain the commonly observed pattern of size divergence in animal cohorts, including fish, we suggest that differential timing of diet shifts or mechanisms not related to exploitative interactions must be taken into account. For diet shifts to lead to size divergence we suggest that individuals with an initial size advantage need access to an exclusive prey which has a high growth potential. This, in turn, allows initially larger individuals to surf on a wave of growing prey while individuals only capable to feed on a depressed initial resource experience low growth rates.     

Foraging theory predicts predator-prey energy fluxes

1. In natural communities, populations are linked by feeding interactions that make up complex food webs. The stability of these complex networks is critically dependent on the distribution of energy fluxes across these feeding links. 2. In laboratory experiments with predatory beetles and spiders, we studied the allometric scaling (body-mass dependence) of metabolism and per capita consumption at the level of predator individuals and per link energy fluxes at the level of feeding links. 3. Despite clear power-law scaling of the metabolic and per capita consumption rates with predator body mass, the per link predation rates on individual prey followed hump-shaped relationships with the predator-prey body mass ratios. These results contrast with the current metabolic paradigm, and find better support in foraging theory. 4. This suggests that per link energy fluxes from prey populations to predator individuals peak at intermediate body mass ratios, and total energy fluxes from prey to predator populations decrease monotonically with predator and prey mass. Surprisingly, contrary to predictions of metabolic models, this suggests that for any prey species, the per link and total energy fluxes to its largest predators are smaller than those to predators of intermediate body size. 5. An integration of metabolic and foraging theory may enable a quantitative and predictive understanding of energy flux distributions in natural food webs.     

Effects of body size and temperature on population growth

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.     

A general model for ontogenetic growth under food restriction

Food restriction (FR) retards animals' growth. Understanding the underlying mechanisms of this phenomenon is important to conceptual problems in life-history theory, as well as to applied problems in animal husbandry and biomedicine. Despite a considerable amount of empirical data published since the 1930s, there is no relevant general theoretical framework that predicts how animals vary their energy budgets and life-history traits under FR. In this paper, we develop such a general quantitative model based on fundamental principles of metabolic energy allocation during ontogeny. This model predicts growth curves under varying conditions of FR, such as the compensatory growth, different age at which FR begins, its degree and its duration. Our model gives a quantitative explanation for the counterintuitive phenomenon that under FR, lower body temperature and lower metabolism lead to faster growth and larger adult size. This model also predicts that the animals experiencing FR reach the same fraction of their adult mass at the same age as their ad libitum counterparts. All predictions are well supported by empirical data from mammals and birds of varying body size, under different conditions of FR.     

Little left in the tank: metabolic scaling in marine teleosts and its implications for aerobic scope

Fish larvae are the world's smallest vertebrates, and their high rates of mortality may be partially owing to a very limited aerobic scope. Unfortunately, however, no complete empirical dataset exists on the relationship between minimal and maximal metabolism (and thus aerobic scope) for any fish species throughout ontogeny, and thus such an association is hard to delineate. We measured standard and maximal metabolism in three marine fish species over their entire life history, and show that while aerobic scope depends greatly on body size and developmental trajectory, it is extremely small during the early life stages (factorial aerobic scope < or =1.5). Our findings strongly suggest that limited scope for aerobic activity early in life is likely to constrain physiological function and ultimately impact behaviour and possibly survival. Furthermore, our results have important implications for ecological models that incorporate metabolic scaling, and provide additional evidence against the existence of 'universal' scaling exponents.     

Size‐abundance rules? Evolution changes scaling relationships between size,metabolism and demography

Body size often strongly covaries with demography across species. Metabolism has long been invoked as the driver of these patterns, but tests of causal links between size, metabolism and demography within a species are exceedingly rare. We used 400 generations of artificial selection to evolve a 2427% size difference in the microalga Dunaliella tertiolecta. We repeatedly measured size, energy fluxes and demography across the evolved lineages. Then, we used standard metabolic theory to generate predictions of how size and demography should covary based on the scaling of energy fluxes that we measured. The size dependency of energy remained relatively consistent in time, but metabolic theory failed to predict demographic rates, which varied unpredictably in strength and even sign across generations. Classic theory holds that size affects demography via metabolism – our results suggest that both metabolism and size act separately to drive demography and that among‐species patterns may not predict within‐species processes.     

Ontogenetic scaling of fish metabolism in the mouse-to-elephant mass magnitude range

Intraspecific or ontogenetic analyses of mass-metabolism relationships do not often conform to the same allometric correlations as those seen in interspecific analyses. A commonly cited reason for this discrepancy is that ontogenetic studies examine smaller mass ranges than interspecific studies, and are therefore not statistically comparable. In this study the metabolic rate of yellowtail kingfish was measured from 0.6 mg-2.2 kg, a mass range comparable to that between a mouse and an elephant. Linear regression of the log transformed data resulted in a scaling exponent of 0.90 and high correlation coefficient. Statistical and information theory comparisons of three other models showed that a segmented linear regression and curvilinear quadratic function were an improvement over a simple linear regression. This confirmed previous observations that the metabolic scaling exponent of fish changes during ontogeny. Ammonia excretion rates were also measured and scaled linearly with an exponent of 0.87. The data showed that the metabolism of yellowtail kingfish during ontogeny did not scale with the commonly cited 2/3 or 3/4 mass exponent. This demonstrates that differences between interspecific and ontogenetic allometries are not necessarily statistical artefacts.     

Effects of body size on biochemical characteristics of trabecular cardiac muscle and plasma of rainbow trout (Oncorhynchus mykiss)

The objective of this study was to characterize biochemical indices of oxidative metabolism in trabecular cardiac muscle of female rainbow trout over a 200-fold size range. We also examined scaling effects on plasma concentrations of protein, albumin, and non-esterified fatty acids (NEFA). Animals were sampled from four size categories (<20 g, 100–200 g, 300–400 g and >2 kg). Ventricle mass relative to body mass was size-dependent, with the smallest trout having smaller hearts. Total protein in cardiac tissue was 20% higher in animals weighing over 300 g compared to fish less than 200 g. Plasma albumin and protein were increased 50–70% in trout over 100 g compared to fish smaller than 20 g. NEFA in plasma were similar for all animals. Activities of carnitine palmitoyltransferase and cytochrome oxidase were elevated 53% and 38%, respectively, in trabecular cardiac muscle of the largest trout compared to the smallest animals. Citrate synthase activity was independent of heart size, suggesting that the increase in oxidative capacity was not due to an increase in mitochondrial density. The increased capacity to bind and transport fatty acids in blood and the higher oxidative capacity of cardiac muscle may reflect a metabolic adaptation for increased oxidation of fatty acids and ventricular performance in larger female trout. These findings are not consistent with the scaling paradigm of oxidative metabolism and may reflect changes in ventricular architecture with ontogeny.     

Pollinator size and its consequences: Robust estimates of body size in pollinating insects

Body size is an integral functional trait that underlies pollination‐related ecological processes, yet it is often impractical to measure directly. Allometric scaling laws have been used to overcome this problem. However, most existing models rely upon small sample sizes, geographically restricted sampling and have limited applicability for non‐bee taxa. Allometric models that consider biogeography, phylogenetic relatedness, and intraspecific variation are urgently required to ensure greater accuracy. We measured body size as dry weight and intertegular distance (ITD) of 391 bee species (4,035 specimens) and 103 hoverfly species (399 specimens) across four biogeographic regions: Australia, Europe, North America, and South America. We updated existing models within a Bayesian mixed‐model framework to test the power of ITD to predict interspecific variation in pollinator dry weight in interaction with different co‐variates: phylogeny or taxonomy, sexual dimorphism, and biogeographic region. In addition, we used ordinary least squares regression to assess intraspecific dry weight ~ ITD relationships for ten bees and five hoverfly species. Including co‐variates led to more robust interspecific body size predictions for both bees and hoverflies relative to models with the ITD alone. In contrast, at the intraspecific level, our results demonstrate that the ITD is an inconsistent predictor of body size for bees and hoverflies. The use of allometric scaling laws to estimate body size is more suitable for interspecific comparative analyses than assessing intraspecific variation. Collectively, these models form the basis of the dynamic R package, “pollimetry,” which provides a comprehensive resource for allometric pollination research worldwide.     

Allometric growth, life-history invariants and population energetics

Population and community level processes must be at least partially determined by variation in the body sizes of constituent individuals, implying quantitative scaling relations can be extended to account for variation in those processes. Here we integrate allometric growth and life‐history invariant theories, and use this approach to develop theory describing the energetics of stationary populations. Our predictions approximate, with no free parameters, the scaling of production/biomass and assimilation/biomass ratios in mammalian populations and work partially for fish populations. This approach appears to be a promising direction and suggests the need for further development of the growth and life‐history models, and extensions of those theories.     

Power and metabolic scope of bird flight: a phylogenetic analysis of biomechanical predictions

For flying animals aerodynamic theory predicts that mechanical power required to fly scales as P proportional, variant m (7/6) in a series of isometric birds, and that the flight metabolic scope (P/BMR; BMR is basal metabolic rate) scales as P (scope) proportional, variant m (5/12). I tested these predictions by using phylogenetic independent contrasts from a set of 20 bird species, where flight metabolic rate was measured during laboratory conditions (mainly in wind tunnels). The body mass scaling exponent for P was 0.90, significantly lower than the predicted 7/6. This is partially due to the fact that real birds show an allometric scaling of wing span, which reduces flight cost. P (scope) was estimated using direct measurements of BMR in combination with allometric equations. The body mass scaling of P (scope) ranged between 0.31 and 0.51 for three data sets, respectively, and none differed significantly from the prediction of 5/12. Body mass scaling exponents of P (scope) differed significantly from 0 in all cases, and so P (scope) showed a positive body mass scaling in birds in accordance with the prediction.