The intraspecific scaling of metabolic rate with body mass in fishes depends on lifestyle and temperature

Climate warming causes life-history evolution in a model for Atlantic cod (Gadus morhua)

Climate change influences the marine environment, with ocean warming being the foremost driving factor governing changes in the physiology and ecology of fish. At the individual level, increasing temperature influences bioenergetics and numerous physiological and life-history processes, which have consequences for the population level and beyond. We provide a state-dependent energy allocation model that predicts temperature-induced adaptations for life histories and behaviour for the North-East Arctic stock (NEA) of Atlantic cod (Gadus morhua) in response to climate warming. The key constraint is temperature-dependent respiratory physiology, and the model includes a number of trade-offs that reflect key physiological and ecological processes. Dynamic programming is used to find an evolutionarily optimal strategy of foraging and energy allocation that maximizes expected lifetime reproductive output given constraints from physiology and ecology. The optimal strategy is then simulated in a population, where survival, foraging behaviour, growth, maturation and reproduction emerge. Using current forcing, the model reproduces patterns of growth, size-at-age, maturation, gonad production and natural mortality for NEA cod. The predicted climate responses are positive for this stock; under a 2°C warming, the model predicted increased growth rates and a larger asymptotic size. Maturation age was unaffected, but gonad weight was predicted to more than double. Predictions for a wider range of temperatures, from 2 to 7°C, show that temperature responses were gradual; fish were predicted to grow faster and increase reproductive investment at higher temperatures. An emergent pattern of higher risk acceptance and increased foraging behaviour was also predicted. Our results provide important insight into the effects of climate warming on NEA cod by revealing the underlying mechanisms and drivers of change. We show how temperature-induced adaptations of behaviour and several life-history traits are not only mediated by physiology but also by trade-offs with survival, which has consequences for conservation physiology.

Body shape shifting during growth permits tests that distinguish between competing geometric theories of metabolic scaling

Metabolism fuels all of life's activities, from biochemical reactions to ecological interactions. According to two intensely debated theories, body size affects metabolism via geometrical influences on the transport of resources and wastes. However, these theories differ crucially in whether the size dependence of metabolism is derived from material transport across external surfaces, or through internal resource-transport networks. We show that when body shape changes during growth, these models make opposing predictions. These models are tested using pelagic invertebrates, because these animals exhibit highly variable intraspecific scaling relationships for metabolic rate and body shape. Metabolic scaling slopes of diverse integument-breathing species were significantly positively correlated with degree of body flattening or elongation during ontogeny, as expected from surface area theory, but contradicting the negative correlations predicted by resource-transport network models. This finding explains strong deviations from predictions of widely adopted theory, and underpins a new explanation for mass-invariant metabolic scaling during ontogeny in animals and plants.

Growth trajectory influences temperature preference in fish through an effect on metabolic rate

Most animals experience temperature variations as they move through the environment. For ectotherms, in particular, temperature has a strong influence on habitat choice. While well studied at the species level, less is known about factors affecting the preferred temperature of individuals; especially lacking is information on how physiological traits are linked to thermal preference and whether such relationships are affected by factors such feeding history and growth trajectory.

This study examined these issues in the common minnow Phoxinus phoxinus, to determine the extent to which feeding history, standard metabolic rate (SMR) and aerobic scope (AS), interact to affect temperature preference.

Individuals were either: 1) food deprived (FD) for 21 days, then fed ad libitum for the next 74 days; or 2) fed ad libitum throughout the entire period. All animals were then allowed to select preferred temperatures using a shuttle-box, and then measured for SMR and AS at 10 °C, estimated by rates of oxygen uptake. Activity within the shuttle-box under a constant temperature regime was also measured.

In both FD and control fish, SMR was negatively correlated with preferred temperature. The SMR of the FD fish was increased compared with the controls, probably due to the effects of compensatory growth, and so these growth-compensated fish preferred temperatures that were on average 2·85 °C cooler than controls fed a maintenance ration throughout the study. Fish experiencing compensatory growth also displayed a large reduction in activity. In growth-compensated fish and controls, activity measured at 10 °C was positively correlated with preferred temperature.

Individual fish prefer temperatures that vary predictably with SMR and activity level, which are both plastic in response to feeding history and growth trajectories. Cooler temperatures probably allow individuals to reduce maintenance costs and divert more energy towards growth. A reduction in SMR at cooler temperatures, coupled with a decrease in spontaneous activity, could also allow individuals to increase surplus AS for coping with environmental stressors. In warming climates, however, aquatic ectotherms could experience frequent fluctuations in food supply with long-lasting effects on metabolic rate due to compensatory growth, while simultaneously having limited access to preferred cooler habitats.

Allometric relationship between body mass and aerobic metabolism in zebrafish Danio rerio

The relationship between body mass (M) and metabolic rate was investigated through the assessment of active (R(A)) and standard (R(S)) metabolic rate at different life stages in zebrafish Danio rerio (5 day-old larvae, 2 month-old juveniles and 6 month-old adults). Scaling exponents and constants were assessed for standard (R(S)  = 0·273M(0·965) in mgO(2)  g(-1)  h(-1)) and active metabolic rate (R(A)  = 0·799M(0·926) in mgO(2)  g(-1)  h(-1)). These data provide the basis for further experiments regarding the effects of environmental factors on aerobic metabolism throughout the life cycle of this species.

Intraspecific mass scaling of metabolic rates in grass carp (Ctenopharyngodon idellus)

We assessed the intraspecific mass scaling of standard metabolic rate (SMR), maximum metabolic rate (MMR), excess post-exercise oxygen consumption (EPOC), and erythrocyte size in grass carp (Ctenopharyngodon idellus), with body masses ranging from 4.0 to 459 g. SMR and MMR scaled with body mass with similar exponents, but neither exponent matched the expected value of 0.75 or 1, respectively. Erythrocyte size scaled with body mass with a very low exponent (0.090), suggests that while both cell number and cell size contribute to the increase in body mass, cell size plays a smaller role. The similar slopes of MMR and SMR in grass carp suggest a constant factorial aerobic scope (FAS) as the body grows. SMR was negatively correlated with FAS, indicating a tradeoff between SMR and FAS. Smaller fish recovered faster from the exhaustive exercises, and the scaling exponent of EPOC was 1.075, suggesting a nearly isometric increase in anaerobic capacity. Our results provide support for the cell size model and suggest that variations of erythrocyte size may partly contribute to the intraspecific scaling of SMR. The scaling exponent of MMR was 0.863, suggesting that the metabolism of non-athletic fish species is less reliant on muscular energy expenditure, even during strenuous exercise.

Conservation physiology across scales: insights from the marine realm

As the field of conservation physiology develops and becomes increasingly integrated with ecology and conservation science, the fundamental concept of scale is being recognized as important, particularly for ensuring that physiological knowledge is contextualized in a manner most relevant to policy makers, conservation practitioners and stakeholders. Failure to consider the importance of scale in conservation physiology-both the challenges and the opportunities that it creates-will impede the ability of this discipline to generate the scientific understanding needed to contribute to meaningful conservation outcomes. Here, we have focused on five aspects of scale: biological, spatial, temporal, allometric and phylogenetic. We also considered the scale of policy and policy application relevant to those five types of scale as well as the merits of upscaling and downscaling to explore and address conservation problems. Although relevant to all systems (e.g. freshwater, terrestrial) we have used examples from the marine realm, with a particular emphasis on fishes, given the fact that there is existing discourse regarding scale and its relevance for marine conservation and management. Our synthesis revealed that all five aspects of scale are relevant to conservation physiology, with many aspects inherently linked. It is apparent that there are both opportunities and challenges afforded by working across scales but, to understand mechanisms underlying conservation problems, it is essential to consider scale of all sorts and to work across scales to the greatest extent possible. Moreover, given that the scales in biological processes will often not match policy and management scales, conservation physiology needs to show how it is relevant to aspects at different policy/management scales, change the scales at which policy/management intervention is applied or be prepared to be ignored.

Low global sensitivity of metabolic rate to temperature in calcified marine invertebrates

Metabolic rate is a key component of energy budgets that scales with body size and varies with large-scale environmental geographical patterns. Here we conduct an analysis of standard metabolic rates (SMR) of marine ectotherms across a 70° latitudinal gradient in both hemispheres that spanned collection temperatures of 0-30 °C. To account for latitudinal differences in the size and skeletal composition between species, SMR was mass normalized to that of a standard-sized (223 mg) ash-free dry mass individual. SMR was measured for 17 species of calcified invertebrates (bivalves, gastropods, urchins and brachiopods), using a single consistent methodology, including 11 species whose SMR was described for the first time. SMR of 15 out of 17 species had a mass-scaling exponent between 2/3 and 1, with no greater support for a 3/4 rather than a 2/3 scaling exponent. After accounting for taxonomy and variability in parameter estimates among species using variance-weighted linear mixed effects modelling, temperature sensitivity of SMR had an activation energy (Ea) of 0.16 for both Northern and Southern Hemisphere species which was lower than predicted under the metabolic theory of ecology (Ea 0.2-1.2 eV). Northern Hemisphere species, however, had a higher SMR at each habitat temperature, but a lower mass-scaling exponent relative to SMR. Evolutionary trade-offs that may be driving differences in metabolic rate (such as metabolic cold adaptation of Northern Hemisphere species) will have important impacts on species abilities to respond to changing environments.

Thermodynamics constrains allometric scaling of optimal development time in insects

Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the "hotter is better" hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes. The remaining unexplained variation in development time likely reflects additional ecological and evolutionary differences among insect species.

Intraspecific scaling of the resting and maximum metabolic rates of the crucian carp (Carassius auratus)

The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M (0.776) and MMR = 0.753M (0.785). The scaling exponents for RMR (b r) and MMR (b m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.

Relationship between fish size and metabolic rate in the oxyconforming inanga Galaxias maculatus reveals size-dependent strategies to withstand hypoxia

The relationship between metabolic rate and body size in animals is unlikely to be a constant but is instead shaped by a variety of intrinsic (i.e., physiological) and extrinsic (i.e., environmental) factors. This study examined the effect of environmental oxygen tension on oxygen consumption as a function of body mass in the galaxiid fish, inanga (Galaxias maculatus). As an oxyconformer, this fish lacks overt intrinsic regulation of oxygen consumption, eliminating this as a factor affecting the scaling relationship at different oxygen tensions. The relationship between oxygen consumption rate and body size was best described by a power function, with an exponent of 0.82, higher than the theoretical values of 0.66 or 0.75. The value of this exponent was significantly altered by environmental P(O2), first increasing as P(O2) decreased and then declining at the lowest P(O2) tested. These data suggest that the scaling exponent is species specific and regulated by extrinsic factors. Furthermore, the external P(O2) at which fish lost equilibrium was related to fish size, an effect explained by the scaling of anaerobic capacity with fish mass. Therefore, although bigger fish were forced to depress aerobic metabolism more rapidly than small fish when exposed to progressive hypoxia, they were better able to enact anaerobic metabolism, potentially extending their survival in hypoxia.

Metabolic divergence between sibling species of cichlids Pundamilia nyererei and Pundamilia pundamilia

This study compared Pundamilia nyererei and Pundamilia pundamilia males in routine metabolic rate (R(R)) and in the metabolic costs males pay during territorial interactions (active metabolic rate, R(A)). Pundamilia nyererei and P. pundamilia males housed in social isolation did not differ in RR . In contrast to expectation, however, P. nyererei males used less oxygen than P. pundamilia males, for a given mass and level of agonistic activity. This increased metabolic efficiency may be an adaptation to limit the metabolic cost that P. nyererei males pay for their higher rate of aggressiveness compared to P. pundamilia males. Thus, the divergence between the species in agonistic behaviour is correlated with metabolic differentiation. Such concerted divergence in physiology and behaviour might be widespread in the dramatically diverse cichlid radiations in East African lakes and may be an important factor in the remarkably rapid speciation of these fishes. The results did not support the hypothesis that higher metabolic rates caused a physiological cost to P. nyererei males that would offset their dominance advantage.

Ontogeny of metabolic rate and red blood cell size in eyelid geckos: species follow different paths

While metabolism is a fundamental feature of all organisms, the causes of its scaling with body mass are not yet fully explained. Nevertheless, observations of negative correlations between red blood cell (RBC) size and the rate of metabolism suggest that size variation of these cells responsible for oxygen supply may play a crucial role in determining metabolic rate scaling in vertebrates. Based on a prediction derived from the Cell Metabolism Hypothesis, metabolic rate should increase linearly with body mass in species with RBC size invariance, and slower than linearly when RBC size increases with body mass. We found support for that prediction in five species of eyelid geckos (family Eublepharidae) with different patterns of RBC size variation during ontogenetic growth. During ontogeny, metabolic rate increases nearly linearly with body mass in those species of eyelid geckos where there is no correlation between RBC size and body mass, whereas non-linearity of metabolic rate scaling is evident in those species with ontogenetic increase of RBC size. Our findings provide evidence that ontogenetic variability in RBC size, possibly correlating with sizes of other cell types, could have important physiological consequences and can contribute to qualitatively different shape of the intraspecific relationship between metabolic rate and body mass.

The effects of temperature and activity on intraspecific scaling of metabolic rates in a lungless salamander

The scaling of metabolic rate with body mass holds substantial predictive power as many biological processes depend on energy. A significant body of theory has been developed based on the assumption that metabolic rate scales with body mass as a power function with an exponent of 0.75, and that this scaling relationship is independent of temperature. Here we test this hypothesis at the intraspecific level in a lungless salamander using data on both standard and maximal metabolic rates (SMR and MMR, respectively). We also address a recently proposed alternative explanation that predicts systematic variation in this mass-scaling exponent, the metabolic level boundaries hypothesis (MLB). Consistent with predictions of the metabolic theory of ecology the mass scaling of SMR and MMR were independent of temperature, however, we find evidence that the mass-scaling exponent for SMR and MMR differ significantly from 0.75. Further, our data do not provide strong support for MLB. Mass-scaling exponents for MMR generally exceed those for SMR, although these differences are rarely statistically significant.

Temporal repeatability of metabolic rate and the effect of organ mass and enzyme activity on metabolism in European eel (Anguilla anguilla)

Intraspecific variation in metabolic rate of fish can be pronounced and have been linked to various fitness-related behavioural and physiological traits, but the underlying causes for this variation have received far less attention than the consequences of it. In the present study we investigated whether European eels (Anguilla anguilla) displayed temporal repeatability of body-mass-corrected (residual) metabolic rate over a two-month period and if variations in organ mass and enzyme activity between individual fish could be the cause for the observed variation in metabolic rate. Both standard metabolic rate (SMR; Pearson's r=0.743) and routine metabolic rate (RMR; r=0.496) were repeatable over the two-month period. Repeatability of RMR is an interesting finding as it indicates that the level of spontaneous activity in respirometer-confined fish is not random. Cumulative organ mass (liver, heart, spleen and intestine; mean 1.6% total body mass) was found to explain 38% of the variation in SMR (r=0.613) with the liver (one of the metabolically most active organs) being the driver for the correlation between organ mass and metabolic rate. No relationships were found for either liver citrate synthase or cytochrome oxidase activity and metabolic rate in the European eels. Reasons for, and contributions to, the observed variation in metabolic rate are discussed.

Idiosyncratic species effects confound size-based predictions of responses to climate change

Understanding and predicting the consequences of warming for complex ecosystems and indeed individual species remains a major ecological challenge. Here, we investigated the effect of increased seawater temperatures on the metabolic and consumption rates of five distinct marine species. The experimental species reflected different trophic positions within a typical benthic East Atlantic food web, and included a herbivorous gastropod, a scavenging decapod, a predatory echinoderm, a decapod and a benthic-feeding fish. We examined the metabolism-body mass and consumption-body mass scaling for each species, and assessed changes in their consumption efficiencies. Our results indicate that body mass and temperature effects on metabolism were inconsistent across species and that some species were unable to meet metabolic demand at higher temperatures, thus highlighting the vulnerability of individual species to warming. While body size explains a large proportion of the variation in species' physiological responses to warming, it is clear that idiosyncratic species responses, irrespective of body size, complicate predictions of population and ecosystem level response to future scenarios of climate change.

Conservation physiology of marine fishes: advancing the predictive capacity of models

At the end of May, 17 scientists involved in an EU COST Action on Conservation Physiology of Marine Fishes met in Oristano, Sardinia, to discuss how physiology can be better used in modelling tools to aid in management of marine ecosystems. Current modelling approaches incorporate physiology to different extents, ranging from no explicit consideration to detailed physiological mechanisms, and across scales from a single fish to global fishery resources. Biologists from different sub-disciplines are collaborating to rise to the challenge of projecting future changes in distribution and productivity, assessing risks for local populations, or predicting and mitigating the spread of invasive species.

Ontogeny of hypoxic modulation of cardiac performance and its allometry in the African clawed frog Xenopus laevis

The ontogeny of cardiac hypoxic responses, and how such responses may be modified by rearing environment, are poorly understood in amphibians. In this study, cardiac performance was investigated in Xenopus laevis from 2 to 25 days post-fertilization (dpf). Larvae were reared under either normoxia or moderate hypoxia (PO₂ = 110 mmHg), and each population was assessed in both normoxia and acute hypoxia. Heart rate (f(H)) of normoxic-reared larvae exhibited an early increase from 77 ± 1 beats min⁻¹ at 2 dpf to 153 ± 1 beats min⁻¹ at 4 dpf, followed by gradual decreases to 123 ± 3 beats min⁻¹ at 25 dpf. Stroke volume (SV), 6 ± 1 nl, and cardiac output (CO), 0.8 ± 0.1 μl min⁻¹, at 5 dpf both increased by more than 40-fold to 25 dpf with rapid larval growth (~30-fold increase in body mass). When exposed to acute hypoxia, normoxic-reared larvae increased f(H) and CO between 5 and 25 dpf. Increased SV in acute hypoxia, produced by increased end-diastolic volume (EDV), only occurred before 10 dpf. Hypoxic-reared larvae showed decreased acute hypoxic responses of EDV, SV and CO at 7 and 10 dpf. Over the period of 2-25 dpf, cardiac scaling with mass showed scaling coefficients of -0.04 (f(H)), 1.23 (SV) and 1.19 (CO), contrary to the cardiac scaling relationships described in birds and mammals. In addition, f(H) scaling in hypoxic-reared larvae was altered to a shallower slope of -0.01. Collectively, these results indicate that acute cardiac hypoxic responses develop before 5 dpf. Chronic hypoxia at a moderate level can not only modulate this cardiac reflex, but also changes cardiac scaling relationship with mass.

Effects of body mass and temperature on routine metabolic rate of juvenile largemouth bronze gudgeon Coreius guichenoti

The effects of body mass (M) and temperature (T) on routine metabolic rate (m(R) ) were assessed in the largemouth bronze gudgeon Coreius guichenoti, from Three Gorges Reservoir, Yangtze River, China. The m(R) increased with increasing M by factors (b-value in the equation m(R) = aM(b) ) of 0·843, 0·800, 0·767, 0·788 and 0·822 at 10, 15, 20, 25 and 30° C, respectively. A significant interaction between M and T on m(R) was observed. The variation in the b-value at different T suggests that the b-values were not consistent with the universal allometric exponent 0·75. After controlling for M, the relationship between the normalized standard metabolic rate (m(S), mg O(2) kg(-1) h(-1)) and T was described by an exponential equation: m(S) = 9·89e((0·093T)) . The results indicate that the effects of M on m(R) depend on T. The increased water temperature induced by dam construction on the Yangtze River may cause a marked increase in energy demand by this species, with potential ecological consequences.

Retention and maternal transfer of environmentally relevant polybrominated dibenzo-p-dioxins and dibenzofurans, polychlorinated dibenzo-p-dioxins and dibenzofurans, and polychlorinated biphenyls in zebrafish (Danio rerio) after dietary exposure

High levels of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs), mono- and non-ortho-polychlorinated biphenyls (PCBs), and polybrominated dibenzo-p-dioxins (PBDDs) are found in fish from coastal areas in the Baltic Sea, which may cause ecotoxicological effects. To increase our understanding of the persistency of the emerging pollutants polybrominated dibenzo-p-dioxins and dibenzofurans (PBDD/Fs), fish feed was spiked with 21 PBDD/Fs, 17 PCDD/Fs, and 30 PCBs and fed to zebrafish (Danio rerio). Concentrations in fish and eggs were examined during a 6- or 12-week uptake period, and a 6-week elimination period. Steady-state was reached for 2-, 3-, 7-, and/or 8-substituted tri- and tetra-BDD/Fs; 2,3,7,8-tetra-BDD (2,3,7,8-TeBDD) was the most strongly retained. Steady-state was not reached for tetra- to hexa-CDDs. Non-2,3,7,8 congeners showed little or no retention. Most PCBs had high retention and did not reach steady state. Half-lives decreased in the order PCBs > PCDD/Fs > PBDD/Fs. Concentrations of 2,3,7,8-substituted penta- to octa-CDD/Fs decreased with their degree of chlorination, suggesting that the rate-limiting factor for uptake is low bioavailability. Maternal transfer was observed for all retained compounds, with most transfer factors <1, indicating that transfer rates are affected by the poor water solubility of the compounds. The limited retention of the major PBDD congeners found in Baltic Sea fish suggests that they are exposed to high or very high concentrations via either food or water.

The effects of acute and chronic hypoxia on cortisol, glucose and lactate concentrations in different populations of three-spined stickleback

The response of individuals from three different populations of three-spined sticklebacks to acute and chronic periods of hypoxia (4.4 kPa DO, 2.2 mg l⁻¹) was tested using measures of whole-body cortisol, glucose and lactate. Although there was no evidence of a neuroendocrine stress response to acute hypoxia, fish from the population least likely to experience hypoxia in their native habitat had the largest response to low oxygen, with significant evidence of anaerobic glycolysis after 2 h of hypoxia. However, there was no measurable effect of a more prolonged period (7 days) of hypoxia on any of the fish in this study, suggesting that they acclimated to this low level of oxygen over time. Between-population differences in the analytes tested were observed in the control fish of the acute hypoxia trial, which had been in the laboratory for 16 days. These differences were not apparent among the control fish in the chronic exposure groups that had been held in the laboratory for 23 days, suggesting that these site-specific trends in physiological status were acclimatory. Overall, the results of this study suggest that local environmental conditions may shape sticklebacks' general physiological profile as well as influencing their response to hypoxia.

Analytic theories of allometric scaling

During the 13 years since it was first advanced, the fractal network theory (FNT), an analytic theory of allometric scaling, has been subjected to a wide range of methodological, mathematical and empirical criticisms, not all of which have been answered satisfactorily. FNT presumes a two-variable power-law relationship between metabolic rate and body mass. This assumption has been widely accepted in the past, but a growing body of evidence during the past quarter century has raised questions about its general validity. There is now a need for alternative theories of metabolic scaling that are consistent with empirical observations over a broad range of biological applications. In this article, we briefly review the limitations of FNT, examine the evidence that the two-variable power-law assumption is invalid, and outline alternative perspectives. In particular, we discuss quantum metabolism (QM), an analytic theory based on molecular-cellular processes. QM predicts the large variations in scaling exponent that are found empirically and also predicts the temperature dependence of the proportionality constant, issues that have eluded models such as FNT that are based on macroscopic and network properties of organisms.