Metabolic Scaling Relationships Research Articles

Earthquake disturbance shifts metabolic energy use and partitioning in a monodominant forest

AbstractAimBoth macroecology and disturbance ecology have long been used to characterize population‐ and community‐level patterns across scales, but the integration of both approaches in characterizing disturbed ecosystems is rare. Here, we use the maximum entropy theory of ecology (METE) to model the individual size distribution (ISD) of trees in pre‐ and post‐disturbance tree populations and estimate the corresponding metabolic scaling exponents.LocationNew Zealand.Time Period1987–1999.Major Taxa StudiedMountain beech (Fuscospora cliffortioides Nothofagaceae).MethodsMETE uses information entropy and empirical macro‐state variables to constrain predictions of ecological distributions related to biodiversity. METE has successfully predicted a range of biodiversity metrics in static or relatively undisturbed conditions. However, METE can fail to accurately model ecological patterns in disturbed ecosystems. We extend existing theoretical predictions to a highly disturbed ecosystem by treating the metabolic scaling exponent and Lagrange multipliers as free parameters in METE.ResultsWe showed that the fully parameterized METE (FP‐METE) model reasonably predicted the ISD of mountain beech populations in a monodominant forest after a strong earthquake, which restructured the forest. Furthermore, the FP‐METE model revealed that decreasing metabolic scaling exponent drove the substantial decline of total metabolic rate energy and the redistribution of energy towards smaller trees after the earthquake. Increased number of small trees was not sufficient to capture the full impact of disturbance on forest energy use.Main ConclusionsOur FP‐METE model applies an informatics approach to estimate the metabolic scaling relationship. We find that instead of maintaining a fixed value, the metabolic scaling exponent is variable among populations, and declines significantly after an earthquake disturbance. This leads to major shifts in the total population metabolic energy and energy distribution. With this approach, we now have the opportunity to advance beyond categorizing forms of mathematical distributions that describe biodiversity patterns and move into a predictive framework where the true constraints on ecosystems and their dynamics emerge.

Multiple stressors, allostasis and metabolic scaling in developing zebrafish.

Deoxygenation and warming affect adult fish physiology in all aquatic ecosystems, but how these stressors impact the energetics of sensitive developing stages is largely unknown. Addressing this knowledge gap, we investigated chronic and acute effects of two stressors (high temperature and hypoxia) in yolk-sac larval (48-168 hpf) zebrafish (Danio rerio) energy budgets measuring, oxygen consumption rate, growth rate (absolute and specific), % net conversion efficiency, net cost of growth and scaling relationships. Embryos and larvae were raised under four chronic treatments: (1) control (28°C and PO221 kPa, T28O21), (2) high temperature (31°C and PO221 kPa, T31O21), (3) hypoxia (28°C and PO211 kPa, T28TO11) and (4) high temperature and hypoxia (31°C and PO211 kPa, T31O11). From each chronic treatment, larvae were acutely exposed to the same combinations of stressors for 1 h in a respirometer. At hatching, larvae from chronic high temperature (T31O21 and T31O11) treatments were larger (higher dry mass and standard length) than controls (T28O21 and T28O11), but by the end of the yolk-sac stage, increased metabolic demands diverted energy away from growth, increasing net cost of growth and lowering % net conversion efficiency. Control metabolic scaling relationships were significant and differed from 0.75, but metabolic levels were lower in acute hypoxia and high temperature/hypoxia. Thus, high temperature dominated larval energetics, acting synergistically with hypoxia to increase cumulative energetic costs and making allostasis difficult compared with older stages.

How Metabolic Rate Relates to Cell Size.

Simple SummaryThe metabolic conversion of resources into living structures and processes is fundamental to all living systems. The rate of metabolism (‘fire of life’) is critical for supporting the rates of various biological processes (‘pace of life’), but why it varies considerably within and among species is little understood. Much of this variation is related to body size, but such ‘metabolic scaling’ relationships also vary extensively. Numerous explanations have been offered, but no consensus has yet been reached. Here, I critically review explanations concerning how cell size and number and their establishment by cell expansion and multiplication may affect metabolic rate and its scaling with body mass. Numerous lines of evidence suggest that cell size and growth can affect metabolic rate at any given body mass, as well as how it changes with increasing body mass during growth or evolution. Mechanisms causing negative associations between cell size and metabolic rate may involve reduced resource supply and/or demand in larger cells, but more research is needed. A cell-size perspective not only helps to explain some (but not all) variation in metabolic rate and its body-mass scaling, but may also foster the conceptual integration of studies of ontogenetic development and body-mass scaling.Metabolic rate and its covariation with body mass vary substantially within and among species in little understood ways. Here, I critically review explanations (and supporting data) concerning how cell size and number and their establishment by cell expansion and multiplication may affect metabolic rate and its scaling with body mass. Cell size and growth may affect size-specific metabolic rate, as well as the vertical elevation (metabolic level) and slope (exponent) of metabolic scaling relationships. Mechanistic causes of negative correlations between cell size and metabolic rate may involve reduced resource supply and/or demand in larger cells, related to decreased surface area per volume, larger intracellular resource-transport distances, lower metabolic costs of ionic regulation, slower cell multiplication and somatic growth, and larger intracellular deposits of metabolically inert materials in some tissues. A cell-size perspective helps to explain some (but not all) variation in metabolic rate and its body-mass scaling and thus should be included in any multi-mechanistic theory attempting to explain the full diversity of metabolic scaling. A cell-size approach may also help conceptually integrate studies of the biological regulation of cellular growth and metabolism with those concerning major transitions in ontogenetic development and associated shifts in metabolic scaling.

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

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

Life in the slow lane: field metabolic rate and prey consumption rate of the Greenland shark (Somniosus microcephalus) modelled using archival biologgers.

Field metabolic rate (FMR) is a holistic measure of metabolism representing the routine energy utilization of a species living within a specific ecological context, thus providing insight into its ecology, fitness and resilience to environmental stressors. For animals that cannot be easily observed in the wild, FMR can also be used in concert with dietary data to quantitatively assess their role as consumers, improving understanding of the trophic linkages that structure food webs and allowing for informed management decisions. Here, we modelled the FMR of Greenland sharks (Somniosus microcephalus) equipped with biologger packages or pop-up archival satellite tags (PSATs) in two coastal inlets of Baffin Island (Nunavut) using metabolic scaling relationships for mass, temperature and activity. We estimated that Greenland sharks had an overall mean (±s.d.) FMR of 21.67±2.30 mg O2 h-1 kg-0.84 (n=30; 1-4 day accelerometer package deployments) while residing inside these cold-water fjord systems in the late summer, and 25.48±0.47 mg O2 h-1 kg-0.84 (n=6; PSATs) over an entire year. When considering prey consumption rate, an average shark in these systems (224 kg) requires a maintenance ration of 61-193 g of fish or marine mammal prey daily. As Greenland sharks are a lethargic polar species, these low FMR estimates, and corresponding prey consumption estimates, suggest they require very little energy to sustain themselves under natural conditions. These data provide the first characterization of the energetics and consumer role of this vulnerable and understudied species in the wild, which is essential given growing pressures from climate change and expanding commercial fisheries in the Arctic.

The negentropic theory of ontogeny: A new model of eutherian life history transitions?

Variations in life history define key comparative and evolutionary biological questions, important for understanding the mechanisms of mammalian evolutionary divergence, developmental adaptability and plasticity. In this regard, the differences among predominantly altricial and precocial species represent a particularly significant, if still poorly understood and contested case. Here, it will be shown how the classical analysis of such ontogenetic variations, going back to the semantic biology of A. Portmann, can be expanded and synthesized with comparative physiological approaches, based on the negentropic theory of ontogeny by I. A. Arshavsky and his school. In this little received but pioneering tradition, extensive comparative and experimental investigations were carried out on the role of musculoskeletal systems and stressors in driving life history variations, particularly in the altricial-precocial spectrum. As shown by Arshavsky and co-workers, by focusing on general allometric regularities, the approximations based on the classical energy rules of surface and mass offer valuable benchmarks, but also predictions that are frequently violated by the variability of physiological and metabolic scaling relationships among altricials and precocials, and thus, a complex and historical approach is needed to describe their local physiological mechanisms and systemic regularities. This paper shows how Arshavsky’s findings and framework can play an integrative role in this context, potentially helping to bridge the mainly descriptive approach of semantic morphology, as developed by Portmann’s school, with the more functional explanations predominating current ecology and life history theory. These problems can be important for biosemiotics by highlighting the contingent, activity-dependent, and surplus anabolic (negentropic, hyper-restorative) stress mechanisms underlying diversification in eutherian developmental systems and possibly, the epigenetic evolution of pace-of-life syndromes.

Activity alters how temperature influences intraspecific metabolic scaling: testing the metabolic-level boundaries hypothesis.

A common belief is that the body-mass scaling of metabolic rate is the result of intrinsic (physical) constraints related to body design. However, many recent studies have shown that extrinsic (ecological) factors significantly affect metabolic scaling relationships, both within and among species. One of these factors is ambient temperature (T), but its influence on the intraspecific (ontogenetic) scaling slope (b) of metabolic rate varies widely. I tested whether the metabolic-level boundaries hypothesis (MLBH) can explain this variation, at least in part. The MLBH predicts that b should correlate negatively with T for resting metabolism, but show variable associations (from negative to positive) for metabolism measured during varying levels of locomotor activity. I tested the MLBH by using a literature survey of T effects on b for resting or routine metabolic rates of 179 animal and plant species. As predicted, sedentary species of ectothermic animals and plants exhibiting no locomotor activity mostly show negative associations between b and T, whereas mobile species exhibiting various low levels of uncontrolled, spontaneous, routine locomotor activity during measurements of resting or routine metabolism show varied associations. A similar difference occurs between teleost fish species exhibiting no locomotor activity versus varying levels of routine locomotor activity. These results show that intrinsic and extrinsic factors (e.g., activity and ambient temperature, respectively) can interactively affect metabolic scaling. Metabolic scaling is highly malleable, and not the simple result of universal physical constraints.

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.

Enzymatic origin and various curvatures of metabolic scaling in microbes

The famous and controversial power law is a basal metabolic scaling model mainly derived from the “surface rule” or a fractal transport network. However, this law neglects biological mechanisms in the important active state. Here, we hypothesized that the relative metabolic rate and growth rate of actively growing microbes are driven by the changeable rate of their rate-limiting enzymes and concluded that natural logarithmic microbial metabolism (lnλ) and growth (or biomass) (lnM) are both dependent on limiting resources, and then developed novel models with interdependence between lnλ and lnM. We tested the models using the data obtained from the literature. We explain how and why the scaling is usually curved with the difference between microbial metabolic and growth (or biomass’s) half-saturation constants (KM, Kλ) in the active state and agree that the linear relationship of the power law is a particular case under the given condition: KM = Kλ, which means that the enzyme dynamics may drive active and basal metabolic scaling relationships. Our interdependent model is more general than the power law, which is important for integrating the ecology and biochemical processes.

Rediscovering and Reviving Old Observations and Explanations of Metabolic Scaling in Living Systems

Why the rate of metabolism varies (scales) in regular, but diverse ways with body size is a perennial, incompletely resolved question in biology. In this article, I discuss several examples of the recent rediscovery and (or) revival of specific metabolic scaling relationships and explanations for them previously published during the nearly 200-year history of allometric studies. I carry out this discussion in the context of the four major modal mechanisms highlighted by the contextual multimodal theory (CMT) that I published in this journal four years ago. These mechanisms include metabolically important processes and their effects that relate to surface area, resource transport, system (body) composition, and resource demand. In so doing, I show that no one mechanism can completely explain the broad diversity of metabolic scaling relationships that exists. Multi-mechanistic models are required, several of which I discuss. Successfully developing a truly general theory of biological scaling requires the consideration of multiple hypotheses, causal mechanisms and scaling relationships, and their integration in a context-dependent way. A full awareness of the rich history of allometric studies, an openness to multiple perspectives, and incisive experimental and comparative tests can help this important quest.

Metabolism drives distribution and abundance in extremophile fish.

Differences in population density between species of varying size are frequently attributed to metabolic rates which are assumed to scale with body size with a slope of 0.75. This assumption is often criticised on the grounds that 0.75 scaling of metabolic rate with body size is not universal and can vary significantly depending on species and life-history. However, few studies have investigated how interspecific variation in metabolic scaling relationships affects population density in different sized species. Here we predict inter-specific differences in metabolism from niche requirements, thereby allowing metabolic predictions of species distribution and abundance at fine spatial scales. Due to the differences in energetic efficiency required along harsh-benign gradients, an extremophile fish (brown mudfish, Neochanna apoda) living in harsh environments had slower metabolism, and thus higher population densities, compared to a fish species (banded kōkopu, Galaxias fasciatus) in physiologically more benign habitats. Interspecific differences in the intercepts for the relationship between body and density disappeared when species mass-specific metabolic rates, rather than body sizes, were used to predict density, implying population energy use was equivalent between mudfish and kōkopu. Nevertheless, despite significant interspecific differences in the slope of the metabolic scaling relationships, mudfish and kōkopu had a common slope for the relationship between body size and population density. These results support underlying logic of energetic equivalence between different size species implicit in metabolic theory. However, the precise slope of metabolic scaling relationships, which is the subject of much debate, may not be a reliable indicator of population density as expected under metabolic theory.

Divergent scaling of respiration rates to nitrogen and phosphorus across four woody seedlings between different growing seasons.

Empirical studies indicate that the exponents governing the scaling of plant respiration rates (R) with respect to biomass (M) numerically vary between three‐fourth for adult plants and 1.0 for seedlings and saplings and are affected by nitrogen (N) and phosphorus (P) content. However, whether the scaling of R with respect to M (or N and P) varies among different phylogenetic groups (e.g., gymnosperms vs. angiosperms) or during the growing and dormant seasons remains unclear. We measured the whole‐plant R and M, and N and P content of the seedlings of four woody species during the growing season (early October) and the dormant season (January). The data show that (i) the scaling exponents of R versus M, R versus N, and R versus P differed significantly among the four species, but (ii), not between the growing and dormant seasons for each of the four species, although (iii) the normalization constants governing the scaling relationships were numerically greater for the growing season compared to the dormant season. In addition, (iv) the scaling exponents of R versus M, R versus N, and R versus P were numerically larger for the two angiosperm species compared to those of the two gymnosperm species, (v) the interspecific scaling exponents for the four species were greater during the growing season than in the dormant season, and (vi), interspecifically, P scaled nearly isometric with N content. Those findings indicate that the metabolic scaling relationships among R, M, N, and P manifest seasonal variation and differ between angiosperm and gymnosperm species, that is, there is no single, canonical scaling exponent for the seedlings of woody species.

The Evolution of Energetic Scaling across the Vertebrate Tree of Life.

Metabolism is the link between ecology and physiology-it dictates the flow of energy through individuals and across trophic levels. Much of the predictive power of metabolic theories of ecology derives from the scaling relationship between organismal size and metabolic rate. There is growing evidence that this scaling relationship is not universal, but we have little knowledge of how it has evolved over macroevolutionary time. Here we develop a novel phylogenetic comparative method to investigate how often and in which clades the macroevolutionary dynamics of the metabolic scaling have changed. We find strong evidence that the metabolic scaling relationship has shifted multiple times across the vertebrate phylogeny. However, shifts are rare and otherwise strongly constrained. Importantly, both the estimated slope and intercept values vary widely across regimes, with slopes that spanned across theoretically predicted values such as 2/3 or 3/4. We further tested whether traits such as ecto-/endothermy, genome size, and quadratic curvature with body mass (i.e., energetic constraints at extreme body sizes) could explain the observed pattern of shifts. Though these factors help explain some of the variation in scaling parameters, much of the remaining variation remains elusive. Our results lay the groundwork for further exploration of the evolutionary and ecological drivers of major transitions in metabolic strategy and for harnessing this information to improve macroecological predictions.

Scaling the respiratory metabolism to phosphorus relationship in plant seedlings.

There are empirical indications of an isometric scaling relationship between plants’ respiratory metabolism rates and nitrogen contents. To test the hypothesis that there may be a similar relationship between plants’ respiratory metabolism and phosphorus contents we used data obtained from 150 laboratory and field-grown seedlings representing 30 herbaceous species and 20 woody deciduous species. Our results show that whole-plant respiration rates strongly scaled to the 0.81-power of the whole-plant phosphorus content, across wide ranges of growth conditions and functional classifications. Moreover, we also found a similar scaling exponent between whole-plant respiration rates and total nitrogen contents for the same set of samples. The similarities of the metabolic scaling relationships suggest that similar mechanisms may be involved in the transport and storage of phosphorus and nitrogen in plants.

High-Throughput Tissue Bioenergetics Analysis Reveals Identical Metabolic Allometric Scaling for Teleost Hearts and Whole Organisms.

Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO2), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO2 scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO2) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism’s vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate—a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in toxicology, evolutionary physiology, and biomedical sciences, particularly in the context of investigating pathogenesis of mitochondrial diseases.

Scaling of Metabolic Scaling within Physical Limits

Both the slope and elevation of scaling relationships between log metabolic rate and log body size vary taxonomically and in relation to physiological or developmental state, ecological lifestyle and environmental conditions. Here I discuss how the recently proposed metabolic-level boundaries hypothesis (MLBH) provides a useful conceptual framework for explaining and predicting much, but not all of this variation. This hypothesis is based on three major assumptions: (1) various processes related to body volume and surface area exert state-dependent effects on the scaling slope for metabolic rate in relation to body mass; (2) the elevation and slope of metabolic scaling relationships are linked; and (3) both intrinsic (anatomical, biochemical and physiological) and extrinsic (ecological) factors can affect metabolic scaling. According to the MLBH, the diversity of metabolic scaling relationships occurs within physical boundary limits related to body volume and surface area. Within these limits, specific metabolic scaling slopes can be predicted from the metabolic level (or scaling elevation) of a species or group of species. In essence, metabolic scaling itself scales with metabolic level, which is in turn contingent on various intrinsic and extrinsic conditions operating in physiological or evolutionary time. The MLBH represents a “meta-mechanism” or collection of multiple, specific mechanisms that have contingent, state-dependent effects. As such, the MLBH is Darwinian in approach (the theory of natural selection is also meta-mechanistic), in contrast to currently influential metabolic scaling theory that is Newtonian in approach (i.e., based on unitary deterministic laws). Furthermore, the MLBH can be viewed as part of a more general theory that includes other mechanisms that may also affect metabolic scaling.

Metabolic Scaling in Complex Living Systems

In this review I show that four major kinds of theoretical approaches have been used to explain the scaling of metabolic rate in cells, organisms and groups of organisms in relation to system size. They include models focusing on surface-area related fluxes of resources and wastes (including heat), internal resource transport, system composition, and various processes affecting resource demand, all of which have been discussed extensively for nearly a century or more. I argue that, although each of these theoretical approaches has been applied to multiple levels of biological organization, none of them alone can fully explain the rich diversity of metabolic scaling relationships, including scaling exponents (log-log slopes) that vary from ~0 to >1. Furthermore, I demonstrate how a synthetic theory of metabolic scaling can be constructed by including the context-dependent action of each of the above modal effects. This “contextual multimodal theory” (CMT) posits that various modulating factors (including metabolic level, surface permeability, body shape, modes of thermoregulation and resource-transport, and other internal and external influences) affect the mechanistic expression of each theoretical module. By involving the contingent operation of several mechanisms, the “meta-mechanistic” CMT differs from most metabolic scaling theories that are deterministically mechanistic. The CMT embraces a systems view of life, and as such recognizes the open, dynamic nature and complex hierarchical and interactive organization of biological systems, and the importance of multiple (upward, downward and reciprocal) causation, biological regulation of resource supply and demand and their interaction, and contingent internal (system) and external (environmental) influences on metabolic scaling, all of which are discussed. I hope that my heuristic attempt at building a unifying theory of metabolic scaling will not only stimulate further testing of all of the various subtheories composing it, but also foster an appreciation that many current models are, at least in part, complementary or even synergistic, rather than antagonistic. Further exploration about how the scaling of the rates of metabolism and other biological processes are interrelated should also provide the groundwork for formulating a general metabolic theory of biology.

One size fits all: stability of metabolic scaling under warming and ocean acidification in echinoderms

Responses by marine species to ocean acidification (OA) have recently been shown to be modulated by external factors including temperature, food supply and salinity. However the role of a fundamental biological parameter relevant to all organisms, that of body size, in governing responses to multiple stressors has been almost entirely overlooked. Recent consensus suggests allometric scaling of metabolism with body size differs between species, the commonly cited ‘universal’ mass scaling exponent (b) of ¾ representing an average of exponents that naturally vary. One model, the Metabolic-Level Boundaries hypothesis, provides a testable prediction: that b will decrease within species under increasing temperature. However, no previous studies have examined how metabolic scaling may be directly affected by OA. We acclimated a wide body-mass range of three common NE Atlantic echinoderms (the sea star Asterias rubens, the brittlestars Ophiothrix fragilis and Amphiura filiformis) to two levels of pCO2 and three temperatures, and metabolic rates were determined using closed-chamber respirometry. The results show that contrary to some models these echinoderm species possess a notable degree of stability in metabolic scaling under different abiotic conditions; the mass scaling exponent (b) varied in value between species, but not within species under different conditions. Additionally, we found no effect of OA on metabolic rates in any species. These data suggest responses to abiotic stressors are not modulated by body size in these species, as reflected in the stability of the metabolic scaling relationship. Such equivalence in response across ontogenetic size ranges has important implications for the stability of ecological food webs.

代谢异速生长理论及其在微生物生态学领域的应用

Metabolisms are fundamental processes of organisms. These processes affect material recycling and energy transfer of the organisms in different environments. Metabolism determines the demands that organisms place on their environment for all resources, and sets powerful constraints on allocation of resources to all components of fitness. As the important index of life process, metabolic rate, setting the pace of life, was found to follow the allometric scaling relationship in many studies. For a heterotroph, the metabolic rate is equal to the rate of respiration because heterotrophs obtain energy by oxidizing carbon compounds. For an autotroph, the metabolic rate is equal to the rate of photosynthesis because the same reaction is run in reverse using energy to fix carbon. Metabolic rate determines the rates of almost all biological activities. The metabolic scaling relationship is the power function existed between the metabolic rate and the body size (or mass) of an organism. Many data including most of the range of biological diversity on the planet, from bacteria to elephant and from algae to sapling trees, showed that metabolism displays a striking degree of homeostasis across all life, despite the enormous biochemical, physiological, and ecological differences between the surveyed species that vary over 1020-fold in body mass, metabolic rates of major taxonomic groups displayed at physiological rest converge on a narrow range from 0. 3 to 8. 7 W/kg. The metabolic scaling theory was proposed as a mechanism model to explain allometric scaling relationship, which was a fundamental phenomenon of life. This theory based on the fractal-like distribution network models and fluid dynamics theory, and explained the allometric scaling relationship using bioenergetics. The fact that metabolic rate scales as three-quarter power was proved in many organisms, but there were also many results indicated that the scale exponent was not a fixed value of 3/4, but between 2/3 and 1 due to the influence of environmental factors such as temperature and stoichiometry. Based on the successful applications on macroorganisms, the metabolic scaling theory was extended to analyze the microorganisms, and revealed the possible universality of the theory to all the organisms in the nature. Much of the variation among ecosystems, including their biological structures, chemical compositions, energy and material fluxes, population processes, and species diversities, depends on the metabolic characteristics of the organisms that are present. Because the body size and other biological characters of the microorganisms were not well defined as the macroorganisms, it was important to define the taxon, the unit of body size and measurement standard of the microorganisms for the studies of their allometric scaling relationships. In the field of microbial ecology, microbial taxon could be defined as a phylogenetic or functional unit, and the application of metabolic scaling theory in the microbial ecology should focus on the consortium or functional community levels instead of individual strain level. Our preliminary work indicated that the microbial diversity was linked with the ecosystem functionality and well expressed using a power law equation with the scale exponents between 0. 71 and 0. 84 for different soils. These exponents (the microbial turnover rate) were well fell in the range of values for the metabolic scaling law, suggesting the possible universality of metabolic scaling theory for the microbial world. This paper introduced metabolic scaling theory and explored its preliminary application to the microbial ecology field, extended and deepened our understanding of the theory. We also foresaw the perspectives of the metabolic scaling theory in the field of microbial ecology.

Forecasting extinction risk of ectotherms under climate warming: an evolutionary perspective

SummaryIt has been postulated that climate warming may pose the greatest threat species in the tropics, where ectotherms have evolved more thermal specialist physiologies. Although species could rapidly respond to environmental change through adaptation, little is known about the potential for thermal adaptation, especially in tropical species.In the light of the limited empirical evidence available and predictions from mutation‐selection theory, we might expect tropical ectotherms to have limited genetic variance to enable adaptation. However, as a consequence of thermodynamic constraints, we might expect this disadvantage to be at least partially offset by a fitness advantage, that is, the ‘hotter‐is‐better’ hypothesis.Using an established quantitative genetics model and metabolic scaling relationships, we integrate the consequences of the opposing forces of thermal specialization and thermodynamic constraints on adaptive potential by evaluating extinction risk under climate warming. We conclude that the potential advantage of a higher maximal development rate can in theory more than offset the potential disadvantage of lower genetic variance associated with a thermal specialist strategy.Quantitative estimates of extinction risk are fundamentally very sensitive to estimates of generation time and genetic variance. However, our qualitative conclusion that therelativerisk of extinction is likely to be lower for tropical species than for temperate species is robust to assumptions regarding the effects of effective population size, mutation rate and birth rate per capita.With a view to improving ecological forecasts, we use this modelling framework to review the sensitivity of our predictions to the model's underpinning theoretical assumptions and the empirical basis of macroecological patterns that suggest thermal specialization and fitness increase towards the tropics. We conclude by suggesting priority areas for further empirical research.