An information-theoretic approach to evaluating the size and temperature dependence of metabolic rate

The effects of body mass and temperature on metabolic rate (MR) are among the most widely examined physiological relationships. Recently, these relationships have been incorporated into the metabolic theory of ecology (MTE) that links the ecology of populations, communities and ecosystems to the MR of individual organisms. The fundamental equation of MTE derives the relation between mass and MR using first principles and predicts the temperature dependence of MR based on biochemical kinetics. It is a deliberately simple, zeroth-order approximation that represents a baseline against which variation in real biological systems can be examined. In the present study, we evaluate the fundamental equation of MTE against other more parameter-rich models for MR using an information-theoretic approach to penalize the inclusion of additional parameters. Using a comparative database of MR measurements for 1359 species, from 11 groups ranging from prokaryotes to mammals, and spanning 16 orders of magnitude in mass and a 59°C range in body temperature, we show that differences between taxa in the mass and temperature dependence of MR are sufficiently large as to be retained in the best model for MR despite the requirement for estimation of 22 more parameters than the fundamental equation of MTE.     

Metabolic rate in the whip-spider, Damon annulatipes (Arachnida: Amblypygi)

Metabolic rate estimates as well as a measure of their repeatability and response to laboratory acclimation are provided for the amblypygid Damon annulatipes (Wood). This species (mean +/- S.E. mass: 640+/-66 mg) shows continuous gas exchange, as might be expected from its possession of book lungs, and at 21 degrees C has a metabolic rate of 30.22+/-2.87 microl CO2 h(-1) (approximately 229.6+/-21.8 microW, R.Q. = 0.72). The intraclass correlation coefficient (r=0.74-0.89) indicated substantial repeatability in metabolic rate which did not change with laboratory acclimation over a period of 2 weeks. By contrast, absolute metabolic rate declined by c. 16-33%, although this was not a consequence of changes in mass (which were non-significant over the same period). Rather, it appears that a reduction in overall stress or activity in the laboratory might have been responsible for the decline in mass-independent metabolic rate. At the intraspecific level, metabolic rate scaled as microW = 342 M(0.857), where mass is in grams. Metabolic rates of this species are in keeping with its sedentary behaviour such that for a given body size they are lower than those of most arthropods (spiders and insects), higher than the very sedentary ticks, and equivalent to scorpions. These findings have implications for the understanding of the evolution of metabolic rates in arthropods.     

Estimation of heritability and repeatability of resting metabolic rate in birds, with free-living pied flycatchers Ficedula hypoleuca (Aves: Passeriformes) as an example

Estimates of a trait heritability and repeatability can get at an idea of its usefulness for being an individual characteristic and its ability to change under selection pressure. Heritability and repeatability of energetic parameters still poorly studied in birds. The most important physiological characteristic of homoiotherms is resting metabolic rate (RMR), which, in the absence of productive processes, does not exceed basal metabolic rate (BMR). We estimated BMR repeatability in free-living pied flycatchers in Moscow Region (55 degrees 44' N, 36 degrees 51' E; 1992-2008) and Tomsk (56 degrees 20' N, 84 degrees 56' E; 2008-2009) populations over intervals from 40 days to 3 years. In Moscow Region population, BMR repeatability amounted to tau = 0.34 +/- 0.10 (n=80) if measured over 1 year interval, tau = 0.60 +/- 0.15 (n=19) if measured over 2 years interval, and tau = 0.85 +/- 0.13 (n=6) if measured over 3 years interval providing that consecutive BMR measurements were done in the same period of reproductive season. In Tomsk population, BMR repeatability, measured over 1 year interval, amounted to tau = 0.49 +/- 0.11 (n=50). Repeatability is a measure of a trait constancy and sets the upper limit of its heritability. To estimate RMR heritability, cross-fostering experiments have been conducted in 2003-2005 with flycatchers of Moscow Region population. RMR of chicks positively correlated with BMR of their biological fathers, whereas such correlation in metabolic rates between chicks and their foster fathers was absent. The RMR heritability estimate turned out to be h2 = 0.43 +/- 0.17 (n=210). The obtained estimates of heritability and repeatability of fundamental energetic traits are rather high for physiological features. This suggests the existence of a potential for direct selection on BMR and evolutionary stable diversity of avian populations with regard to basal metabolic rate.     

Temperature dependence of evolutionary diversification: differences between two contrasting model taxa support the metabolic theory of ecology

Biodiversity patterns are largely determined by variation of diversification rates across clades and geographic regions. Although there are multiple reasons for this variation, it has been hypothesized that metabolic rate is the crucial driver of diversification of evolutionary lineages. According to the metabolic theory of ecology (MTE), metabolic rate – and consequently speciation – is driven mainly by body size and environmental temperature. As environmental temperature affects metabolic rate in ecto‐ and endotherms differently, its impact on diversification rate should also differ between the two types of organisms. Employing two independent approaches, we analysed correlates of speciation rates and, ultimately, net diversification rates for two contrasting taxa: plethodontid salamanders and carnivoran mammals. Whereas in the ectothermic plethodontids speciation rates positively correlated with environmental temperature, in the endothermic carnivorans a reverse, negative correlation was detected. These findings comply with predictions of the MTE and suggest that similar geographic patterns of biodiversity across taxa (e.g. ecto‐ and endotherms) might have been generated by different ecological and evolutionary processes.     

Intraspecific allometry of standard metabolic rate in green iguanas, Iguana iguana

To study the allometric relationship between standard metabolic rate and body mass (mass range 16-3627 g) in green iguanas, Iguana iguana (n=32), we measured rates of oxygen consumption (V(O(2))) at 30 degrees C during scotophase. The relationship could be described as: V(O(2))(ml h(-1))=0.478W(0.734). The resulting mass exponent was similar to the 3/4 power commonly used in interspecific curves (P>0.05), but differed from a proposed intraspecific value of 2/3 (P<0.05). The mass exponents of male (n=8) and female (n=11) iguanas did not differ (P>0.05). The mass adjusted V(O(2)) was higher than predicted from generalized squamate curves. The mean mass exponent of intra-individual allometric equations of iguanas (n=7) at varying masses during ontogeny did not differ from that of the pooled equation, indicating that scaling of V(O(2)) is similar for both between and within individuals. Thermal acclimation, compensatory changes in V(O(2)) with prolonged exposure to a constant temperature, was not observed in juvenile iguanas (n=11) between 1 and 5 weeks of acclimation at 30 degrees C.     

Testing the metabolic theory of ecology

The metabolic theory of ecology (MTE) predicts the effects of body size and temperature on metabolism through considerations of vascular distribution networks and biochemical kinetics. MTE has also been extended to characterise processes from cellular to global levels. MTE has generated both enthusiasm and controversy across a broad range of research areas. However, most efforts that claim to validate or invalidate MTE have focused on testing predictions. We argue that critical evaluation of MTE also requires strong tests of both its theoretical foundations and simplifying assumptions. To this end, we synthesise available information and find that MTE's original derivations require additional assumptions to obtain the full scope of attendant predictions. Moreover, although some of MTE's simplifying assumptions are well supported by data, others are inconsistent with empirical tests and even more remain untested. Further, although many predictions are empirically supported on average, work remains to explain the often large variability in data. We suggest that greater effort be focused on evaluating MTE's underlying theory and simplifying assumptions to help delineate the scope of MTE, generate new theory and shed light on fundamental aspects of biological form and function.     

Elevational variation in adult body size and growth rate but not in metabolic rate in the tree weta Hemideina crassidens

Populations of the same species inhabiting distinct localities experience different ecological and climatic pressures that might result in differentiation in traits, particularly those related to temperature. We compared metabolic rate (and its thermal sensitivity), growth rate, and body size among nine high- and low-elevation populations of the Wellington tree weta, Hemideina crassidens, distributed from 9 to 1171 m a.s.l across New Zealand. Our results did not indicate elevational compensation in metabolic rates (metabolic cold adaptation). Cold acclimation decreased metabolic rate compared to warm-acclimated individuals from both high- and low-elevation populations. However, we did find countergradient variation in growth rates, with individuals from high-elevation populations growing faster and to a larger final size than individuals from low-elevation populations. Females grew faster to a larger size than males, although as adults their metabolic rates did not differ significantly. The combined physiological and morphological data suggest that high-elevation individuals grow quickly and achieve larger size while maintaining metabolic rates at levels not significantly different from low-elevation individuals. Thus, morphological differentiation among tree weta populations, in concert with genetic variation, might provide the material required for adaptation to changing conditions.     

Constant intravenous ghrelin infusion in healthy young men: clinical pharmacokinetics and metabolic effects

Ghrelin levels fluctuate rapidly and dynamically with surges before meal times and postprandial troughs, and ghrelin increases appetite and food intake. Circulating ghrelin correlates negatively with body mass index (BMI), but obese individuals have a reduced postprandial decrease in ghrelin levels. Whether this reflects changes in secretion or clearance of ghrelin is uncertain. We therefore studied the pharmacokinetics of ghrelin in relation to anthropometric and biochemical measures. We also studied the effects of ghrelin on hormones and metabolites. In fasting humans, we used a constant infusion rate of ghrelin lasting 180 min at 5 pmol.kg body wt(-1).min(-1) in a randomized, double-blind, placebo-controlled crossover study. Serum ghrelin (s-ghrelin; total levels) was distributed and eliminated according to a two-compartment model. s-Ghrelin initial half-life was 24 +/- 2 min and terminal half-life 146 +/- 36 min, respectively. Mean residence time (MRT) of ghrelin was 93 +/- 16 min. MRT correlated positively with both BMI (r = 0.51, P < 0.001) and high-density cholesterol (HDL) levels (r = 0.75, P < 0.001). Serum insulin levels remained constant during ghrelin infusion, whereas plasma glucose increased 0.3 +/- 0.1 mmol/l (P < 0.01) and free fatty acid levels more than doubled (to 1.03 +/- 0.08 mmol/l, P < 0.001), translating into a significant reduction of insulin sensitivity (P < 0.001). In conclusion, 1) we describe novel pharmacokinetics of ghrelin that are useful when tailoring ghrelin infusion rates in clinical experiments, 2) BMI and HDL correlate positively with MRT of infused ghrelin, and 3) supraphysiological ghrelin levels impair insulin sensitivity.     

Repeatable inter‐individual variation in the thermal sensitivity of metabolic rate

Assessing whether trait variations among individuals are consistent over time and among environmental conditions is crucial to understand evolutionary responses to new selective pressures such as climate change. According to the universal thermal dependence hypothesis, thermal sensitivity of metabolic rate should not vary strongly and consistently among organisms, implying limited evolutionary response for metabolic traits under climate change. However, this hypothesis has been rarely tested at an individual level, leaving a gap in our understanding of climate change impacts on metabolic responses and their potential evolution. Using the amphipod Gammarus fossarum, we investigated the variability and repeatability of individual metabolic thermal reaction norms over time. We found large variations in both the thermal sensitivity (i.e. slope) and expression level (i.e. intercept) of individual metabolic reaction norms. Moreover, differences among individuals were consistent over time, and therefore repeatable. Inter‐individual variations in body mass resulted in a high repeatability of metabolic expression level but had no significant effect on the repeatability of thermal sensitivity. Overall, our results highlight that inter‐individual variability and repeatability of thermal reaction norms can be substantial. We conclude that these consistent differences among individuals should not be overlooked when apprehending the ecological and evolutionary effects of climate change.     

VCO2 and VE kinetics during moderate- and heavy-intensity exercise after acetazolamide administration.

The effect of carbonic anhydrase inhibition with acetazolamide (Acz) on CO2 output (VCO2) and ventilation (VE) kinetics was examined during moderate- and heavy-intensity exercise. Seven men [24 +/- 1 (SE) yr] performed cycling exercise during control (Con) and Acz (10 mg/kg body wt iv) sessions. Each subject performed step transitions (6 min) in work rate from 0 to 100 W [below ventilatory threshold (VET)]. VE and gas exchange were measured breath by breath. The time constant (tau) was determined for exercise VET by using a three-component model (fit from the start of exercise). VCO2 kinetics were slower in Acz (VET, MRT = 75 +/- 10 s) than Con (VET, MRT = 54 +/- 7 s). During VET kinetics were faster in Acz (MRT = 85 +/- 17 s) than Con (MRT = 106 +/- 16 s). Carbonic anhydrase inhibition slowed VCO2 kinetics during both moderate- and heavy-intensity exercise, demonstrating impaired CO2 elimination in the nonsteady state of exercise. The slowed VE kinetics in Acz during exercise 相似文献   

Temperature-dependent rate of clutch production in a tropical lizard (Paroedura picta: Gekkonidae): Intraspecific test of the metabolic theory of ecology

Recently, a general model based on scaling of metabolic rate and reaction kinetics that predicts dependence of various biological rates on temperature and body size has been proposed as a core of the “Metabolic Theory of Ecology” (MTE). However, its thermal component has been rarely explicitly tested and its usefulness for prediction of thermal effect on key life-history traits such as reproductive rate and hence fitness is still questionable. Here, we tested its applicability to temperature-dependent rate of clutch production in a tropical gecko. The thermal effects on reproductive rates in reptiles are only poorly known and difficult to estimate, because most species lay clutches largely infrequently. Females of the Madagascar ground gecko (Paroedura picta) lay clutches in unusually short intervals, which allowed us to use this species as a model for estimation of dependence of rate of clutch production on temperature. We kept adult females at three constant temperatures (24, 27, 30 °C) and recorded their reproductive characteristics. Increasing temperature positively influences rate of clutch production, but in a manner not predicted by a simple model of reaction kinetics. The results in P. picta suggest that predictions of fitness consequences of shifts in thermal environment can be more complicated than expected under the general relationship of the MTE.     

A metabolic theory of ecology applied to temperature and mass dependence of N and P excretion by common carp

Our study used a metabolic theory of ecology (MTE) to explore scaling of metabolic rates by body size and temperature, and to predict nutrient excretion by common carp (Cyprinus carpio). At high biomasses, common carp have negative impacts on water quality, and one mechanism is excretion of the nutrients N and P. We measured whole-body and mass-specific excretion rates during summer and winter for fish of different sizes (wet mass range 28–1,196 g) to produce an allometric scaling model capable of predicting excretion at different temperatures. We found positive relationships between both dissolved and total nutrient concentrations and fish wet mass in summer and winter, with greater excretion rates in summer (mean water temperature 24.2°C) than in winter (mean water temperature 9.2°C). Mass-specific excretion rates decreased with increasing fish size, consistent with the MTE, and the temperature-adjusted model explained more variation for N excretion than for P. The proportion of dissolved nutrients (NH₄ and PO₄) to total nutrients increased with increasing fish size. The significance of these models is that they can be used to predict population-based nutrient excretion by common carp when thermal history, fish density and size distribution in a water body are known.     

The metabolism of lake plankton does not support the metabolic theory of ecology

We tested if the metabolic theory of ecology (MTE) correctly predicts plankton metabolism in a temperate lake, based on a long-term (about 15 years), high-frequency dataset of body size, abundance and production, using two different techniques: least squares regression and maximum likelihood. For phytoplankton, the general fit was relatively poor (r²=0.53). The assumption of the MTE on temperature dependence of metabolism was not supported, and the assumed value of ¾ of the allometric exponent was barely within 95% confidence limits. For some of the models, the value of b was significantly higher than ¾. When radiation was included as an additional predictor, it improved the model considerably (r²=0.67). Including grazing by zooplankton reduced the model residuals during the summer period, when grazing is a dominant factor. The allometric exponent had virtually no effect for phytoplankton, due to little variability in average individual size. Zooplankton production, on the other hand, was better predicted by MTE, showing stronger effects of temperature and body size, the average of which varied by a factor of more than a hundred. However, the best-fitting value of the allometric exponent for zooplankton was 0.85, and significantly higher than the ¾ predicted by the theory. The ratio of observed production to biomass for the entire plankton community declined linearly with the body size (in log-log) with a slope corresponding to a value of b=0.85. We conclude that the MTE has little predictive power for the metabolism of lacustrine plankton, in particular for phytoplankton, and especially at the scale of variability of this study, and that this could be improved by incorporating radiation into the model.     

Specific metabolic rate, longevity and "Rubner constant" for birds

An assumption was made that age constituent alpha x(beta) of mortality of individuals in a population in Weibull equation mx = m0 + alpha x(beta) (Ricklefs, 2000) reflects change of specific metabolic rate of one individual with age. Based upon that hypothesis a formula was proposed for relationship of specific metabolic rate of an adult individual after cessation of growth, when mass W is attained, and age t: q(t) = q0(1-omega(beta) + 1t(beta)) where q0 = aW(-b) is value q(t) at the moment of growth cessation and omega = alpha(1/(beta + 1)) is "ageing rate", determined and estimated by R. Ricklefs. Maximum longevity of an individual was determined as [equation: see text], where qcrit is specific metabolic rate at the age tmax. Parameter beta and relationships omega(W) and (qcrit/q0)(W) were approximated for birds from data of Ricklefs. Statistical comparison of results of calculations of tmax was carried out on the basis of the above formula and other known formulas for groups of Passeriformes and non-Passeriformes. Rubner constant [equation: see text] was calculated assuming that body mass of an adult individual (W) is attained in the first year of life (tA = 0). Average values of 602.4 +/- 2.5 kcal g(-1) (n = 83) for non-Passeriformes and 963 +/- 6.3 kcal g(-1) (n = 41) for Passeriformes were obtained.     

Adult age of vascular plant species along an elevational land‐use and climate gradient

Trait variation across species plays a fundamental role in ecology and evolution, but quantitative analyses of key life‐history traits under natural conditions generally do not include a large number of species. In a comparative study, we analyzed interspecific variation in adult age as a minimum estimate of the lifespan of 708 vascular plant species along elevational gradients from 263–3175 m a.s.l. and compared this variation with predictions from r‐K selection theory and the metabolic theory of ecology (MTE). Age data based on annual ring counts of root collars and rhizomes were combined with a systematic sample of current species distributions in Switzerland (453 plots, each 1 km²). Elevation and temperature trends were investigated by regression analyses of the variation in adult age across species and species assemblages (median adult age) at the landscape level. We included climate, land use and geology as environmental predictors in multiple regressions and considered phylogeny by eigenvector filtering. We found a general increase in adult age towards higher elevations at the level of overall interspecific variation, and this trend was also detectable within individual plant families. Species generally had a shorter lifespan under warmer climates and, in agreement with r‐K prediction, in lowland agricultural landscapes. We found an exponential adult age–temperature relationship that is consistent with MTE. The estimate of the MTE parameter ‘activation energy’ for median adult age in multiple regression was 0.65 eV (95% CI 0.62–0.69 eV) which coincided with the predicted range of 0.60–0.70 eV. Our results imply that climate warming could accelerate species turnover rates by favoring short‐lived species over the whole range of life histories and species assemblages. Besides the strong temperature relationship, residual variability and confounding factors demonstrate the need for additional research about interactions between broad‐scale constraints and more local drivers of life‐history variation.     

Mass and temperature dependence of metabolic rate in litter and soil invertebrates

Metabolic scaling theory provides a framework for modeling the combined mass and temperature dependence of metabolic rate. The theory predicts that whole-organism metabolic rate should scale with body mass raised to the 3/4 power as a consequence of the physical characteristics of internal distribution networks. Metabolic rate is predicted to vary with absolute body temperature, T, according to the Boltzmann factor, e(-E/kT), where E is the apparent activation energy of biochemical reactions, 0.2-1.2 eV, and k is Boltzmann's constant. I evaluated those predictions, using a compilation of published data on the metabolic rates of litter- and soil-dwelling earthworms, isopods, oribatid mites, springtails, and spiders. Earthworms, oribatid mites, springtails, and spiders had mass-scaling exponents that were statistically indistinguishable from the expected value of 0.75. The scaling exponent for terrestrial isopods, 0.91, was significantly greater than expected. All taxa had apparent activation energies within the predicted range of 0.2-1.2 eV. Activation energies for isopods, oribatid mites, springtails, and spiders were not significantly different from the average expected value of 0.6 eV, while the activation energy for earthworms, 0.25 eV, was significantly lower than 0.6 eV. Updated equations for estimating metabolic rate from body mass and environmental temperature are given for investigations into the ecological energetics of litter and soil animals.     

Warming reduces metabolic rate in marine snails: adaptation to fluctuating high temperatures challenges the metabolic theory of ecology

The universal temperature-dependence model (UTD) of the metabolic theory of ecology (MTE) proposes that temperature controls mass-scaled, whole-animal resting metabolic rate according to the first principles of physics (Boltzmann kinetics). Controversy surrounds the model''s implication of a mechanistic basis for metabolism that excludes the effects of adaptive regulation, and it is unclear how this would apply to organisms that live in fringe environments and typically show considerable metabolic adaptation. We explored thermal scaling of metabolism in a rocky-shore eulittoral-fringe snail (Echinolittorina malaccana) that experiences constrained energy gain and fluctuating high temperatures (between 25°C and approximately 50°C) during prolonged emersion (weeks). In contrast to the prediction of the UTD model, metabolic rate was often negatively related to temperature over a benign range (30–40°C), the relationship depending on (i) the temperature range, (ii) the degree of metabolic depression (related to the quiescent period), and (iii) whether snails were isolated within their shells. Apparent activation energies (E) varied between 0.05 and −0.43 eV, deviating excessively from the UTD''s predicted range of between 0.6 and 0.7 eV. The lowering of metabolism when heated should improve energy conservation in a high-temperature environment and challenges both the theory''s generality and its mechanistic basis.     

Body condition helps to explain metabolic rate variation in wolf spiders

1. Metabolism is the fundamental process that powers life. Understanding what drives metabolism is therefore critical to our understanding of the ecology and behaviour of organisms in nature. 2. Metabolic rate generally scales with body size according to a power law. However, considerable unexplained variation in metabolic rate remains after accounting for body mass with scaling functions. 3. We measured resting metabolic rates (oxygen consumption) of 227 field‐caught wolf spiders. Then, we tested for effects of body mass, species, and body condition on metabolic rate. 4. Metabolic rate scales with body mass to the 0.85 power in these wolf spiders, and there are metabolic rate differences between species. After accounting for these factors, residual variation in metabolic rate is related to spider body condition (abdomen:cephalothorax ratio). Spiders with better body condition consume more oxygen. 5. These results indicate that recent foraging history is an important determinant of metabolic rate, suggesting that although body mass and taxonomic identity are important, other factors can provide helpful insights into metabolic rate variation in ecological communities.     

Large‐scale patterns of tree species richness and the metabolic theory of ecology

The metabolic theory of ecology (MTE) endeavours to explain ecosystem structure and function in terms of the effects of temperature and body size on metabolic rate. In a recent paper (Wang et al., 2009, Proceedings of the National Academy of Sciences USA, 106 , 13388), we tested the MTE predictions of species richness using tree distributions in eastern Asia and North America. Our results supported the linear relationship between log‐transformed species richness and the inverse of absolute temperature predicted by the MTE, but the slope strongly depends on spatial scale. The results also indicate that there are more tree species in cold climate at high latitudes in North America than in eastern Asia, but the reverse is true in warm climate at low latitudes. Qian & Ricklefs (2011, Global Ecology and Biogeography, 20 , 362–365) recently questioned our data and some of the analyses. Here we reply to them, and provide further analyses to show that their critiques are primarily based on unsuitable data and subjective conjecture.