Herbivore metabolism and stoichiometry each constrain herbivory at different organizational scales across ecosystems

Plant-herbivore interactions mediate the trophic structure of ecosystems. We use a comprehensive data set extracted from the literature to test the relative explanatory power of two contrasting bodies of ecological theory, the metabolic theory of ecology (MTE) and ecological stoichiometry (ES), for per-capita and population-level rates of herbivory across ecosystems. We found that ambient temperature and herbivore body size (MTE) as well as stoichiometric mismatch (ES) both constrained herbivory, but at different scales of biological organization. Herbivore body size, which varied over 11 orders of magnitude, was the primary factor explaining variation in per-capita rates of herbivory. Stoichiometric mismatch explained more variation in population-level herbivory rates and also in per-capita rates when we examined data from within functionally similar trophic groups (e.g. zooplankton). Thus, predictions from metabolic and stoichiometric theories offer complementary explanations for patterns of herbivory that operate at different scales of biological organization.     

Linking life‐history theory and metabolic theory explains the offspring size‐temperature relationship

Temperature often affects maternal investment in offspring. Across and within species, mothers in colder environments generally produce larger offspring than mothers in warmer environments, but the underlying drivers of this relationship remain unresolved. We formally evaluated the ubiquity of the temperature–offspring size relationship and found strong support for a negative relationship across a wide variety of ectotherms. We then tested an explanation for this relationship that formally links life‐history and metabolic theories. We estimated the costs of development across temperatures using a series of laboratory experiments on model organisms, and a meta‐analysis across 72 species of ectotherms spanning five phyla. We found that both metabolic and developmental rates increase with temperature, but developmental rate is more temperature sensitive than metabolic rate, such that the overall costs of development decrease with temperature. Hence, within a species’ natural temperature range, development at relatively cooler temperatures requires mothers to produce larger, better provisioned offspring.     

WBE 模型及其在生态学中的应用：研究概述

介绍了WBE模型,综述了该模型在生态学中的应用进展。WBE模型,以及以该模型为基础的MTE模型,假设生物体为自相似分形网络结构,提出代谢速率和个体大小之间存在3/4指数关系,分别预测了从个体到生物圈多个尺度上的生物属性之间的异速生长关系,而且部分得到了验证。WBE模型的应用涵盖了个体组织生物量、年生长率,种群密度和生态系统单位面积产量、能量流动率等多个方面;即使在生物圈大尺度上,WBE模型也可用来预测试验中无法直接测量的特征变量的属性,如全球碳储量的估算等。至今,关于WBE和MTE模型仍然存在各种褒贬争论,讨论焦点主要集中于模型建立的前提假设以及权度指数的预测。今后的研究工作应规范试验技术和方法,考虑物种多样性和环境等因素的影响,提出符合各类生物的模型结构体系,使其具有更广泛的应用性和预测性。     

Does universal temperature dependence apply to communities? An experimental test using natural marine plankton assemblages

The metabolic theory of ecology (MTE) is an intriguing but controversial theory that tries to explain ecological patterns at all scales on the basis of first principles. Temperature plays a pivotal role in this theory. According to MTE, the Arrhenius relationship that describes the effect of temperature on biochemical reactions extends to a 'universal temperature dependence' that encompasses all kinds of processes and scales up to the cellular, the organismal, and the community level. In this study we test the prediction that community growth rate is temperature dependent in an Arrhenius-like way. First, we performed a literature review of the scanty data on the temperature dependence of the rates of metabolism, photosynthesis and growth of communities. In contrast to the predictions of MTE, the community activation energies did not cluster around 0.32 eV, the activation energy of photosynthesis and primary production or around 0.65 eV, the activation energy of metabolism. However, in none of the published studies the conditions were sufficiently controlled to allow firm conclusions. We therefore also performed replicated and controlled experiments using natural assemblages of marine plankton. As predicted by MTE, the maximal growth rates of community biomass increased linearly in an Arrhenius plot, with a slope close to 0.32 eV. However, a diversity of other models for the temperature dependence of community growth rates fit our data equally well. Hence, our results are at best a weak confirmation of MTE.     

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.     

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.     

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.     

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.     

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.     

Do yearly temperature cycles reduce species richness? Insights from calanoid copepods

The metabolic theory of ecology (MTE) has explained the taxonomic richness of ectothermic species as an inverse function of habitat mean temperature. Extending this theory, we show that yearly temperature cycles reduce metabolic rates of taxa having short generation times. This reduction is due to Jensen’s inequality, which results from a nonlinear dependency of metabolic rate of organisms on temperature. It leads to a prediction that relatively lower species richness is found in habitats with larger amplitudes of yearly temperature cycles where mean temperatures and other conditions are similar. We show that metabolically driven generation time of a taxon also relates functionally to species richness, and similarly, its yearly cycles reduce richness. We test these hypotheses on marine calanoid copepods with 46,377 records of data collected by scientific cruise surveys in Mediterranean regions, across which the temperature amplitudes vary dramatically. We test both bio-energetic and phenomenological effects of temperature cycles on richness in 86 1° × 1° latitudinal and longitudinal spatial units. The models incorporated the effect of both periodic fluctuations and mean temperature explained 21.6% more variation in the data, with lower AIC, compared to models incorporated only the mean temperature. The study also gives insight into the basis of energetic-equivalence rule in MTE determining richness, which can be governed by generation time of taxon. The results of this study lead to the proposition that amplitude of yearly temperature cycles may contribute to both the longitudinal and the latitudinal differences in species richness and show how the metabolic theory can explain macro-ecological patterns arising from yearly temperature cycles.     

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.     

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.     

A model for optimal offspring size in fish, including live-bearing and parental effects

Since Smith and Fretwell's seminal article in 1974 on the optimal offspring size, most theory has assumed a trade-off between offspring number and offspring fitness, where larger offspring have better survival or fitness, but with diminishing returns. In this article, we use two ubiquitous biological mechanisms to derive the shape of this trade-off: the offspring's growth rate combined with its size-dependent mortality (predation). For a large parameter region, we obtain the same sigmoid relationship between offspring size and offspring survival as Smith and Fretwell, but we also identify parameter regions where the optimal offspring size is as small or as large as possible. With increasing growth rate, the optimal offspring size is smaller. We then integrate our model with strategies of parental care. Egg guarding that reduces egg mortality favors smaller or larger offspring, depending on how mortality scales with size. For live-bearers, the survival of offspring to birth is a function of maternal survival; if the mother's survival increases with her size, then the model predicts that larger mothers should produce larger offspring. When using parameters for Trinidadian guppies Poecilia reticulata, differences in both growth and size-dependent predation are required to predict observed differences in offspring size between wild populations from high- and low-predation environments.     

Evidence that gestation duration and lactation duration are coupled traits in primates

Gestation duration and lactation duration are usually treated as independently evolving traits in primates, but the metabolic theory of ecology (MTE) suggests both durations should be determined by metabolic rate. We used phylogenetic generalized least-squares linear regression to test these different perspectives. We found that the allometries of the durations are divergent from each other and different from the scaling exponent predicted by the MTE (0.25). Gestation duration increases much more slowly (0.06 < m < 0.12), and lactation duration much more quickly (0.36 < m < 0.52) with body mass than the MTE predicts. By contrast, we found that the combined duration of gestation and lactation is consistent with the MTE''s predictions (0.22 < m < 0.35). These results suggest that gestation duration and lactation duration might best be viewed as distinct but coupled adaptations. When transferring energy to their offspring, primate mothers must meet metabolically dictated physiological requirements while optimizing the timing of the switch from gestation to lactation in relation to some as-yet-unidentified body-size-related factor.     

Metabolic theory or metabolic models?

The metabolic theory of ecology (MTE) claims to derive ecological relationships from the structure of resource distribution networks, which is assumed to determine the scaling of metabolism with body mass, and from the effect of temperature on the rate of biological processes. MTE is controversial. I propose that some of the controversy stems from the implicit adoption of different views of science by the proponents and critics of MTE. The perspective of proponents is consistent with the theory-centric view of science called the received view, whereas many of the critics implicitly adopt an alternative view consistent with a model-centric view of science. I propose that adopting the model-centric view can help to settle some of the differences among proponents and critics of MTE.     

A general model for the scaling of offspring size and adult size

Understanding evolutionary coordination among different life-history traits is a key challenge for ecology and evolution. Here we develop a general quantitative model predicting how offspring size should scale with adult size by combining a simple model for life-history evolution with a frequency-dependent survivorship model. The key innovation is that larger offspring are afforded three different advantages during ontogeny: higher survivorship per time, a shortened juvenile phase, and advantage during size-competitive growth. In this model, it turns out that size-asymmetric advantage during competition is the factor driving evolution toward larger offspring sizes. For simplified and limiting cases, the model is shown to produce the same predictions as the previously existing theory on which it is founded. The explicit treatment of different survival advantages has biologically important new effects, mainly through an interaction between total maternal investment in reproduction and the duration of competitive growth. This goes on to explain alternative allometries between log offspring size and log adult size, as observed in mammals (slope = 0.95) and plants (slope = 0.54). Further, it suggests how these differences relate quantitatively to specific biological processes during recruitment. In these ways, the model generalizes across previous theory and provides explanations for some differences between major taxa.     

Genetic variance and covariance patterns of larval development in the small white butterflyPieris rapae crucivora Boisduval

Quantitative genetic theory indicates that genetic covariance patterns among life history characters should have played an important role as genetic constraint in life history evolution. Highly positve (and negative) genetic correlations between larval development time (or larval growth rate) and adult size characters were detected by means of sib analysis for the small white butterfly Pieris rapae crucivora. The genetic associations suggested that evolution of developmental characteristics and adult phenotypic traits were constrained by pleiotropy. The positive genetic correlations between development time and adult body size may be compatible with the trade-off between them, but the negative genetic correlations between larval growth rate and adult body size are not predicted from theories of optimal energy allocation. That phenotypic correlations drastically differed from the genetic correlations indicates limitations of evolutionary inferences based only on phenotypic variation.     

Rate of egg maturation in marine turtles exhibits 'universal temperature dependence'

1. The metabolic theory of ecology (MTE) predicts that, after correcting for body mass variation among organisms, the rates of most biological processes will vary as a universal function of temperature. However, empirical support for 'universal temperature dependence' (UTD) is currently equivocal and based on studies of a limited number of traits. 2. In many ectothermic animals, the rate at which females produce mature eggs is temperature dependent and may be an important factor in determining the costs of reproduction. 3. We tested whether the rate of egg maturation in marine turtles varies with environmental temperature as predicted by MTE, using the time separating successive clutches of individual females to estimate the rate at which eggs are formed. We also assessed the phenotypic contribution to this rate, by using radio telemetry to make repeated measurements of interclutch intervals for individual green turtles (Chelonia mydas). 4. Rates of egg maturation increased with seasonally increasing water temperatures in radio-tracked green turtles, but were not repeatable for individual females, and did not vary according to maternal body size or reproductive investment (number and size of eggs produced). 5. Using a collated data set from several different populations and species of marine turtles, we then show that a single relationship with water temperature explains most of the variation in egg maturation rates, with a slope that is statistically indistinguishable from the UTD predicted by MTE. However, several alternative statistical models also described the relationship between temperature and egg maturation rates equally parsimoniously. 6. Our results offer novel support for the MTE's predicted UTD of biological rates, although the underlying mechanisms require further study. The strong temperature dependence of egg maturation combined with the apparently weak phenotypic contribution to this rate has interesting behavioural implications in ectothermic animals. We suggest that maternal thermoregulatory behaviour in marine turtles, and many other reptiles, is consistent with a strategy of adaptively increasing body temperatures to accelerate egg maturation.     

Reproductive allometry and the size-number trade-off for lizards

Fundamental to life-history theory is the assumed inverse proportionality between the number of offspring and the resource allocation per offspring. Lizards have been model organisms for empirical tests of this theory for decades; however, the expected negative relationship between clutch size and offspring size is often not detected. Here we use the approach developed by Charnov and Ernest to demonstrate that this often concealed trade-off can be made apparent in an interspecific comparison by correcting for size-dependent resource allocation. Our data set also shows a tight allometry for annual production that is consistent with life-history models for indeterminate growers. To account for nonindependence of species data we also compare the fit of nonphylogenetic and phylogenetic regression models to test for phylogenetic signal in these allometry and trade-off patterns. When combined, these results demonstrate that the offspring size/clutch size trade-off is not isolated to a single clutch but is shaped by the resource investment made over an entire year. We conclude that, across diverse lizard species, there is strong evidence for the predicted trade-off between offspring size and the annual number of eggs produced.