Dynamic energy budget theory and population ecology: lessons from Daphnia

Dynamic energy budget (DEB) theory offers a perspective on population ecology whose starting point is energy utilization by, and homeostasis within, individual organisms. It is natural to ask what it adds to the existing large body of individual-based ecological theory. We approach this question pragmatically--through detailed study of the individual physiology and population dynamics of the zooplankter Daphnia and its algal food. Standard DEB theory uses several state variables to characterize the state of an individual organism, thereby making the transition to population dynamics technically challenging, while ecologists demand maximally simple models that can be used in multi-scale modelling. We demonstrate that simpler representations of individual bioenergetics with a single state variable (size), and two life stages (juveniles and adults), contain sufficient detail on mass and energy budgets to yield good fits to data on growth, maturation and reproduction of individual Daphnia in response to food availability. The same simple representations of bioenergetics describe some features of Daphnia mortality, including enhanced mortality at low food that is not explicitly incorporated in the standard DEB model. Size-structured, population models incorporating this additional mortality component resolve some long-standing questions on stability and population cycles in Daphnia. We conclude that a bioenergetic model serving solely as a 'regression' connecting organismal performance to the history of its environment can rest on simpler representations than those of standard DEB. But there are associated costs with such pragmatism, notably loss of connection to theory describing interspecific variation in physiological rates. The latter is an important issue, as the type of detailed study reported here can only be performed for a handful of species.     

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。     

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.     

Quantitative aspects of metabolic organization: a discussion of concepts

Metabolic organization of individual organisms follows simple quantitative rules that can be understood from basic physical chemical principles. Dynamic energy budget (DEB) theory identifies these rules, which quantify how individuals acquire and use energy and nutrients. The theory provides constraints on the metabolic organization of subcellular processes. Together with rules for interaction between individuals, it also provides a basis to understand population and ecosystem dynamics. The theory, therefore, links various levels of biological organization. It applies to all species of organisms and offers explanations for body-size scaling relationships of natural history parameters that are otherwise difficult to understand. A considerable number of popular empirical models turn out to be special cases of the DEB model, or very close numerical approximations. Strong and weak homeostasis and the partitionability of reserve kinetics are cornerstones of the theory and essential for understanding the evolution of metabolic organization.     

The offspring-development-time/offspring-number trade-off

The metabolic theory of ecology (MTE) states that metabolic rate, ruled mainly by individual mass and temperature, determines many other biological rates. This view of ecology as ruled by the laws of physics and thermodynamics contrasts with life-history-optimization (LHO) theories, where traits are shaped by evolutionary processes. Integrating the MTE and LHO can lead, however, to a synthetic theory of ecology. In this work, we link the two theories to show that offspring development time is the result of both maternal investment in offspring and the metabolic constraints on offspring growth. We formulate a model that captures how offspring development time is the consequence of both offspring growth rate, determined by temperature and allometric scaling in accordance with the MTE, and the size reached by offspring at the end of the developmental period, determined mainly by LHO and reproductive strategies. We first extend the trade-off between offspring size and offspring number to ectotherms, showing that increased body temperatures result in increased resources available for reproduction. We then combine this trade-off with the general ontogenetic growth model to show that there is a trade-off between the number of offspring produced and offspring development time. The model predicts a shorter developmental time in organisms producing larger numbers of offspring.     

What is the status of metabolic theory one century after Pütter invented the von Bertalanffy growth curve?

Metabolic theory aims to tackle ecological and evolutionary problems by explicitly including physical principles of energy and mass exchange, thereby increasing generality and deductive power. Individual growth models (IGMs) are the fundamental basis of metabolic theory because they represent the organisational level at which energy and mass exchange processes are most tightly integrated and from which scaling patterns emerge. Unfortunately, IGMs remain a topic of great confusion and controversy about the origins of the ideas, their domain and breadth of application, their logical consistency and whether they can sufficiently capture reality. It is now 100 years since the first theoretical model of individual growth was put forward by Pütter. His insights were deep, but his model ended up being attributed to von Bertalanffy and his ideas largely forgotten. Here I review Pütter's ideas and trace their influence on existing theoretical models for growth and other aspects of metabolism, including those of von Bertalanffy, the Dynamic Energy Budget (DEB) theory, the Gill-Oxygen Limitation Theory (GOLT) and the Ontogenetic Growth Model (OGM). I show that the von Bertalanffy and GOLT models are minor modifications of Pütter's original model. I then synthesise, compare and critique the ideas of the two most-developed theories, DEB theory and the OGM, in relation to Pütter's original ideas. I formulate the Pütter, DEB and OGM models in the same structure and with the same notation to illustrate the major similarities and differences among them. I trace the confusion and controversy regarding these theories to the notions of anabolism, catabolism, assimilation and maintenance, the connections to respiration rate, and the number of parameters and state variables their models require. The OGM model has significant inconsistencies that stem from the interpretation of growth as the difference between anabolism and maintenance, and these issues seriously challenge its ability to incorporate development, reproduction and assimilation. The DEB theory is a direct extension of Pütter's ideas but with growth being the difference between assimilation and maintenance rather than anabolism and catabolism. The DEB theory makes the dynamics of Pütter's ‘nutritive material’ explicit as well as extending the scheme to include reproduction and development. I discuss how these three major theories for individual growth have been used to explain ‘macrometabolic’ patterns including the scaling of respiration, the temperature–size rule (first modelled by Pütter), and the connection to life history. Future research on the connections between theory and data in these macrometabolic topics have the greatest potential to advance the status of metabolic theory and its value for pure and applied problems in ecology and evolution.     

Experimental testing of dynamic energy budget models

1. Dynamic energy budget (DEB) models describing the allocation of assimilate to the competing processes of growth, reproduction and maintenance in individual organisms have been applied to a variety of species with some success. There are two contrasting model formulations based on dynamic allocation rules that have been widely used (net production and net assimilation formulations). However, the predictions of these two classes of DEB models are not easily distinguished on the basis of simple growth and fecundity data.
2. It is shown that different assumptions incorporated in the rules determining allocation to growth and reproduction in two classes of commonly applied DEB models predict qualitatively distinct patterns for an easily measured variable, cumulative reproduction by the time an individual reaches an arbitrary size.
3. A comparison with experimental data from Daphnia pulex reveals that, in their simplest form, neither model predicts the observed qualitative pattern of reproduction, despite the fact that both formulations capture basic growth features.
4. An examination of more elaborate versions of the two models, in which the allocation rules are modified to account for brief periods of starvation experienced in the laboratory cultures, reveals that a version of the net production model can predict the qualitative pattern seen for cumulative eggs as a function of mass in D. pulex . The analysis leads to new predictions which can be easily tested with further laboratory experiments.     

Parameter Estimations of Dynamic Energy Budget (DEB) Model over the Life History of a Key Antarctic Species: The Antarctic Sea Star Odontaster validus Koehler, 1906

Marine organisms in Antarctica are adapted to an extreme ecosystem including extremely stable temperatures and strong seasonality due to changes in day length. It is now largely accepted that Southern Ocean organisms are particularly vulnerable to global warming with some regions already being challenged by a rapid increase of temperature. Climate change affects both the physical and biotic components of marine ecosystems and will have an impact on the distribution and population dynamics of Antarctic marine organisms. To predict and assess the effect of climate change on marine ecosystems a more comprehensive knowledge of the life history and physiology of key species is urgently needed. In this study we estimate the Dynamic Energy Budget (DEB) model parameters for key benthic Antarctic species the sea star Odontaster validus using available information from literature and experiments. The DEB theory is unique in capturing the metabolic processes of an organism through its entire life cycle as a function of temperature and food availability. The DEB model allows for the inclusion of the different life history stages, and thus, becomes a tool that can be used to model lifetime feeding, growth, reproduction, and their responses to changes in biotic and abiotic conditions. The DEB model presented here includes the estimation of reproduction handling rules for the development of simultaneous oocyte cohorts within the gonad. Additionally it links the DEB model reserves to the pyloric caeca an organ whose function has long been ascribed to energy storage. Model parameters described a slowed down metabolism of long living animals that mature slowly. O. validus has a large reserve that—matching low maintenance costs- allow withstanding long periods of starvation. Gonad development is continuous and individual cohorts developed within the gonads grow in biomass following a power function of the age of the cohort. The DEB model developed here for O. validus allowed us to increase our knowledge on the ecophysiology of this species, providing new insights on the role of food availability and temperature on its life cycle and reproduction strategy.     

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.     

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.     

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 effects of reward quality on risk-sensitivity in Rattus norvegicus

Risk-sensitive foraging theory (RSFT) was developed to explain a choice between a variable (risk-prone) or constant (risk-averse) option. In the RSFT literature, qualitative shifts in risk-sensitivity have been explained by fluctuations in daily caloric energy budget (DEB). The DEB rule describes foragers’ choices as being based on fitness and rate of gain. If the DEB rule is correct, rewards that differ in caloric returns should cause differences in foragers’ sensitivity to risk. However, few studies have explored the influence of reward quality on risk-sensitivity in mammals. The present study was designed to examine the effects of reward quality on risk-sensitivity when reward magnitude, delay to reward, body mass, and response effort were controlled. Results from the current study demonstrated that subjects rewarded with a high calorie reward (i.e., sugar) made significantly fewer choices for a variable option than subjects rewarded with a lower calorie reward (i.e., grain). These results are consistent with the predictions of the DEB rule, and add to the RSFT literature where reward quality was manipulated by describing difference in risk-sensitivity in mammals. Suggestions for future research include an examination of risk-sensitivity where flavor and caloric return are manipulated.     

Dynamic energy budget approaches for modelling organismal ageing

Ageing is a complex multifactorial process involving a progressive physiological decline that, ultimately, leads to the death of an organism. It involves multiple changes in many components that play fundamental roles under healthy and pathological conditions. Simultaneously, every organism undergoes accumulative 'wear and tear' during its lifespan, which confounds the effects of the ageing process. The scenario is complicated even further by the presence of both age-dependent and age-independent competing causes of death. Various manipulations have been shown to interfere with the ageing process. Calorie restriction, for example, has been reported to increase the lifespan of a wide range of organisms, which suggests a strong relation between energy metabolism and ageing. Such a link is also supported within the main theories for ageing: the free radical hypothesis, for instance, links oxidative damage production directly to energy metabolism. The Dynamic Energy Budgets (DEB) theory, which characterizes the uptake and use of energy by living organisms, therefore constitutes a useful tool for gaining insight into the ageing process. Here we compare the existing DEB-based modelling approaches and, then, discuss how new biological evidence could be incorporated within a DEB framework.     

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.     

Variation in scorpion metabolic rate and rate-temperature relationships: implications for the fundamental equation of the metabolic theory of ecology

The fundamental equation of the metabolic theory of ecology (MTE) indicates that most of the variation in metabolic rate are a consequence of variation in organismal size and environmental temperature. Although evolution is thought to minimize energy costs of nutrient transport, its effects on metabolic rate via adaptation, acclimatization or acclimation are considered small, and restricted mostly to variation in the scaling constant, b(0). This contrasts strongly with many conclusions of evolutionary physiology and life-history theory, making closer examination of the fundamental equation an important task for evolutionary biologists. Here we do so using scorpions as model organisms. First, we investigate the implications for the fundamental equation of metabolic rate variation and its temperature dependence in the scorpion Uroplectes carinatus following laboratory acclimation. During 22 days of acclimation at 25 degrees C metabolic rates declined significantly (from 127.4 to 78.2 microW; P = 0.0001) whereas mean body mass remained constant (367.9-369.1 mg; P = 0.999). In field-fresh scorpions, metabolic rate-temperature (MRT) relationships varied substantially within and among individuals, and therefore had low repeatability values (tau = 0.02) and no significant among-individual variation (P = 0.181). However, acclimation resulted in a decline in within-individual variation of MRT slopes which subsequently revealed significant differences among individuals (P = 0.0031) and resulted in a fourfold increase in repeatability values (tau = 0.08). These results highlight the fact that MRT relationships can show substantial, directional variation within individuals over time. Using a randomization model we demonstrate that the reduction in metabolic rate with acclimation while body mass remains constant causes a decline both in the value of the mass-scaling exponent and the coefficient of determination. Furthermore, interspecific comparisons of activation energy, E, demonstrated significant variation in scorpions (0.09-1.14 eV), with a mean value of 0.77 eV, significantly higher than the 0.6-0.7 eV predicted by the fundamental equation. Our results add to a growing body of work questioning both the theoretical basis and empirical support for the MTE, and suggest that alternative models of metabolic rate variation incorporating explicit consideration of life history evolution deserve further scrutiny.     

Spatial patterns of species richness in New World coral snakes and the metabolic theory of ecology

The metabolic theory of ecology (MTE) has attracted great interest because it proposes an explanation for species diversity gradients based on temperature-metabolism relationships of organisms. Here we analyse the spatial richness pattern of 73 coral snake species from the New World in the context of MTE. We first analysed the association between ln-transformed richness and environmental variables, including the inverse transformation of annual temperature (1/kT). We used eigenvector-based spatial filtering to remove the residual spatial autocorrelation in the data and geographically weighted regression to account for non-stationarity in data. In a model I regression (OLS), the observed slope between ln-richness and 1/kT was ?0.626 (r² = 0.413), but a model II regression generated a much steeper slope (?0.975). When we added additional environmental correlates and the spatial filters in the OLS model, the R² increased to 0.863 and the partial regression coefficient of 1/kT was ?0.676. The GWR detected highly significant non-stationarity, in data, and the median of local slopes of ln-richness against 1/kT was ?0.38. Our results expose several problems regarding the assumptions needed to test MTE: although the slope of OLS fell within that predicted by the theory and the dataset complied with the assumption of temperature-independence of average body size, the fact that coral snakes consist of a restricted taxonomic group and the non-stationarity of slopes across geographical space makes MTE invalid to explain richness in this case. Also, it is clear that other ecological and historical factors are important drivers of species richness patterns and must be taken into account both in theoretical modeling and data analysis.     

Thermodynamic and metabolic effects on the scaling of production and population energy use

Ecosystem properties result in part from the characteristics of individual organisms. How these individual traits scale to impact ecosystem‐level processes is currently unclear. Because metabolism is a fundamental process underlying many individual‐ and population‐level variables, it provides a mechanism for linking individual characteristics with large‐scale processes. Here we use metabolism and ecosystem thermodynamics to scale from physiology to individual biomass production and population‐level energy use. Temperature‐corrected rates of individual‐level biomass production show the same body‐size dependence across a wide range of aerobic eukaryotes, from unicellular organisms to mammals and vascular plants. Population‐level energy use for both mammals and plants are strongly influenced by both metabolism and thermodynamic constraints on energy exchange between trophic levels. Our results show that because metabolism is a fundamental trait of organisms, it not only provides a link between individual‐ and ecosystem‐level processes, but can also highlight other important factors constraining ecological structure and dynamics.