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。     

Sanio's laws revisited. Size-dependent changes in the xylem architecture of trees

Early observations led Sanio [ Wissen. Bot. , 8 , (1872) 401] to state that xylem conduit diameters and lengths in a coniferous tree increase from the apex down to a height below which they begin to decrease towards the tree base. Sanio's law of vertical tapering has been repeatedly tested with contradictory results and the debate over the scaling of conduit diameters with distance from the apex has not been settled. The debate has recently acquired new vigour, as an accurate knowledge of the vertical changes in wood anatomy has been shown to be crucial to scaling metabolic properties to plant and ecosystem levels. Contrary to Sanio's hypothesis, a well known model (MST, metabolic scaling theory) assumes that xylem conduits monotonically increase in diameter with distance from the apex following a power law. This has been proposed to explain the three-fourth power scaling between size and metabolism seen across plants. Here, we (i) summarized available data on conduit tapering in trees and (ii) propose a new numerical model that could explain the observed patterns. Data from 101 datasets grouped into 48 independent profiles supported the notions that phylogenetic group (angiosperms versus gymnosperms) and tree size strongly affected the vertical tapering of conduit diameter. For both angiosperms and gymnosperms, within-tree tapering also varied with distance from the apex. The model (based on the concept that optimal conduit tapering occurs when the difference between photosynthetic gains and wall construction costs is maximal) successfully predicted all three major empirical patterns. Our results are consistent with Sanio's law only for large trees and reject the MST assumptions that vertical tapering in conduit diameter is universal and independent of rank number.     

An empirical assessment of tree branching networks and implications for plant allometric scaling models

Several theories predict whole‐tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self‐similar within trees. However, differences among scaling exponents calculated at node‐ and whole‐tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.     

代谢异速生长理论及其在微生物生态学领域的应用

新陈代谢是生物的基本生理过程,影响生物在不同环境中参与物质循环和能量转化的过程.代谢速率作为生物体重要的生命过程指标,几乎影响所有的生物活性速率,且在很多研究中均表现出异速生长现象.所谓代谢异速是指生物体代谢速率与其个体大小(或质量)之间存在的幂函数关系.代谢异速生长理论的提出,从机制模型角度解释了代谢异速关系这一普遍存在的生命现象.该理论利用分形几何学及流体动力学等原理,从生物能量学角度阐释了异速生长规律的机理,证实了3/4权度指数的存在;但同时有研究表明,权度指数因环境因素等影响处于2/3-1范围之间而非定值.随着研究工作的深入,代谢异速生长理论研究从起初的宏观动植物领域拓展到了微生物领域,在研究微生物的代谢异速生长理论时,可将微生物的可操作分类单元(Operational taxonomic unit,OTU)或具有特定功能的功能群视为一个微生物个体,基于其遗传多样性和功能多样性特征进行表征,以便于将微生物群落多样性与其生态功能性联系起来,使该理论在微生物生态学领域得到有效的补充和完善.尽管细菌具有独特的生物学特性,但与宏观生物系统中观测到的现象表现出明显的一致性.有研究表明,3个农田土壤细菌基于遗传多样性的OTU数的平均周转率分别为0.71、0.80和0.84,介于2/3与1之间,可能与生物代谢异速指数有一定关联,为微生物代谢异速指数的研究提出了一个参考解决方案.鉴于微生物个体特征和生物学特性,在分析代谢速率与个体大小关系中,从微生物单位个体的定义、个体大小表征到计量单位的统一,仍需更多的理论支持.分析了代谢异速生长理论在微生物与生态系统功能关系研究中的可能应用,延伸了该理论的应用范围,并对尚待加强的研究问题进行了评述和展望.     

Towards an integration of ecological stoichiometry and the metabolic theory of ecology to better understand nutrient cycling

Ecologists have long recognized that species are sustained by the flux, storage and turnover of two biological currencies: energy, which fuels biological metabolism and materials (i.e. chemical elements), which are used to construct biomass. Ecological theories often describe the dynamics of populations, communities and ecosystems in terms of either energy (e.g. population-dynamics theory) or materials (e.g. resource-competition theory). These two classes of theory have been formulated using different assumptions, and yield distinct, but often complementary predictions for the same or similar phenomena. For example, the energy-based equation of von Bertalanffy and the nutrient-based equation of Droop both describe growth. Yet, there is relatively little theoretical understanding of how these two distinct classes of theory, and the currencies they use, are interrelated. Here, we begin to address this issue by integrating models and concepts from two rapidly developing theories, the metabolic theory of ecology and ecological stoichiometry theory. We show how combining these theories, using recently published theory and data along with new theoretical formulations, leads to novel predictions on the flux, storage and turnover of energy and materials that apply to animals, plants and unicells. The theory and results presented here highlight the potential for developing a more general ecological theory that explicitly relates the energetics and stoichiometry of individuals, communities and ecosystems to subcellular structures and processes. We conclude by discussing the basic and applied implications of such a theory, and the prospects and challenges for further development.     

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.     

A test of the metabolic theory of ecology with two longevity data sets reveals no common cause of scaling in biological times

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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.     

Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests

The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 old-growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory's predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests.     

Testing the Metabolic Scaling Theory of tree growth

1.  Metabolic Scaling Theory (MST) predicts a 'universal scaling law' of tree growth. Proponents claim that MST has strong empirical support: the size-dependent growth curves of 40 out of 45 species in a Costa Rican forest have scaling exponents indistinguishable from the MST prediction.
2.  Here, we show that the Costa Rican study has been misinterpreted. Using Standardized Major Axis (SMA) line-fitting to estimate scaling exponents, we find that four out of five species represented by more than 100 stems have scaling exponents that deviate significantly from the MST prediction. On the other hand, sample sizes were too small to make strong inferences in the cases of 33 species represented by fewer than 50 stems.
3.  Recently, it has been argued that MST is useful for predicting average scaling exponents, even if individual species do not conform to the theory. We find that the mean scaling exponent of the Costa Rican trees is greater than predicted (across-species mean  =  0.44), and hypothesize that scaling exponents in natural forests will generally be greater than predicted, because the theory fails to model asymmetric competition for light.
4.   Synthesis . We highlight shortcomings in the interpretation of data used in support of a key MST prediction. We recommend that future research into biological scaling should compare the merits of alternative models rather than focusing attention on tests of a single theory.     

Plant physiology in theory and practice: An analysis of the WBE model for vascular plants

The theoretical model of West, Brown and Enquist (hereafter WBE) proposed the fractal geometry of the transport system as the origin of the allometric scaling laws observed in nature. The WBE model has either been criticized for some restrictive and biologically unrealistic constraints or its reliability debated on the evidence of empirical tests. In this work, we revised the structure of the WBE model for vascular plants, highlighting some critical assumptions and simplifications and discuss them with regard to empirical evidence from plant anatomy and physiology. We conclude that the WBE model had the distinct merit of shedding light on some important features such as conduit tapering. Nonetheless, it is over-simplistic and a revised model would be desirable with an ontogenetic perspective that takes some important phenomena into account, such as the transformation of the inner sapwood into heartwood and the effect of hydraulic constraints in limiting the growth in height.     

Latitude,tree species diversity and the metabolic theory of ecology

The latitudinal diversity gradient (LDG) has been known for over a century, but its origin remains poorly understood. Because both latitude and species richness are broadly related to temperature, environmental temperature has been proposed as a driver of the LDG. Recently, Wang et al. (2009, Proceedings of the National Academy of Sciences USA, 106 ,13388–13392) used datasets compiled from tree distributions in eastern Asia and North America to compare the species richness?temperature relationship between the two regions at several spatial scales and framed their analyses in the context of the metabolic theory of ecology. Here, we show that their datasets lack comparability between eastern Asia and North America and that some aspects of their analyses probably biased their results, casting doubt on some of their conclusions.     

植物代谢速率与个体生物量关系研究进展

植物的各项生理生态功能（例如,呼吸、生长和繁殖）都与个体生物量成异速生长关系。West, Brown及Enquist基于分形网络结构理论所提出的WBE模型认为：植物的代谢（呼吸）速率正比于个体生物量的3/4次幂。然而,恒定的“3/4异速生长指数”与实测数据、植物生理生态学等研究之间存在矛盾,引发激烈的争论。论文分析了不同回归方法对代谢指数的影响,重点对植物代谢速率与个体生物量异速生长关系研究进展进行了综述,分析并得出了植物代谢指数在小个体时接近1.0,并随着生物量的增加而系统减小,且其密切依赖于氮含量的调控的结论。据此,提出了进一步深入研究植物代谢速率个体生物量关系需要解决的一些科学问题。     

Computer simulations support a core prediction of a contentious plant model

? Premise of the study: An overarching but vigorously debated plant model proposed by the West, Brown, Enquist (WBE) theory predicts the scaling relationships for numerous botanical phenomena. However, few studies have evaluated this model's basic assumptions, one of which is that natural selection has resulted in hierarchal networks that minimize the energy required to distribute nutrients internally and have thus produced highly efficient organisms. ? Methods: If these core assumptions are correct, an "idealized" plant complying with all of the scaling relationships emerging from the WBE plant model should rapidly outcompete other plants, even those that differ slightly from it. To test this reasoning, a computer model was used to simulate competition between an idealized WBE plant, a generic "average" angiosperm (GA), and one of seven variants of the idealized WBE plant, each being similar to the GA in one of the GA's scaling parameters. ? Key results: Replicate simulations show that the idealized WBE plant rapidly outcompetes all other plants under light-shade and open-field conditions. However, changing only one of the WBE's scaling parameters results in death or in the coexistence of WBE and GA plants. ? Conclusions: These simulations support a core assumption of the WBE plant model and suggest why this idealized plant has not evolved.     

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.     

Effects of metabolic rate on protein evolution

Since the modern evolutionary synthesis was first proposed early in the twentieth century, attention has focused on assessing the relative contribution of mutation versus natural selection on protein evolution. Here we test a model that yields general quantitative predictions on rates of protein evolution by combining principles of individual energetics with Kimura's neutral theory. The model successfully predicts much of the heterogeneity in rates of protein evolution for diverse eukaryotes (i.e. fishes, amphibians, reptiles, birds, mammals) from different thermal environments. Data also show that the ratio of non-synonymous to synonymous nucleotide substitution is independent of body size, and thus presumably of effective population size. These findings indicate that rates of protein evolution are largely controlled by mutation rates, which in turn are strongly influenced by individual metabolic rate.