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。     

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。     

7种木本植物的分支指数与代谢指数

West、Brown和Enquist提出的植物分形网络模型(简称WBE模型)认为: 植物的分支指数(1/a, 1/b)决定植物的代谢指数, 当分支指数1/a、1/b分别为理论值2.0、3.0时, 代谢速率与个体大小的3/4次幂成正比, 但是恒定的3/4代谢指数并不能全面地反映植物的代谢情况。基于分支指数的协同变化, Price、Enquist和Savage对WBE模型进行扩展, 提出植物分支参数协同变化模型(简称PES模型)。该文借助于PES模型分析了7种木本植物的分支指数和代谢指数。结果表明: 物种间叶面积与叶生物量呈异速生长关系, 基于叶面积得到的分支指数1/a和代谢指数θ在物种间无显著差异, 基于叶生物量得到的分支指数1/a、1/b和代谢指数θ在物种间均存在显著差异, 但基于叶面积和叶生物量分别拟合出的整体分支指数1/a、1/b和代谢指数θ与理论值均无显著差异, 且用叶面积作为代谢速率的替代指标比用叶生物量分析得出的代谢指数与理论值更接近。今后研究应当关注植物叶面积与叶生物量的异速生长关系对植物代谢速率及相关功能特性的影响。     

Branching and metabolic exponents in seven woody plants

West、Brown和Enquist提出的植物分形网络模型(简称WBE模型)认为: 植物的分支指数(1/a, 1/b)决定植物的代谢指数, 当分支指数1/a、1/b分别为理论值2.0、3.0时, 代谢速率与个体大小的3/4次幂成正比, 但是恒定的3/4代谢指数并不能全面地反映植物的代谢情况。基于分支指数的协同变化, Price、Enquist和Savage对WBE模型进行扩展, 提出植物分支参数协同变化模型(简称PES模型)。该文借助于PES模型分析了7种木本植物的分支指数和代谢指数。结果表明: 物种间叶面积与叶生物量呈异速生长关系, 基于叶面积得到的分支指数1/a和代谢指数θ在物种间无显著差异, 基于叶生物量得到的分支指数1/a、1/b和代谢指数θ在物种间均存在显著差异, 但基于叶面积和叶生物量分别拟合出的整体分支指数1/a、1/b和代谢指数θ与理论值均无显著差异, 且用叶面积作为代谢速率的替代指标比用叶生物量分析得出的代谢指数与理论值更接近。今后研究应当关注植物叶面积与叶生物量的异速生长关系对植物代谢速率及相关功能特性的影响。     

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Scaling, as the translation of information across spatial, temporal, and organizational scales, is essential to predictions and understanding in all sciences and has become a central issue in ecology. A large body of theoretical and empirical evidence concerning allometric scaling in terrestrial individual plants and plant communities has been constructed around the fractal volume-filling theory of West, Brown, and Enquist （the WBE model）. One of the most thought-provoking findings has been that the metabolic rates of plants, like those of animals, scale with their size as a 3/4 power law. The earliest, single most-important study cited in support of the application of the WBE model to terrestrial plants claims that whole-plant resource use in terrestrial plants scales as the 3/4 power of total mass, as predicted by the WBE model. However, in the present study we show that empirical data actually do not support such a claim. More recent studies cited as evidence for 3/4 scaling also suffer from several statistical and data-related problems. Using a forest biomass dataset including 1 266 plots of 17 main forest types across China, we explored the scaling exponents between tree productivity and tree mass and found no universal value across forest stands. We conclude that there is not sufficient evidence to support the existence of a single constant scaling exponent for the metabolism-biomass relationship for terrestrial plants.     

Sizing up allometric scaling theory

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks-the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets.     

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Scaling, as the translation of information across spatial, temporal, and organizational scales, is essential to predictions and understanding in all sciences and has become a central issue in ecology. A large body of theoretical and empirical evidence concerning allometric scaling in terrestrial individual plants and plant communities has been constructed around the fractal volume-filling theory of West, Brown, and Enquist (the WBE model). One of the most thought-provoking findings has been that the metabolic rates of plants, like those of animals, scale with their size as a 3/4 power law. The earliest, single most-important study cited in support of the application of the WBE model to terrestrial plants claims that whole-plant resource use in terrestrial plants scales as the 3/4 power of total mass, as predicted by the WBE model.However, in the present study we show that empirical data actually do not support such a claim. More recent studies cited as evidence for 3/4 scaling also suffer from several statistical and data-related problems. Using a forest biomass dataset including 1 266 plots of 17 main forest types across China, we explored the scaling exponents between tree productivity and tree mass and found no universal value across forest stands. We conclude that there is not sufficient evidence to support the existence of a single constant scaling exponent for the metabolism-biomass relationship for terrestrial plants.     

The Scaling Relationships between Leaf Mass and Leaf Area of Vascular Plant Species Change with Altitude

The scaling relationship between leaf dry mass and leaf surface area has important implications for understanding the ability of plants to harvest sunlight and grow. Whether and how the scaling relationships vary across environmental gradients are poorly understood. We analyzed the scaling relationships between leaf mass and leaf area of 121 vascular plant species along an altitudinal gradient in a subtropical monsoon forest. The slopes increased significantly with altitude, it varied from less than 1 at low altitude to more than 1 at high altitude. This means that plants growing at high altitude allocate proportionately more biomass to support tissues in larger leaves and less in smaller leaves, whereas the reverse is true at low altitude. This pattern can be explained by different leaf strategies in response to environmental pressure and constrains.     

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.     

Allometric scaling among tree components in Pinus massoniana stands with different sites

The WBE model was used to predict intraspecific scaling relationships among mean branch, needle, stem, root, and above-ground masses across eight stands of Pinus massoniana to test whether the scaling exponent was (1) dependent on site and (2) in accordance with WBE theory. The results showed that mean stem and root masses as well as mean above-ground and root masses scaled in a near-isometric manner across sites, except at two sites, which exhibited an exponent slightly less than unity. Mean needle mass scaled as 3/4 power of mean stem mass, except at one site, which exhibited an exponent slightly higher than 3/4. Mean branch mass scaled isometrically with mean stem mass at each site. These results supported the WBE theory. However, mean branch mass across sites scaled neither as 3/4 nor 1 power of mean stem mass, indicating that the scaling relationship predicted by WBE theory for these two components did not hold in P. massoniana stands.     

Foliar production and decomposition rates in urban forests invaded by the exotic invasive shrub, <Emphasis Type="Italic">Lonicera maackii</Emphasis>

Exotic invasive shrubs can form dense monocultures in forest understories, which can have cascading effects on ecosystem structure and function. Amur honeysuckle, an exotic shrub that forms dense canopies in eastern forests, has the potential to alter plant community structure and ecosystem functions, such as primary production and decomposition. The goal of this study was to examine foliar productivity and leaf litter decomposition in forests invaded by Amur honeysuckle (Lonicera maackii) and to determine the extent to which the presence of this dominant exotic species may alter ecosystem function in these forests. We found that forests invaded by Amur honeysuckle had 16 times greater honeysuckle foliar biomass and 1.5 times lower total foliar biomass than forests of equivalent tree basal area, but having few honeysuckle shrubs. This suggests that productivity of native tree and shrub species may be reduced where honeysuckle density is high. Additionally, honeysuckle litter decayed four times faster and released nitrogen more rapidly than sugar maple litter, and sugar maple litter decayed 19% faster in forests invaded by Amur honeysuckle. These findings suggest that forests invaded by Amur honeysuckle may exhibit lower rates of organic matter accrual and less nitrogen retention in the forest floor. Since honeysuckle leaves develop in early spring before those of other shrubs or trees in the area, the rapid release of nitrogen from honeysuckle litter that we measured in early spring is timed to benefit this invasive species. The temporally coincident phenologies of nitrogen release during decomposition with the foliar growth needs of this shrub indicates that a potential positive feedback loop may exist between these processes that promotes continued growth and dominance of honeysuckle shrubs in these forested systems.     

干热河谷草本植物生物量分配及其对环境因子的响应

以干热河谷6种草本植物为对象,研究了水分、养分、刈割对生物量在根、茎、叶的分配及异速生长关系的影响.结果表明:刈割处理叶生物量质量分数从25.1%显著增加到31.2%,茎生物量质量分数从43.7%显著降低到34.2%;养分添加处理根生物量质量分数从34.0%显著降低到30.8%;水分处理对生物量分配没有显著影响.物种对根、茎、叶生物量分配有显著影响,适应贫瘠土壤的物种将更多生物量分配给叶和根,对茎生物量的分配相对较低.物种与环境因子存在显著的互作效应,表明环境因子对不同物种的生物量分配影响不同.适应贫瘠土壤的物种叶-茎标度指数和异速生长常数大于其他物种,而茎-根标度指数和异速生长常数小于其他物种.养分显著增加了叶-茎和叶-根的异速生长常数,刈割显著降低了茎-根的标度指数,水分处理则没有显著效应.环境因素对器官间异速生长关系的影响存在种间差异.生物量分配的种间差异及其对环境因素的响应特征可能对植物适应环境变化产生重要影响.     

Soil Respiration and Belowground Carbon Allocation in Mangrove Forests

Mangrove forests cover large areas of tropical and subtropical coastlines. They provide a wide range of ecosystem services that includes carbon storage in above- and below ground biomass and in soils. Carbon dioxide (CO₂) emissions from soil, or soil respiration is important in the global carbon budget and is sensitive to increasing global temperature. To understand the magnitude of mangrove soil respiration and the influence of forest structure and temperature on the variation in mangrove soil respiration I assessed soil respiration at eleven mangrove sites, ranging from latitude 27°N to 37°S. Mangrove soil respiration was similar to those observed for terrestrial forest soils. Soil respiration was correlated with leaf area index (LAI) and aboveground net primary production (litterfall), which should aid scaling up to regional and global estimates of soil respiration. Using a carbon balance model, total belowground carbon allocation (TBCA) per unit litterfall was similar in tall mangrove forests as observed in terrestrial forests, but in scrub mangrove forests TBCA per unit litter fall was greater than in terrestrial forests, suggesting mangroves allocate a large proportion of their fixed carbon below ground under unfavorable environmental conditions. The response of soil respiration to soil temperature was not a linear function of temperature. At temperatures below 26°C Q10 of mangrove soil respiration was 2.6, similar to that reported for terrestrial forest soils. However in scrub forests soil respiration declined with increasing soil temperature, largely because of reduced canopy cover and enhanced activity of photosynthetic benthic microbial communities.     

Metabolic scaling in insects supports the predictions of the WBE model

The functional association between body size and metabolic rate (BS-MR) is one of the most intriguing issues in ecological physiology. An average scaling exponent of 3/4 is broadly observed across animal and plant taxa. The numerical value of 3/4 is theoretically predicted under the optimized version of West, Brown, and Enquist's vascular resource supply network model. Insects, however, have recently been proposed to express a numerically different scaling exponent and thus application of the WBE network model to insects has been rejected. Here, we re-analyze whether such variation is indeed supported by a global deviation across all insect taxa at the order and family levels to assess if specific taxa influence insect metabolic scaling. We show that a previous reported deviation is largely due to the effect of a single insect family (Termitidae). We conclude that the BS-MR relationship in insects broadly supports the core predictions of the WBE model. We suggest that the deviation observed within the termites warrants further investigation and may be due to either difficulty in accurately measuring termite metabolism and/or particularities of their life history. Future work on allometric scaling should assess the nature of variation around the central tendencies in scaling exponents in order to test if this variation is consistent with core assumptions and predictions of the WBE model that stem by relaxing its secondary optimizing assumptions that lead to the 3/4 exponent.     

Relationships among the Stem, Aboveground and Total Biomass across Chinese Forests

Forest biomass plays a key role in the global carbon cycle. In the present study, a general allometric model was derived to predict the relationships among the stem biomass Ms, aboveground biomass MA and total biomass MT, based on previously developed scaling relationships for leaf, stem and root standing biomass. The model predicted complex scaling exponents for MT and/or MA with respect to Ms. Because annual biomass accumulation in the stem, root and branch far exceeded the annual increase in standing leaf biomass, we can predict that MT ∝MA ∝ Ms as a simple result of the model. Although slight variations existed in different phyletic affiliations （i.e. conifers versus angiosperms）, empirical results using Model Type Ⅱ （reduced major axis） regression supported the model＇s predictions. The predictive formulas among stem, aboveground and total biomass were obtained using Model Type I （ordinary least squares） regression to estimate forest biomass. Given the low mean percentage prediction errors for aboveground （and total biomass） based on the stem biomass, the results provided a reasonable method to estimate the biomass of forests at the individual level, which was insensitive to the variation in local environmental conditions （e.g. precipitation, temperature, etc.）.     

On the vegetative biomass partitioning of seed plant leaves, stems, and roots

A central goal of comparative life-history theory is to derive the general rules governing growth, metabolic allocation, and biomass partitioning. Here, we use allometric theory to predict the relationships among annual leaf, stem, and root growth rates (GL, GS, and GR, respectively) across a broad spectrum of seed plant species. Our model predicts isometric scaling relationships among all three organ growth rates: GL is proportional to GS is proportional to GR. It also provides a conceptual basis for understanding the differences in the absolute amounts of biomass allocated to construct the three organ types. Analyses of a large compendium of biomass production rates across diverse seed plant species provide strong statistical support for the predictions of the theory and indicate that reproductive investments may scale isometrically with respect to vegetative organ growth rates. The general rules governing biomass allocation as indexed by the scaling exponents for organ growth rates are remarkably indifferent to plant size and taxonomic affiliation. However, the allometric "constants" for these relationships differ numerically as a function of phenotypic features and local environmental conditions. Nonetheless, at the level of both inter- and intraspecific comparisons, the same proportional biomass allocation pattern holds across extant seed plant species.     

Allometric scaling laws for water uptake by plant roots

This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as . (2) The basic allometric scaling for root radius branches (r_i+1=β*r_i) is of the form , where f(N)=A(N)/(n_b*(1+A(N))), n_b is the number of branches, and A(N) and ε(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, β converges to the β from the WBE model. For small N, the β's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.     

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.     

Ecological importance of large-diameter trees in a temperate mixed-conifer forest

Large-diameter trees dominate the structure, dynamics and function of many temperate and tropical forests. Although both scaling theory and competition theory make predictions about the relative composition and spatial patterns of large-diameter trees compared to smaller diameter trees, these predictions are rarely tested. We established a 25.6 ha permanent plot within which we tagged and mapped all trees ≥1 cm dbh, all snags ≥10 cm dbh, and all shrub patches ≥2 m(2). We sampled downed woody debris, litter, and duff with line intercept transects. Aboveground live biomass of the 23 woody species was 507.9 Mg/ha, of which 503.8 Mg/ha was trees (SD?=?114.3 Mg/ha) and 4.1 Mg/ha was shrubs. Aboveground live and dead biomass was 652.0 Mg/ha. Large-diameter trees comprised 1.4% of individuals but 49.4% of biomass, with biomass dominated by Abies concolor and Pinus lambertiana (93.0% of tree biomass). The large-diameter component dominated the biomass of snags (59.5%) and contributed significantly to that of woody debris (36.6%). Traditional scaling theory was not a good model for either the relationship between tree radii and tree abundance or tree biomass. Spatial patterning of large-diameter trees of the three most abundant species differed from that of small-diameter conspecifics. For A. concolor and P. lambertiana, as well as all trees pooled, large-diameter and small-diameter trees were spatially segregated through inter-tree distances <10 m. Competition alone was insufficient to explain the spatial patterns of large-diameter trees and spatial relationships between large-diameter and small-diameter trees. Long-term observations may reveal regulation of forest biomass and spatial structure by fire, wind, pathogens, and insects in Sierra Nevada mixed-conifer forests. Sustaining ecosystem functions such as carbon storage or provision of specialist species habitat will likely require different management strategies when the functions are performed primarily by a few large trees as opposed to many smaller trees.     

Challenges to the generality of WBE theory

The West, Brown and Enquist (WBE) theory has attracted great interest because it makes general predictions about scaling of ecological processes with body size. Recent research by Muller-Landau and co-workers challenges the generality of this theory by showing that demographic processes in natural forests do not scale in the way that the theory predicts. For WBE theory to be relevant to plant community dynamics, more complex models are required to deal with the influences of competition for light, nutrient supply and disturbance experienced by such communities.