General allometric equations and biomass allocation of <Emphasis Type="Italic">Pinus massoniana</Emphasis> trees on a regional scale in southern China

Applying allometric equations in combination with forest inventory data is an effective approach to use when qualifying forest biomass and carbon storage on a regional scale. The objectives of this study were to (1) develop general allometric tree component biomass equations and (2) investigate tree biomass allocation patterns for Pinus massoniana, a principal tree species native to southern China, by applying 197 samples across 20 site locations. The additive allometric equations utilized to compute stem, branch, needle, root, aboveground, and total tree biomass were developed by nonlinear seemingly unrelated regression. Results show that the relative proportion of stem biomass to tree biomass increased while the contribution of canopy biomass to tree biomass decreased as trees continued to grow through time. Total root biomass was a large biomass pool in itself, and its relative proportion to tree biomass exhibited a slight increase with tree growth. Although equations employing stem diameter at breast height (dbh) alone as a predictor could accurately predict stem, aboveground, root, and total tree biomass, they were poorly fitted to predict the canopy biomass component. The inclusion of the tree height (H) variable either slightly improved or did not in any way increase model fitness. Validation results demonstrate that these equations are suitable to estimate stem, aboveground, and total tree biomass across a broad range of P. massoniana stands on a regional scale.     

基于树木起源、立地分级和龄组的单木生物量模型

以马尾松(Pinus massoniana)和落叶松(Larix)的大样本实测资料为建模样本,以独立抽取的样本为验证样本,把样本按起源、立地和龄组进行分级,采用与材积相容的两种相对生长方程,分普通最小二乘和两种加权最小二乘,对地上部分总生物量、地上各部分生物量和地下生物量进行模型拟合和验证,使用决定系数、均方根误差、总相对误差和估计精度等8项统计量对结果进行分析。结果表明:两个树种地上部分总生物量,立地分类方法,模型的拟合结果和适用性都最优;马尾松VAR模型较优,而落叶松CAR模型较好;两种加权最小二乘方法,在建模样本和验证样本中表现得不一致。在建模样本中,加权回归2(权重函数1/f^0.5)略优于加权回归1(权重函数1/y^0.5),但在验证样本中,加权回归1却明显优于加权回归2。而同时满足建模样本拟合结果最优和验证样本检验结果最优的组合中,只有加权回归1。两个树种地上部分各分量生物量,模型拟合结果和适用性,均为干材最优,树叶最差、树枝和树皮居中,样本分类、模型类型和加权最小二乘方法对干材生物量的影响,规律和地上部分总生物量相同;样本分类、模型类型和加权最小二乘方法的最优组合,用验证样本检验的结果,总相对误差树枝不超过±10.0%,树皮不超过±5.0%,树叶马尾松不超过±30.0%,落叶松不超过±20.0%。两个树种地下部分(根)生物量,样本按龄组分类方法,模型拟合结果最优,与材积相容的模型总体上优于与地上部分总生物量相容模型。     

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.     

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.     

Scaling relationship between tree respiration rates and biomass

The WBE theory proposed by West, Brown and Enquist predicts that larger plant respiration rate, R, scales to the three-quarters power of body size, M. However, studies on the R versus M relationship for larger plants (i.e. trees larger than saplings) have not been reported. Published respiration rates of field-grown trees (saplings and larger trees) were examined to test this relationship. Our results showed that for larger trees, aboveground respiration rates R_A scaled as the 0.82-power of aboveground biomass M_A, and that total respiration rates R_T scaled as the 0.85-power of total biomass M_T, both of which significantly deviated from the three-quarters scaling law predicted by the WBE theory, and which agreed with 0.81–0.84-power scaling of biomass to respiration across the full range of measured tree sizes for an independent dataset reported by Reich et al. (Reich et al. 2006 Nature 439, 457–461). By contrast, R scaled nearly isometrically with M in saplings. We contend that the scaling exponent of plant metabolism is close to unity for saplings and decreases (but is significantly larger than three-quarters) as trees grow, implying that there is no universal metabolic scaling in plants.     

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.     

Root and stem partitioning of Pinus taeda

We measured root and stem mass at three sites (Piedmont (P), Coastal Plain (C), and Sandhills (S)) in the southeastern United States. Stand density, soil texture and drainage, genetic makeup and environmental conditions varied with site while differences in tree size at each site were induced with fertilizer additions. Across sites, root mass was about one half of stem mass when estimated on a per hectare basis. Stem mass per hectare explained 91% of the variation in root mass per hectare, while mean tree diameter at breast height (D), site, and site by measurement year were significant variables explaining an additional 6% of the variation in root mass per hectare. At the S site, the root:stem ratio decreased from 0.7 to 0.5 when mean tree D increased from 10 to 22 cm. At the P and C sites, where mean root:stem ratios were 0.40 and 0.47, respectively, no significant slope in the root:stem to mean tree D relationship was found over a more narrow range in mean tree D (12–15 and 12–18 cm, respectively). Roots were observed in the deepest layers measured (190, 190, and 290 cm for the P, C, and S sites, respectively); however, the asymptotically decreasing root mass per layer indicated the bulk of roots were measured. Root growth relative to stem growth would need to change with increased mean tree D to explain the results observed here. While these changes in growth rate among plant components may differ across sites, stem mass alone does a good job of estimating root mass across sites.     

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。     

Intraspecific mass scaling of metabolic rates in grass carp (Ctenopharyngodon idellus)

We assessed the intraspecific mass scaling of standard metabolic rate (SMR), maximum metabolic rate (MMR), excess post-exercise oxygen consumption (EPOC), and erythrocyte size in grass carp (Ctenopharyngodon idellus), with body masses ranging from 4.0 to 459 g. SMR and MMR scaled with body mass with similar exponents, but neither exponent matched the expected value of 0.75 or 1, respectively. Erythrocyte size scaled with body mass with a very low exponent (0.090), suggests that while both cell number and cell size contribute to the increase in body mass, cell size plays a smaller role. The similar slopes of MMR and SMR in grass carp suggest a constant factorial aerobic scope (FAS) as the body grows. SMR was negatively correlated with FAS, indicating a tradeoff between SMR and FAS. Smaller fish recovered faster from the exhaustive exercises, and the scaling exponent of EPOC was 1.075, suggesting a nearly isometric increase in anaerobic capacity. Our results provide support for the cell size model and suggest that variations of erythrocyte size may partly contribute to the intraspecific scaling of SMR. The scaling exponent of MMR was 0.863, suggesting that the metabolism of non-athletic fish species is less reliant on muscular energy expenditure, even during strenuous exercise.     

Development of biomass proportions in Norway spruce (Picea abies [L.] Karst.)

This study tests the hypotheses that (1) the above-ground structure of Norway spruce (Picea abies [L] Karst.) is derivable from the functional balance theory, and that (2) crown ratio is a key source of structural variation in trees of different age and social position. Twenty-nine trees were measured in three stands (young, middle-aged, and mature), with three thinning treatments (unthinned, normal, and intensive) in the two older stands. There was a strong linear relationship between the total cross-sectional area of branches and that of stem at crown base. Foliage mass was linearly related with stem basal area at crown base. Also an allometric relationship was found between foliage mass and crown length. The mean length (weighted by basal area) of branches obeyed an exponential function of crown length. The parameters of most of these relationships were independent of slenderness (tree height/breast height diameter) and tree age However, total branch cross-sectional area per stem cross-sectional area in the young trees was greater than in the older trees. The young trees also had slightly shorter branches than predicted by the mean branch length equation. This was probably caused by branch senescence which had not yet started in the young stand. The older trees had a relatively long lower crown segment which was growing slowly and senescing. It was proposed that a segmented crown structure is characteristic of shade tolerant tree species, and that the structural model could be further developed by making the two segments explicit.     

Effects of experimental warming on growth,biomass allocation,and needle chemistry of <Emphasis Type="Italic">Abies faxoniana</Emphasis> in even-aged monospecific stands

The response and adaption mechanisms of seedlings under long-term warming have remained largely unknown. In this study, we investigated the effects of warming for 6 years on growth, and needle carbon, nitrogen, chlorophyll, and carbohydrate levels in a coniferous tree species, Abies faxoniana. Seedlings were grown in even-aged monospecific stands under ambient and warming (ambient +2.2°C) temperature in climate control chambers. Warming caused statistically significant increases in the specific leaf area, leaf area ratio, root biomass, leaf biomass, branch biomass, stem biomass, and total mass of the seedlings, and reduced the root/shoot ratio. Warming also increased total chlorophyll concentrations, specific chlorophyll pigments, and Chlorophyll a/b ratios in both studied needle age classes. In addition, C/N ratios of current-year and 1-year-old needles increased by warming. In contrast, warming decreased the levels of N, sugar, cellulose, and starch in needles, while warming had no effect on the height, stem diameter, needle mass ratio, root mass ratio, and root/needle ratio. We conclude that warming increases branch growth and changes needle chemistry, which enhances the light capture potential of seedlings.     

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。     

不同林龄和密度马尾松人工林针叶和根系的生态化学计量特征

为了解不同林龄和密度马尾松人工林针叶和根系的养分变化特征,该文在广西南宁市横县镇龙林场选择了四种林龄(幼龄林、中龄林、成熟林和过熟林)和四种密度(低密度林、中低密度林、中高密度林和高密度林)马尾松林共八种林分,分析了马尾松针叶和根系的C、N、P含量和比值及其与土壤养分的关系。结果表明:(1)所有龄林与密度林的马尾松针叶N∶P比值均大于16,表明该地区马尾松明显受P限制,幼龄林更加明显。(2)马尾松针叶C含量随着林龄增长逐渐增大后下降,N与P含量呈微弱下降趋势,导致C∶N比值、C∶P比值和N∶P比值呈微弱上升趋势,但没达到显著水平;根系C含量、P含量和C∶N比值逐渐增大,N含量、C∶P比值和N∶P比值呈U字型且都在幼龄林最大;针叶和根系在成熟林阶段均具有较高的P含量和最高的C含量。(3)中密度林的马尾松针叶的C和N含量较高且P含量最高,C∶N比值较低且C∶P比值和N∶P比值最低;根系的C、N和P含量较高,而C∶N比值、C∶P比值和N∶P比值较低。(4)马尾松的根系养分尤其是P含量在不同龄林和不同密度林之间的变化比针叶更加剧烈,且其与土壤养分之间的相关性比针叶更强。综上结果表明,马尾松人工林受P限制,在低龄林加强P肥管理和选择合适的林分密度(中等密度)则有利于缓解马尾松受P限制的状态。     

Nitrogen acquisition,net production and allometry of <Emphasis Type="Italic">Alnus fruticosa</Emphasis> at a young moraine in Koryto Glacier Valley,Kamchatka, Russian Far East

Alders (Alnus spp.) often dominate at nutrient-poor sites by symbiotic relations with atmospheric nitrogen-fixing bacteria. However, little is known about quantitative relationships between root nodule as a nitrogen acquisition organ and leaf as a carbon acquisition organ. To examine carbon allocation, nitrogen acquisition and net production in nutrient-poor conditions, we examined allocation patterns among organs of shrub Alnus fruticosa at a young 80-year-old moraine in Kamchatka. Slopes of double-log allometric equations were significantly smaller than 1.0 for the root mass, leaf mass and root nodule mass against stem mass, and for the root nodule mass against root mass, indicating that smaller individuals invested disproportionally more biomass into resource-acquiring leaf and root tissues than to supportive tissues compared to older individuals. The slope of allometric equation of root depth against stem height was 0.542, indicating that smaller/younger individuals allocate disproportionally more biomass into root length growth than stem height growth. On the contrary, the root nodule mass isometrically scaled to leaf mass. The whole-plant nitrogen content also isometrically scaled to root nodule mass, indicating that a certain ratio of nitrogen acquisition depended on root nodules, irrespective of plant size. Although the net production per plant increased with the increase in stem mass, the slope of the double-log regression was smaller than 1.0. On the contrary, the net production per plant isometrically increased with leaf mass, root nodule mass and leaf nitrogen content per plant. Since the leaf mass isometrically scaled to root nodule mass, growth of each individual occurred at the leaves and root nodules in a coordinated manner. It is suggested that their isometric increase contributes to the increase in net production per plant for A. fruticosa in nutrient-poor conditions.     

Growth of Typha latifolia in boreal forest habitats,as measured by double sampling

Seasonal growth of Typha latifolia L. stands in five oxbow lakes of the Athabasca River in the boreal forest zone of Alberta, Canada, was monitored by both the harvest technique and double sampling by regression. The technique for calculating mean biomass and variance for the double sampling procedure is described. The relationship between stem weight and height was linear for flowering stems, but a logarithmic transformation of weight was used for the non-flowering stem regressions. Growth began in late May and stems reached maximum weight by mid-August. Stem mortality (up to 14%) was highest at sites with high stem density, but mortality was limited to small stems at all sites. Total biomass of these stems was less than 4% of the peak above-ground standing crop. In nutrient-poor sites, Typha was found on floating organic mats, but in more nutrient rich sites on grounded substrates. Peak above-ground biomass ranged from 456 to 848 g m^?2, generally in response to the successional and nutrient status of the oxbow lake. Sites returned to an earlier stage of succession by flooding had larger stems and greater biomass.     

Effects of age and site quality on the distribution of biomass in Scots pine (Pinus sylvestris L.)

The distribution of the above-ground and below-ground biomass of Scots pine in southern Finland were investigated in trees of different ages (18–212 years) from two types of growth site. Secondly, some structural regularities were tested for their independence of age and growth site. Trees were sampled from dominant trees which could be expected to have a comparable position in stands of all ages. All stands were on sorted sediments. The biomass of the sample trees (18 trees) was divided into needles, branch sapwood and heartwood, stem sapwood and heartwood, stem bark, stump, large roots (diameter >20 cm), coarse roots (five classes) and fine roots. The amount of sapwood and heartwood was also estimated from the below-ground compartments. Trees on both types of growth site followed the same pattern of development of the relative shares of biomass compartments, although the growth rates were faster on the more fertile site. The relative amount of sapwood peaked after canopy closure, coinciding with the start of considerable heartwood accumulation. The relative amount of needles and fine roots decreased with age. The same was true of branches but to a lesser degree. The relative share of the below-ground section was independent of tree age. Foliage biomass and sapwood cross-sectional area were linearly correlated, but there were differences between the growth sites. Needle biomass was linearly correlated with crown surface area. The fine root to foliage biomass ratio showed an increasing trend with tree age.     

Scaling Relationships between Leaf Mass and Total Plant Mass across Chinese Forests

Biomass partitioning is important for illustrating terrestrial ecosystem carbon flux. West, Brown and Enquist (WBE) model predicts that an optimal 3/4 allometric scaling of leaf mass and total biomass of individual plants will be applied in diverse communities. However, amount of scientific evidence suggests an involvement of some biological and environmental factors in interpreting the variation of scaling exponent observed in empirical studies. In this paper, biomass information of 1175 forested communities in China was collected and categorized into groups in terms of leaf form and function, as well as their locations to test whether the allocation pattern was conserved or variable with internal and/or environmental variations. Model Type II regression protocol was adopted to perform all the regressions. The results empirically showed that the slopes varied significantly across diverse forested biomes, between conifer and broadleaved forests, and between evergreen and deciduous forests. Based on the results, leaf form and function and their relations to environments play a significant role in the modification of the WBE model to explore more accurate laws in nature.     

Allometric theory and the mechanical stability of large trees: proof and conjecture

Recent allometric theory has postulated that standing leaf mass will scale as the 3/4 power of stem mass and as the 3/4 power of root mass such that stem mass scales isometrically with respect to root mass across very large vascular plant species with self-supporting stems. We show that the isometric scaling of stem mass with respect to root mass (i.e., M(S) ∝ M(R)) can be derived directly from mechanical theory, specifically from the requirement that wind-induced bending moments acting at the base of stems must be balanced by a counter-resisting moment provided by the root system to prevent uprooting. This derivation provides indirect verification of the allometric theory. It also draws attention to the fact that leaf, stem, and root biomass partitioning patterns must accommodate the simultaneous performance of manifold functional obligations.     

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.