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。     

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。     

塔克拉玛干沙漠南缘三种防护林植物根系构型及其生态适应策略

采用全根挖掘法挖取塔克拉玛干沙漠南缘3种主要防护林植物种——多枝柽柳(Tamarix ramosissima)、梭梭(Haloxylon ammodendron)和新疆杨(Populus albavar. pyramidalis)成年植株根系, 测定并分析了根系构型及其拓扑结构。结果表明: 1)多枝柽柳和梭梭的根系趋向于鱼尾状分支结构, 新疆杨根系为叉状分支结构, 根系分支结构的差异使其资源获取能力和对环境的适应能力有所差异; 2)三种植物最小的根系平均连接长度为33.67 cm, 多枝柽柳和梭梭的根系连接长度大于新疆杨, 增加连接长度对植物在资源贫瘠的沙质土壤环境的生存有利; 3)新疆杨的根系分支率显著高于多枝柽柳和梭梭, 但其对干旱的适应性不如多枝柽柳和梭梭。4)三种植物根系分支均遵循Leonardo da Vinci法则, 且不受根系直径的约束。三种防护林植物在水、养资源获取与土壤空间拓展方面具有差异性, 表明在相似的极端干旱环境中3种植物采取了不同的生态适应策略。     

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。     

毛乌素沙地旱柳生长和生理特征对遮荫的反应

在一个控制试验中,旱柳经历了全不遮荫、部分遮荫和全部遮荫处理．比较了全不遮荫枝、全部遮荫枝、部分遮荫阳生枝(阳生枝)和部分遮荫阴生枝(阴生枝)的生长和生理特征,结果表明：阳生枝和全部遮荫枝的叶出生率和死亡率分别大于全不遮荫枝和阴生枝;遮荫处理明显影响净光合速率和夜间呼吸速率;阳生枝的分枝生物量、总校长度、枝叶生物量和枝叶重比显著大于全不遮荫枝,而阴生枝的分枝数、分枝生物量、叶面积、叶生物量、基茎、总校长度、枝叶生物量和枝叶重比都显著小于全部遮荫枝．     

密度对四季竹地上生物量分配格局及异速增长模式的制约性调节

为了给四季竹(Oligostachyum lubricum)高效培育的林分结构建立提供理论依据,对立竹胸径基本一致的4种立竹密度(24600 ～ 29800株·hm-2,D1;37500 ～ 42600株·hm-2,D2;46500 ～ 52800株·hm-2,D3;76500～ 85500株·hm-2,D4)四季竹纯林进行了1～3 a立竹地上生物量积累、分配与异速生长模式的研究.结果表明:四季竹立竹构件生物量分配比例秆＞叶＞枝.随着立竹年龄增大,不同密度的四季竹林立竹秆、枝、叶生物量和地上生物量及叶/枝、叶/秆、枝/秆构件生物量比总体上均呈增大趋势,且2 a、3 a立竹显著高于1 a立竹,枝、叶生物量分配比例呈升高趋势,而秆生物量分配比例呈下降趋势.随着立竹密度增大,1～3a立竹地上生物量、构件生物量总体上呈“∧”型变化,D1～D3密度时逐渐升高,D4密度时显著下降,各年龄立竹枝、叶生物量分配比例降低,而秆生物量比例增大,叶/枝、叶/秆、枝/秆生物量比总体上1 a立竹呈倒“N”型变化,2 a、3 a立竹呈下降趋势.叶-枝构件生物量符合近等速增长模式,异速生长指数随密度的增大而小幅度下降,叶-秆、枝-秆构件生物量符合简单异速增长模式,异速生长指数随密度的增大分别呈升高、先升高后降低的变化趋势.研究表明,当超出一定密度时(D2密度以上),四季竹立竹生物量分配更趋向于支撑构件(秆),以促进立竹纵向生长来获取更多的光资源;46500～ 52800株·hm-2是试验四季竹林立竹生物量高效积累和有效分配的密度.     

黄土高原北部典型灌丛枝条生物量估算模型

于2015年8月末在陕西神木县六道沟小流域采集200个柠条和210个沙柳枝条,测定枝条的基径(D)、长度(H)、含水量(W₀)、鲜质量(W_F)和干质量(W),选用指数函数和异速生长方程建立了4种由枝条形态指标估算枝条生物量的简易模型,并对模型的拟合效果进行验证. 结果表明: 对于柠条和沙柳灌丛,基于D、H二者组合变量(D²H)的异速生长方程是估算枝条生物量的最优模型,该模型经线性转化后可以消除生物量数据的异方差性,且拟合效果最优,决定系数(R²)最大,平均误差(ME)、平均绝对误差(MAE)、总相对误差(TRE)、平均系统误差(MSE)和平均绝对百分误差(MPSE)整体上最小,基本满足生态学研究的精度要求.     

人工抚育措施对油松林生长及结构特征的影响

研究了人工抚育年后油松林的生长状况、群落组织和结构.结果表明,不同人工抚育措施的油松林平均胸径、树高、冠幅均有极显著差异(P＜0.01),采取抚育措施的两个样地间的油松胸径和冠幅差异均达到显著水平,其中既打枝又间伐的油松林的胸径(7.8±0.29cm)、树高(5.5±0.09m)和平均冠幅(249±7.24cm)最大,未打枝和间伐的油松林最大;随着人工抚育措施加强,单株油松的平均新叶、老叶和枝的生物量逐渐增加,达到极显著水平(P＜0.01);在不同抚育措施下,既打枝又间伐的油松林地上生物量最大(44.0t·hm^-2)、未打枝和间伐油松林地上生物量最大(14.9t·hm^-2);油松新叶和老叶长度的差异性显著;油松的比叶面积在生长初期(5月和月)和末期(9月)差异性显著;人工抚育措施增加了林下植被的种类数量和盖度.     

开敞度调控对次生林林冠下红松径高生长量和地上生物量的影响

以同处于演替层15年生(龄级Ⅰ)和22年生(龄级Ⅱ)的人工红松-天然阔叶混交林为对象,对林下栽植红松个体的开敞度(K)进行调整(K=1.0,1.5,2.0),研究调整后4年间林下红松直径和树高生长量及第4年的红松生物量状况.结果表明:2个龄级红松地径/胸径和树高定期生长量和地上部生物量均以K=1.0处理最大;随时间的延伸,K=1.5和K=2.0处理对年生长量的促进效果不断增强,接近或超过K=1.0处理.龄级Ⅰ的K=1.0处理的树干生物量比例显著高于其他处理和对照,而龄级Ⅱ各处理的差异不明显;龄级Ⅰ各处理的枝叶生物量比值均显著高于对照,而龄级Ⅱ则差异不显著;两个龄级不同年龄针叶的比例及分布状态不同.开敞度为1.0 ～2.0时有利于次生林林冠下栽植的15 ～22年生红松的生长发育.     

The cost of departure from optimal radii in microvascular networks

In the Murray optimality model of branching vasculatures, the radii of vessels are related to blood viscosity, vascular metabolic rate, and blood flow rate, in such a way as to minimize the total work (hydraulic and metabolic) of the system. The model predicts that flow is proportional to the cube of a vessel radius, and that at junctions the cube of the radius of the parent vessel equals the sum of the cubes of the daughter radii. In comparing real vasculatures to the Murray model, we have previously had no expressions for evaluating the apparent energy cost for departures from the optimal junction exponent of 3. Such expressions are derived here. They show that junction exponents, from about 1.5 to large positive values, are within 5% of the energy minimum. With the new equations, observed individual junctions or entire vascular trees can be compared, energy-wise, with the Murray optimum. Junctions in the transverse arteriolar trees of cat sartorius muscle were compared to the Murray optimality model, using these new expressions. The junction exponents for these small pre-capillary vessels had a broad range, with a median value greater than the Murray optimum of 3. The exponents were restricted, however, to values requiring, at individual junctions, little increase in energy. The majority of junctions had energy costs less than 1% above the Murray minimum. For entire trees involving many junctions the departures from optimality averaged less than 10%. Thus, while the branching geometry for these microvascular trees deviates significantly from the Murray optimum in the direction of larger daughter to parent ratios, the departures are small in energy terms.     

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.     

异速生长模型研究概述

最近,关于异速生长模型的讨论再次成为焦点,讨论热点为异速生长指数的取值及其理论解释.本文综述了WBE 97、BMR(99)模型的相关研究,重点介绍了MGL模型及由此模型得到的结果:个体整体的新陈代谢率与个体的质量没有明显依赖关系,其标度指数不是一个固定的值,而是一个区间[2/3,1].考虑的视角从个体整体的新陈代谢率转到单位质量的新陈代谢率,通过对不同物种、不同环境的单位质量新陈代谢率的研究,发现对大多数物种,其值落在一个具有普适性的上、下界的区间内;认为存在单位质量的新陈代谢率最小值确定了个体的大小,并建立基于该最小值的描述个体大小与温度关系的数学模型,该模型得到实验数据验证.     

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.     

Critical exponents for sol–gel transition in aqueous alginate solutions induced by cupric cations

The sol–gel transition in aqueous alginate solutions of four alginate samples having different molecular weights (M_W) and M/G ratios induced by cupric cations was monitored by rheology measurements. The gel point f_gel and the relaxation critical exponent n were determined using the Winter’s criterion over the alginate concentration C_Alg of 1–4 wt%. The scaling for the zero shear viscosity η₀ before the gel point and the equilibrium modulus G_e after the gel point was established against the relative distance ε from the gel point at the concentration of C_Alg = 1 wt%, giving the critical exponents k and z. The results indicated that f_gel was almost independent of the alginate concentration and became higher for the sample with lower molecular weight. The critical exponent n decreased with the increase in C_Alg for these four Cu-alginate samples and the fractal dimension d_f estimated from n suggested a denser structure in the critical gel with high G content. The critical exponent n evaluated from k and z agreed well with n determined from the Winter’s criterion.     

On the relationship between mass and diameter distributions in tree communities

It has been suggested that frequency distributions of individual tree masses in natural stands are characterized by power-law distributions with exponents near -3/4, and that therefore tree communities exhibit energetic equivalence among size classes. Because the mass of trees is not measured directly, but estimated from diameter, this supposition is based on the fact that the observed distribution of tree diameters is approximately characterized by a power-law with an exponent approximately -2. Here we show that diameter distributions of this form are not equivalent to mass distributions with exponents of -3/4, but actually to mass distributions with exponents of -11/8. We discuss the implications of this result for the metabolic theory of ecology and for understanding energetic equivalence and the processes structuring tree communities.