幂指数异速生长机制模型综述

 个体大小对生物的各种生理属性有重要意义, 描述个体大小和生理属性关系的规律叫做异速生长。生物的异速生长通常以幂函数的形 式表示, 在众多的异速生长关系中, Kleiber定律所描述的新陈代谢率和个体大小的3/4幂指数关系最为重要和基本, 解释此有充分数据支持的 定律的机理也最具挑战性。围绕该著名的3/4幂指数异速生长关系, 该文回顾历史上主要的有关模型假说, 并重点介绍1990年代中期以来, 由 West等提出的分形分配网络模型和由其它研究人员建立的代表性模型: 最少载体网络模型、多因理论、最小总熵理论、构造理论、细胞优化生 长理论和能量消耗理论。     

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.     

浮游生物异速生长关系研究进展

生物个体的生物学特征(新陈代谢速率等)与个体大小(体积和生物量等)的依赖性关系称为异速生长关系, 这种关系经过尺度转换之后, 还影响着种群、群落和生态系统等。海洋环境较为复杂, 浮游生物的代谢速率不仅受到个体大小影响, 同时光照、温度和营养物质也是重要的影响因素, 因此3/4 规律只有在理想环境状况下才能实现。对于大多数浮游生物来讲, 其尺度因子并非单一的, 存在着多元尺度指数。由于单一和多元尺度指数都忽略了环境温度的影响, 生态学代谢理论在考虑个体大小的基础上, 加上温度这个参数后能够解释不同层次的生态学过程。在综述了异速生长关系发展历史的基础上, 着重探讨了该关系在浮游生物中的研究进展。     

四种一年生荒漠植物构件形态与生物量间的异速生长关系

1年生草本植物是古尔班通古特沙漠夏秋季节草本层片的主要组成部分。选择4种藜科1年生草本植物(刺沙蓬、沙蓬、角果藜和对节刺)作为研究对象,对比分析了各物种构件形态特征、生物量分配以及它们之间的异速生长关系。结果表明:沙蓬个体最大,其次为刺沙蓬,角果藜和对节刺个体最小;对节刺具有最大的根冠比(R/S),其次是刺沙蓬,沙蓬和角果藜R/S最小。4种植物构件形态与生物量间均呈显著正相关,表现出强烈的协同变化趋势。R/S与绝大部分指标间呈显著负相关,表明随个体增大地下生物量分配比例逐渐减小。4种植物各构件形态、地上及地下生物量间大部分呈指数1.0的异速生长关系,但各物种间的异速生长指数绝大部分无显著差异且具有共同的异速生长指数。研究表明:尽管物种不同、个体大小迥异,但4种1年生植物构件特征间多具有相同的生长速率和协同变化特征,体现了1年生植物这一生活型内的不同物种对干旱荒漠环境的趋同适应。     

甘肃南部7种高寒杜鹃生物量分配的异速生长关系

生物量分配模式影响着植物个体生长和繁殖到整个群落的质量和能量流动等所有层次的功能, 揭示高寒灌丛的生物量分配模式不仅可以掌握植物的生活史策略, 而且对理解灌丛碳汇不确定性具有重要意义。该研究以甘肃南部高山-亚高山区的常绿灌丛——杜鹃(Rhododendron spp.)灌丛的7个典型种为对象, 采用全株收获法研究了不同物种个体水平上各器官生物量的分配比例和异速生长关系。结果表明: 7种高寒杜鹃根、茎、叶生物量的分配平均比例为35.57%、45.61%和18.83%, 各器官生物量分配比例的物种差异显著; 7种高寒杜鹃的叶与茎、叶与根、茎与根以及地上生物量与地下生物量之间既有异速生长关系, 也有等速生长关系, 异速生长指数不完全支持生态代谢理论和小个体等速生长理论的参考值; 各器官异速生长关系的物种差异显著。结合最优分配理论和异速生长理论能更好地解释陇南山地7种高寒杜鹃生物量的变异及适应机制。     

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。     

浙江天童木本植物Corner法则的检验:个体密度的影响

Corner法则反映了植物枝叶大小和数量配置的构型策略,但是,对于个体密度如何影响枝叶关系的理解仍不够深入。该研究选择浙江天童的25个植物群落,通过比较枝大小(横截面积)-叶大小(总叶面积)关系和枝大小(横截面积)-枝数量(分梢密度)关系,分析个体竞争对植物Corner法则的影响。结果显示:1)在不同密度区间,枝横截面积和总叶面积均显著异速正相关。2)个体水平上,枝大小-叶大小回归方程的截距在低密度区间显著小于高密度区间,表明在枝大小一定的条件下,高密度群落的植物当年生枝条会支撑更大的总叶面积;而物种水平上,枝大小-叶大小回归方程的截距在不同密度区间没有显著性差异。3)枝横截面积与分梢密度显著负相关,且各密度区间也存在显著小于–1的共斜率。4)个体水平和物种水平的分析结果都显示,枝横截面积与分梢密度回归方程的截距在不同密度区间无显著差异,表明高密度植物并没有比低密度植物在单位大小枝条上配置更多的分枝。总之,植物枝大小-叶大小关系和枝大小-枝数量关系各自在不同的密度区间具有共同的变化斜率,反映了天童地区植物Corner法则不随个体密度变化而改变。但是,枝叶关系回归方程截距的改变表明,个体竞争的加大会使得植物在枝叶大小的配置策略上进行调整,从而可能通过生态位分化促进物种共存。     

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。     

森林自然更新过程中地上氮贮量与生物量异速生长的关系

研究植物氮贮量与生物量(M)之间的异速生长关系对于开展生态系统碳收支和氮循环研究具有重要意义。目前大量对氮贮量与生物量关系的研究主要集中在个体水平,对于群落水平的氮贮量和生物量之间的异速生长关系,以及群落自然更新过程如何影响该关系仍有待深入研究。利用3种森林类型皆伐后20多年自然更新过程中氮贮量和生物量的数据,采用简化主轴回归方法(reduced major axis,RMA)对不同自然更新阶段的森林氮贮量和生物量之间的异速生长指数和常数进行比较。结果表明:在不同的更新阶段,3种森林类型的植物氮贮量和生物量之间的异速生长指数均接近于1.0(即N∝M0.91-1.07)。异速生长常数随更新时间的增加而逐渐降低,导致3种森林类型整体上氮贮量正比于生物量的0.85次幂。异速生长常数的降低可能是由于在更新过程中叶生物量占整体生物量的比例逐渐下降,导致其对N吸收的生态化学计量制约所造成。     

Importance of scaling exponents and other parameters in growth mechanism: an analytical approach

The growth process of a living organism is studied with the help of a mathematical model where a part of the surplus power is assumed to be used for growth. In the present study, the basic mathematical framework of the growth process is based on a pioneering theory proposed by von Bertalanffy and his work is the main intellectual driving force behind the present analysis. Considering the existence of an optimum size for which the surplus power becomes maximum, it has been found that the scaling exponent for the intake rate must be smaller than the exponent for the metabolic cost. A relationship among the empirical constants in allometric scaling has also been established on the basis of the fact that an organism never ceases to generate surplus energy. The growth process is found to continue forever, although with a decreasing rate. Beyond the optimum point the percentage of shortfall in energy has been calculated and its dependence on scaling exponents has been determined. The dependence of optimum mass on the empirical constants has been shown graphically. The functional dependence of mass variation on time has been obtained by solving a differential equation based on the concept of surplus energy. The dependence of the growth process on scaling exponent and empirical constants has been shown graphically.     

The origin of allometric scaling laws in biology

The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon-specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.     

Allometric scaling in animals and plants

In this paper we give a derivation for the allometric scaling relation between the metabolic rate and the mass of animals and plants. We show that the characteristic scaling exponent of 3/4 occurring in this relation is a result of the distribution of sources and sinks within the living organism. We further introduce a principle of least mass and discuss the kind of flows that arise from it.     

Scaling of metabolic rate in the lesser wax moth Achroia grisella does not fit the 3/4‐power law and shows significant sex differences

Allometric scaling of metabolic rates is commonly described as a power function and 0.75 is a widely accepted exponent. The universality of this exponent is in doubt and, particularly for insects, contradictory results have been obtained. Furthermore, sexual differences in scaling exponents are observed for several species that could lead to artefacts when they are not considered in intra‐ and interspecific scaling. Whether the metabolic scaling exponent in the lesser wax moth Achroia grisella differs significantly from 0.75 is tested, as well as whether it differs between the sexes. Adults of this moth neither feed nor drink, rendering them as suitable subjects for a study of metabolic rates. Neglecting sex differences, a metabolic scaling exponent of 0.8 is recorded. However, there are significant differences in metabolic scaling between the sexes. When considered separately, males scale with 0.96 and females with 0.67. Thus, in this species, a scaling exponent of 0.75 does not appear to exist either for males or females. The body size optimization model offers a potential explanation for the sex differences in metabolic scaling, although it remains to be tested in wax moths. With insects in particular, there is the need for more detailed studies on the scaling of metabolic rates that also take sexual differences into account.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

Intraspecific temperature dependence of the scaling of metabolic rate with body mass in fishes and its ecological implications

Metabolism constitutes a fundamental property of all organisms. Metabolic rate is commonly described to scale as a power function of body size and exponentially with temperature, thereby treating the effects of body size and temperature independently. Mounting evidence shows that the scaling of metabolic rate with body mass itself depends on temperature. Across‐species analyses in fishes suggest that the mass‐scaling exponent decreases with increasing temperature. However, whether this relationship holds at the within‐species level has rarely been tested. Here, we re‐analyse data on the metabolic rates of four freshwater fish species, two coregonids and two cyprinids, that cover wide ranges of body masses and their naturally experienced temperatures. We show that the standard metabolic rate of the coregonids is best fit when accounting for a linear temperature dependence of the scaling of metabolic rate with body mass, whereas a constant mass‐scaling exponent is supported in case of the cyprinids. Our study shows that phenotypic responses to temperature can result in temperature‐dependent scaling relationships at the species level and that these responses differ between taxa. Together with previous findings, these results indicate that evolutionarily adaptive and phenotypically plastic responses to temperature affect the scaling of metabolic rate with body mass in fishes.     

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.     

Changes in body temperature influence the scaling of VO2max and aerobic scope in mammals

Debate on the mechanism(s) responsible for the scaling of metabolic rate with body size in mammals has focused on why the maximum metabolic rate (VO2max ) appears to scale more steeply with body size than the basal metabolic rate (BMR). Consequently, metabolic scope, defined as VO2max/BMR, systematically increases with body size. These observations have led some to suggest that VO2max, and BMR are controlled by fundamentally different processes, and to discount the generality of models that predict a single power-law scaling exponent for the size dependence of the metabolic rate. We present a model that predicts a steeper size dependence for VO2max than BMR based on the observation that changes in muscle temperature from rest to maximal activity are greater in larger mammals. Empirical data support the model's prediction. This model thus provides a potential theoretical and mechanistic link between BMR and VO2 max.     

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.