Trade-offs between the metabolic rate and population density of plants

The energetic equivalence rule, which is based on a combination of metabolic theory and the self-thinning rule, is one of the fundamental laws of nature. However, there is a progressively increasing body of evidence that scaling relationships of metabolic rate vs. body mass and population density vs. body mass are variable and deviate from their respective theoretical values of 3/4 and -3/4 or -2/3. These findings questioned the previous hypotheses of energetic equivalence rule in plants. Here we examined the allometric relationships between photosynthetic mass (M(p)) or leaf mass (M(L)) vs. body mass (beta); population density vs. body mass (delta); and leaf mass vs. population density, for desert shrubs, trees, and herbaceous plants, respectively. As expected, the allometric relationships for both photosynthetic mass (i.e. metabolic rate) and population density varied with the environmental conditions. However, the ratio between the two exponents was -1 (i.e. beta/delta = -1) and followed the trade-off principle when local resources were limited. Our results demonstrate for the first time that the energetic equivalence rule of plants is based on trade-offs between the variable metabolic rate and population density rather than their constant allometric exponents.     

Scaling of myocardial mass to flow and morphometry of coronary arteries.

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5 +/- 32.7) were used in this study. Various coronary subtrees of the left anterior descending, right coronary, and left circumflex arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter, and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters, and volumetric flow show an approximately 3/4, 3/8, and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease.     

Size–abundance relationships in Florida ant communities reveal how ants break the energetic equivalence rule

1. Ants are among the most abundant terrestrial organisms, yet little is known of how ant communities divide resources because it is difficult to measure the number of individuals in colonies and the density of colonies. 2. The body size–abundance relationships of the ants of five upland ecosystems in Florida were examined. The study tested whether abundance, energy use, and total biomass were distributed among species and body sizes as predicted by Damuth's energetic equivalence rule. Estimates of average worker body size, colony size, colony mass, and field metabolic rates were used to examine the relationships among body sizes, energy use, and total biomass. 3. Analyses revealed significant variation in energy use and did not support the energetic equivalence hypothesis. Specifically, the energy use and total standing biomass of species with large workers and colonies was much greater than smaller species. 4. These results suggest that larger species with larger colonies account for a disproportionate fraction of the total abundance and biomass of ants. A general model of resource allocation in colonies provides a possible explanation for why ants do not conform to the predictions of the energetic equivalence rule and for why ants are so abundant.     

Discontinuities and alternative scalings in the density–mass relationship of anuran larvae

Size–density relationships (SDRs) frequently follow a power-law relationship, with exponents that compensate for the increase in population-level metabolic demand—the energetic equivalence rule. However, these exponents present a range of values, and elucidating its methodological and biological determinants has become a main issue. So far, a restricted set of potential relationships, mechanisms, and taxa have been considered. Here, we analyzed SDR in a population of tadpoles inhabiting a network of 16 temporal ponds. Alternative scaling regimes were detected using pacewise regressions and estimating exponents with maximum likelihood (ML). If discontinuities in the SDR are ignored, a scaling close to values reported elsewhere is observed. However, estimated slopes between discontinuities are steeper (threefold to fivefold) than those often reported, but congruent with the performance predicted for ML and the biases reported for other methods. Our estimations largely deviate from an energetic equivalence, suggesting that large individuals use less energy per unit area. The detection of different SDRs in the same database, with a strong decay in abundance with body size, points to a pattern poorly considered in previous studies, widening the range of patterns, mechanisms, and ecological, or evolutionary consequences of the SDRs.     

Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New species are introduced through mutation. Both models are amenable to exact linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations, obtaining the population size as a function of an average interspecies interaction strength. Over time, the models self-optimize through mutation and selection to approximately maximize a community potential function, subject only to constraints internal to the particular model. If the interspecies interactions are randomly distributed on an interval including positive values, the system evolves toward self-sustaining, mutualistic communities. In contrast, for the predator–prey case the matrix of interactions is antisymmetric, and a nonzero population size must be sustained by an external resource. Time series of the diversity and population size for both models show approximate 1/f noise and power-law distributions for the lifetimes of communities and species. For the mutualistic model, these two lifetime distributions have the same exponent, while their exponents are different for the predator–prey model. The difference is probably due to greater resilience toward mass extinctions in the food-web like communities produced by the predator–prey model.      

Body mass, population density, and offspring number in mammals

The negative relationship between population density and body mass with the body mass exponent of -0.75 implies that the energy flow through populations of small- and large-bodied species is the same, for individual metabolism scales to body mass raised to the power of +0.75. This relationship called the energetic equivalence rule, has often been observed for mammal species assemblages studied at regional scales. Here we suggest a demography-based mechanism that may generate it. Having analyzed about 130 literature sources, mostly in Russian, we collected demography and body-mass data for 88 mammalian species from the territory and coastal waters of the former Soviet Union. The data were used to construct a number of interspecific relationships. It is shown that (1) the number of offspring per lifetime is approximately inversely proportional to the relative mass at birth (the exponent is not significantly different from -1), (2) the average lifespan is proportional to body mass to the 0.25 power, (3) body mass at birth is proportional to the adult body mass. We develop a simple theory to demonstrate that relations (1) to (3) entail the energetic equivalence rule. The theory also allows us to explain violation of this rule (in non-flying birds, for example), namely, to predict the exponent of relation (1) for any given exponent of the relation between population density and body mass. This is possible because relations (2) and (3) are likely to more universally hold than relation (1). Finally, since natural selection acts on individual traits rather than on population-level ones such as population density, the theory opens up the way to an evolutionary explanation for the energetic equivalence rule.     

Growth-size scaling relationships of woody plant species differ from predictions of the Metabolic Ecology Model

The Metabolic Ecology Model predicts that tree diameter ( D ) growth ( dD/dt ) scales with D ^1/3. Using data on diameter growth and height–diameter relationships for 56 and 40 woody species, respectively, from forests throughout New Zealand, we tested one prediction and two assumptions of this model: (i) the exponent of the growth–diameter scaling relationship equals 1/3 and is invariant among species and growth forms, (ii) small and large individuals are invariant in their exponents and (iii) tree height scales with D ^2/3. We found virtually no support for any prediction or assumption: growth–diameter scaling exponents varied substantially among species and growth forms, correlated positively with species' maximum height, and shifted significantly with increasing individual size. Tree height did not scale invariantly with diameter. Based on a quantitative test, violation of these assumptions alone could not explain the model's poor fit to our data, possibly reflecting multiple, unsound assumptions, as well as unaccounted-for variation that should be incorporated.     

Cluster size distributions: signatures of self-organization in spatial ecologies

Three different lattice-based models for antagonistic ecological interactions, both nonlinear and stochastic, exhibit similar power-law scalings in the geometry of clusters. Specifically, cluster size distributions and perimeter-area curves follow power-law scalings. In the coexistence regime, these patterns are robust: their exponents, and therefore the associated Korcak exponent characterizing patchiness, depend only weakly on the parameters of the systems. These distributions, in particular the values of their exponents, are close to those reported in the literature for systems associated with self-organized criticality (SOC) such as forest-fire models; however, the typical assumptions of SOC need not apply. Our results demonstrate that power-law scalings in cluster size distributions are not restricted to systems for antagonistic interactions in which a clear separation of time-scales holds. The patterns are characteristic of processes of growth and inhibition in space, such as those in predator-prey and disturbance-recovery dynamics. Inversions of these patterns, that is, scalings with a positive slope as described for plankton distributions, would therefore require spatial forcing by environmental variability.     

Tree size frequency distributions, plant density, age and community disturbance

We show that explicit mathematical and biological relationships exist among the scaling exponents and the allometric constants (α and β, respectively) of log–log linear tree‐community size frequency distributions, plant density N_T, and minimum, maximum and average stem diameters (D_min, D_max, and , respectively). As individuals grow in size and D_max increases, N_T is predicted to decrease as reflected by a decrease in the numerical value of α and an increase in the value of β. Our derivations further show that N_T decreases as increases even if D_min or D_max remain unchanged. Because D_max and the age of the largest individuals in a community are correlated, albeit weakly, we argue that the interdependent relationships among the numerical values of α, β, N_T, and shed light on the extent to which communities have experienced recent global disturbance. These predicted relationships receive strong statistical support using two large datasets spanning a broad spectrum of tree‐dominated communities.     

川西亚高山3个优势树种不同径级根系分解特征

采用埋袋法对川西亚高山3个优势树种(岷江冷杉、粗枝云杉和红桦)细根(≤2 mm)、中根(2～5 mm)和粗根(≥5 mm)质量损失率及碳(C)、氮(N)、磷(P)在经历生长季和非生长季之后释放特征进行研究.结果表明： 红桦质量残留率低于岷江冷杉和粗枝云杉.同一树种,质量残留率总体上随根系径级增加而增加.非生长季的质量损失率占全年质量损失率的52.1%～64.4%.红桦C释放率最高,岷江冷杉最低,且随根系直径的增粗,C释放率降低.岷江冷杉和粗枝云杉N释放模式为非生长季富集、生长季释放,而红桦反之.富集期间,径级越大,富集量越多.3个树种各径级根系P动态在非生长季和生长季皆表现为富集-释放模式,且岷江冷杉P富集程度显著高于粗枝云杉和红桦,但各径级之间差异总体不显著.根系径级对川西亚高山森林根系分解具有显著影响,而径级影响与树种和分解时期有一定关系.     

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。     

Size-dependent species richness: trends within plant communities and across latitude

We examine how species richness and species‐specific plant density (number of species and number of individuals per species, respectively) vary within community size frequency distributions and across latitude. Communities from Asia, Africa, Europe, and North, Central and South America were studied (60°4′N–41°4′S latitude) using the Gentry data base. Log–log linear stem size (diameter) frequency distributions were constructed for each community and the species richness and species‐specific plant density within each size class were determined for each frequency distribution. Species richness in the smallest stem size class correlated with the Y‐intercepts (β‐values) of the regression curves describing each log–log linear size distributions. Two extreme community types were identified (designated as type A and type B). Type A communities had steep size distributions (i.e. large β‐values), log–log linear species‐richness size distributions, low species‐specific plant density distributions, and a small size class (2–4 cm) containing the majority of all species but rarely conspecifics of the dominant tree species. Type B communities had shallow size distributions (i.e. small β‐values), more or less uniform (and low) size class species‐ richness and species‐specific density distributions and size‐dominant species resident in the smallest size class. Type A communities were absent in the higher latitudes but increased in number towards the equator, i.e. in the smallest size class, species richness increased (and species‐specific density decreased) towards the tropics. Based on our survey of type A and type B communities (and their intermediates), species richness evinces size‐dependent and latitudinal trends, i.e. species richness increased with decreasing body size and most species increasingly reside in the smallest plant size class towards the tropics. Across all latitudes, a trade‐off exists between the number of species and the number of individuals per species residing in the smaller size classes.     

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.     

Measurement of body size and abundance in tests of macroecological and food web theory

1. Mean body mass (W) and mean numerical (N) or biomass (B) abundance are frequently used as variables to describe populations and species in macroecological and food web studies. 2. We investigate how the use of mean W and mean N or B, rather than other measures of W and/or accounting for the properties of all individuals, can affect the outcome of tests of macroecological and food web theory. 3. Theoretical and empirical analyses demonstrate that mean W, W at maximum biomass (W(mb)), W when energy requirements are greatest (W(me)) and the W when a species uses the greatest proportion of the energy available to all species in a W class (W(mpe)) are not consistently related. 4. For a population at equilibrium, relationships between mean W and W(me) depend on the slope b of the relationship between trophic level and W. For marine fishes, data show that b varies widely among species and thus mean W is an unreliable indicator of the role of a species in the food web. 5. Two different approaches, 'cross-species' and 'all individuals' have been used to estimate slopes of abundance-body mass relationships and to test the energetic equivalence hypothesis and related theory. The approaches, based on relationships between (1) log(10) mean W and log(10) mean N or B, and (2) log(10) W and log(10) N or B of all individuals binned into log(10) W classes (size spectra), give different slopes and confidence intervals with the same data. 6. Our results show that the 'all individuals' approach has the potential to provide more powerful tests of the energetic equivalence hypothesis and role of energy availability in determining slopes, but new theory and empirical analysis are needed to explain distributions of species relative abundance at W. 7. Biases introduced when working with mean W in macroecological and food web studies are greatest when species have indeterminate growth, when relationships between W and trophic level are strong and when the range of species'W is narrow.     

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.     

Species-specific allometric scaling under self-thinning: evidence from long-term plots in forest stands

Experimental plots covering a 120 years' observation period in unthinned, even-aged pure stands of common beech (Fagus sylvatica), Norway spruce (Picea abies), Scots pine (Pinus sylvestris), and common oak (Quercus Petraea) are used to scrutinize Reineke's (1933) empirically derived stand density rule [see text], N=tree number per unit area, [see text]=mean stem diameter), Yoda's (1963) self-thinning law based on Euclidian geometry ([see text] [see text]=mean biomass per tree), and basic assumptions of West, Brown and Enquist's (1997, 1999) fractal scaling rules ([see text] [see text] w=biomass per tree, d=stem diameter). RMA and OLS regression provides observed allometric exponents, which are tested against the exponents, expected by the considered rules. Hope for a consistent scaling law fades away, as observed exponents significantly correspond with the considered rules only in a minority of cases: (1) exponent r of [see text] varies around Reineke's constant -1.605, but is significantly different from r=-2, supposed by Euclidian or fractal scaling, (2) Exponent c of the self-thinning line [see text] roams roughly about the Euclidian scaling constant -3/2, (3) Exponent a of [see text] tends to follow fractal scaling 8/3. The unique dataset's evaluation displays that (4) scaling exponents and their oscillation are species-specific, (5) Euclidian scaling of one relation and fractal scaling of another are coupled, depending on species. Ecological implications of the results in respect to self-tolerance (common oak>Norway spruce>Scots pine>common beech) and efficiency of space occupation (common beech>Scots pine>Norway spruce>common oak) are stressed and severe consequences for assessing, regulating and scheduling stand density are discussed.     

Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone

Cortical and trabecular bone have similar creep behaviors that have been described by power-law relationships, with increases in temperature resulting in faster creep damage accumulation according to the usual Arrhenius (damage rate approximately exp (-Temp.-1)) relationship. In an attempt to determine the phase (collagen or hydroxyapatite) responsible for these similar creep behaviors, we investigated the creep behavior of demineralized cortical bone, recognizing that the organic (i.e., demineralized) matrix of both cortical and trabecular bone is composed primarily of type I collagen. We prepared waisted specimens of bovine cortical bone and demineralized them according to an established protocol. Creep tests were conducted on 18 specimens at various normalized stresses sigma/E0 and temperatures using a noninvasive optical technique to measure strain. Denaturation tests were also conducted to investigate the effect of temperature on the structure of demineralized bone. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates at all applied normalized stresses and temperatures. Strong (r2 > 0.79) and significant (p < 0.01) power-law relationships were found between the damage accumulation parameters (steady-state creep rate d epsilon/dt and time-to-failure tf) and the applied normalized stress sigma/E0. The creep behavior was also a function of temperature, following an Arrhenius creep relationship with an activation energy Q = 113 kJ/mole, within the range of activation energies for cortical (44 kJ/mole) and trabecular (136 kJ/mole) bone. The denaturation behavior was characterized by axial shrinkage at temperatures greater than approximately 56 degrees C. Lastly an analysis of covariance (ANCOVA) of our demineralized cortical bone regressions with those found in the literature for cortical and trabecular bone indicates than all three tissues creep with the same power-law exponents. These similar creep activation energies and exponents suggest that collagen is the phase responsible for creep in bone.     

Mass invariance of population nitrogen flux by terrestrial mammalian herbivores: an extension of the energetic equivalence rule

According to the energetic equivalence rule, energy use by a population is independent of average adult body mass. Energy use can be equated with carbon flux, and it has been suggested that population fluxes of other materials, such as nitrogen and phosphorus, might also be independent of body mass. We compiled data on individual nitrogen deposition rates (via faeces and urine) and average population densities of 26 species of mammalian herbivores to test the hypothesis of elemental equivalence for nitrogen. We found that the mass scaling of individual nitrogen flux was opposite to that of population density for the species in our dataset. By computing the product of individual nitrogen flux and average population density for each species in our dataset, we found that population-level nitrogen flux was independent of species mass, averaging c. 3.22 g N ha⁻¹ day⁻¹. Results from this analysis can be used to understand the influence of mammalian herbivore communities on nitrogen cycling in terrestrial ecosystems.     

Exploring predictions of abundance from body mass using hierarchical comparative approaches

Understanding and predicting how and why abundance varies is one of the central questions in ecology. One of the few consistent predictors of variation in abundance between species has been body mass, but the nature of this relationship has been contentious. Here I explore the relationship between body mass and abundance in birds of North America, using hierarchical partitioning of variance and regressions at taxonomic levels above the species. These analyses show that much variation in abundance is found across space, while a moderate amount of variation is found at the species/genus and also at the family/order level. However, body size and trophic level primarily vary at the family/order level, suggesting that mechanisms based on body size and energy should primarily explain only this moderate-sized, taxonomically conserved component of variation in abundance. Body size does explain more than 50% of the variation at this level (and almost 75% when trophic level is also included). This tighter relationship makes clear that energetic equivalence (slope = -3/4) sets an upper limit but does not describe the relationship between body mass and average abundance for birds of North America. Finally, I suggest that this hierarchical, multivariate approach should be used more often in macroecology.     

7个林木大小多样性指数表达能力比较

林木大小多样性直接反映森林生态系统的健康与稳定, 客观恰当地表达大小多样性对于评价天然林或人工林的经济、生态、社会价值及其经营效果至关重要。本研究选用7个林木大小多样性指数, 其中4个与距离无关(Simpson大小多样性指数D_N、Shannon大小多样性指数H_N、断面积Gini系数GC和直径变异系数CV_d), 3个与距离有关(Simpson大小分化度指数D_T、Shannon大小分化度指数H_T和大小分化度均值指数$\bar{T}$), 通过6组模拟林分和4块实测林分比较分析了它们的表达能力。结果表明: 不考虑极端情况(极端情况为对比林分林木大小混交不同但林木直径构成完全相同), GC、CV_d、$\bar{T}$、D_T和H_T能客观恰当地表达不同径级分布林分的林木大小多样性差异, 其中CV_d区分能力最强, GC次之。若考虑极端情况, 只有$\bar{T}$、D_T和H_T能区分出不同大小混交程度林分的林木大小多样性差异。本研究认为CV_d和GC因计算简单, 易于实际应用, 在营林活动中可作为分析林木大小多样性的首选指数; $\bar{T}$因能识别不同大小混交程度林分的空间差异, 即对林分更新变化敏感, 适用于动态分析林分的结构特征。