水文尺度转换探讨

水文尺度问题是当今水文学研究的热点和前沿.水文尺度包括过程尺度、观测尺度和模拟尺度三方面含义.主导过程尺度作为尺度的特征量,是水文研究中的重点.水文尺度转换工作包括了对水文模式、参数、状态变量和输入的尺度转换四方面,每一方面都有其特殊的研究方法.水文系统的有组织复杂性、时空变异性和数据不足是当前水文研究的难点所在.自然河网的自相似特性使其成为水文尺度研究的重要组成部分.进一步深入研究水文尺度问题需要多种研究思路、技术手段和理论工具的结合.     

Linux与人类代谢的自相似性实证研究

对现实世界复杂网络的自相似性进行实证分析是当前该领域的一个热点问题。文章首先介绍了复杂网络自相似性的基本概念,随后阐述了自相似指数及其计算方法盒覆盖算法的基本原理和方法,最后对Linux与人类代谢这两种不同类型的复杂系统进行自相似性实证研究。研究结果表明,它们都是自相似的。     

中国湿地物种多样性与生境面积关系及其生态学机理的模拟研究

生物群落中的物种多样性是群落生态学研究的一个基本问题。大量的实验研究表明物种多样性和生境面积的常数次幂成比例,这说明它们的对数数量级呈线性正相关。我们研究了中国境内15块湿地的高等植物和32块湿地鸟类多样性,发现它们分别和湿地面积在对数尺度上呈线性正相关．进一步支持了种数与面积的幂指数关系。我们还借助计算机模拟系统地讨论了产生这种简单规律的生态学机理,包括中性理论、集合种群动态和物种分布的自相似性。中性理论假设了群落中物种的个体之间只有竞争关系,忽略了其它的种间关系。集合种群动态理论考虑的是由多个亚群落构成的集合群落,在研究种数和面积关系时也忽略了种间关系,所以也是中性的。尽管物种分布的自相似性可导致这种面积幂指数关系,但在自然界中自相似性也可能不成立。     

不同植被类型森林火灾及雷击火自组织临界性

利用黑龙江省大兴安岭林区呼中区 196 5～ 2 0 0 2年的雷击火数据、黑龙江省 1981～ 2 0 0 0年森林火灾数据及森林资源数据 ,对雷击造成的森林火灾的自组织临界性及不同植被类型条件下的自组织临界性作了研究 ,比较了在不同尺度和植被类型条件下火干扰的自组织临界性、自相似性 ,并与传统的森林火灾元胞自动机模型模拟的结果进行比较。结果表明 :中国黑龙江省不同森林类型的火干扰具有自组织临界行为 ,森林可燃物已经达到临界状态 ,其临界值在 1.8～ 2 .86之间 ,具有自相似性 ;当森林的面积过小时 ,森林火灾的“面积 -频率”分布曲线上会出现频率峰 ,表现出“有限面积效应”现象。     

水文尺度转换研究进展

介绍了水文尺度、尺度问题和尺度转换的概念,重点与难点在流域的空间异质性和水文通量的时空变异性;给出了进行尺度转换的3种途径,即分布式水文模拟、分形理论和统计自相似性分析;最后在已有成果的基础上,提出了目前研究中存在的问题及未来的发展方向。     

森林生物量遥感降尺度研究

森林生物量是评价全球碳氧平衡、气候变化的重要指标。目前已有基于星载激光雷达数据的全球森林生物量产品,但空间分辨率较低,不能很好地满足小区域森林调查和动态监测的需要。针对这一现状,以美国马里兰州两个森林分布状况不同的区域为研究区,基于CMS(Carbon Monitoring System)30 m分辨率和GEOCARBON 1 km分辨率森林地上生物量产品以及TM等数据源,通过升尺度模拟低分辨率生物量数据和直接使用低分辨率产品两种方式,分别尝试建立了多光谱地表参数和低分辨率森林地上生物量之间的统计关系,以此作为降尺度模型实现了森林地上生物量空间分辨率从1 km到30 m的转换,并对降尺度结果进行精度评价和误差分析。结果表明:模拟数据降尺度后的30 m分辨率森林地上生物量空间分布和CMS森林地上生物量分布状况大致相同,RMSE=59.2—65.5 Mg/hm~2,相关系数约为0.7;其降尺度结果优于GEOCARBON产品直接降尺度结果RMSE=75.3—79.9 Mg/hm~2;相较于线性模型,非线性模型能更好地呈现森林地上生物量和地表参数间的关系;总体上,降尺度生物量呈现高值区低估,低值区高估的现象。     

石臼湖原生动物种群分布及其同质化

石臼湖地处长江中下游,是国内为数不多的通江淡水湖。为探讨湖泊与入湖支流不同生境中原生动物种群结构及其相似性,于2012年平水期和枯水期分别对石臼湖及其周边入湖支流进行原生动物调查,研究河流和湖泊区域原生动物的种类组成及其季节变化,同时与同一地区的相邻湖泊固城湖作对比,通过计算相似性指数,探讨原生动物对生境同质化的响应。结果表明:调查共采集到原生动物57种,平水期种类多于枯水期;石臼湖河流区各站点原生动物相似性指数在Ⅰ~Ⅲ级之间,为完全不同-轻度相似;湖区站点相似性指数在Ⅱ~Ⅳ之间,为极不相似-中度相似;河流区种类季节之间的相似度极低(0.050~0.267),而湖泊区种类季节之间处于中等相似水平(0.250~0.375),说明河流区原生动物种类的季节变化较湖泊区明显,生物组成的异质性也高于湖泊;原生动物分布对水质有很好的响应关系,氮磷元素在影响原生动物种类组成和分布中起了主要作用;通过石臼湖与固城湖及长江中下游其他湖泊的对比分析,表明在一定范围内,随着生境尺度的增加,生境的同质化会提高生物同质化水平,但超过景观尺度,原生动物地域性特征逐渐显现,即使生境同质,其生物也未必同质;且随着距离的增加,不同区域的生物相似性呈降低的趋势。     

古尔班通古特沙漠白茎绢蒿和准噶尔沙蒿种群多尺度多参数空间分布格局

以往种群空间格局的研究大多基于植株点位或株数(0维),极少针对植冠的投影盖度(2维)和生物量(3维,由植冠体积体现).目前对三者所体现的种群空间格局特征尚不清楚.本研究以古尔班通古特沙漠广布的小半灌木白茎绢蒿和准噶尔沙蒿种群为对象,测定每株的点位、投影盖度及地上生物量,通过GIS技术对坐标系进行6次尺度划分,利用聚集度分析、变异系数及其与尺度的幂函数关系,分析了3个参数的种群分布格局特征.结果表明: 在各尺度下,两种群的株数(白茎绢蒿0.5 m尺度除外)和生物量均为集群分布,聚集强度随尺度增加而增大;而投影盖度多为均匀分布(准噶尔沙蒿5 m和8 m尺度除外).随尺度增大,两种群各参数的变异系数均逐渐下降;株数的幂指数的绝对值(k值)高于投影盖度和生物量,且后两者无显著差异.白茎绢蒿各参数的k值均高于准噶尔沙蒿,可能与群落种间关系及个体大小有关.总之,株数和生物量的空间格局类型相似,而投影盖度和生物量具有近乎相同的格局复杂性和尺度变化特征.     

云南省两栖动物地理分布格局的聚类分析

为了量化云南省两栖动物地理分布格局及其相似性,对云南省102种两栖动物在地理小区的分布格局尺度上进行了聚类分析。建立物种有无分布的二元数据列联表,利用联合系数表示每两个地理小区内两栖动物的相似程度,以类平均法进行了聚类分析。结果表明,云南两栖动物可以归类为两大类群,相邻动物地理小区相似程度较高,南北差异显著。云南两栖动物地理分布格局与地势的阶梯变化基本一致。受地形、河流和气候的影响,分布格局的纬度变化规律不明显。在此基础上对结果与地理区划进行了对比。     

利用Bayesian-MCMC方法进行畜禽复杂离散性状QTL定位

复杂离散性状由于表型数据呈离散分布并且提供信息量过小, 因此很难用常规的统计方法对此类性状的QTL进行定位研究. Bayesian-MCMC方法是复杂离散性状QTL定位的重要手段, 该方法通过所有先验信息来推导QTL参数的后验分布并利用Markov Chain随机过程进行抽样的方法对目标参数进行统计推断. 利用Monte Carlo方法, 针对畜禽远交群体模拟产生多个全同胞家系的2级分类复杂离散性状, 然后基于IBD方差组分的随机模型的定位策略, 同时利用MCMC的3种不同抽样技术(Gibbs抽样、Metropolis抽样和Reversible Jump MCMC抽样)产生相应QTL参数的后验样本, 并进行了目标参数的Bayesian统计推断. 结果表明: Bayesian-MCMC方法能够对不同家系结构和QTL效应水平下复杂离散性状QTL进行有效检测; 当家系含量增加时, QTL定位的精确性和准确性提高, 并可适用于效应更小QTL的检测.     

Hierarchical ordering of reticular networks

The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the "root" of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.     

Evaluating scaling models in biology using hierarchical Bayesian approaches

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity.     

Estimation of Global Network Statistics from Incomplete Data

Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible. Previous work addressing the impacts of partial network data is surprisingly limited, focuses primarily on missing nodes, and suggests that network statistics derived from subsampled data are not suitable estimators for the same network statistics describing the overall network topology. We generate scaling methods to predict true network statistics, including the degree distribution, from only partial knowledge of nodes, links, or weights. Our methods are transparent and do not assume a known generating process for the network, thus enabling prediction of network statistics for a wide variety of applications. We validate analytical results on four simulated network classes and empirical data sets of various sizes. We perform subsampling experiments by varying proportions of sampled data and demonstrate that our scaling methods can provide very good estimates of true network statistics while acknowledging limits. Lastly, we apply our techniques to a set of rich and evolving large-scale social networks, Twitter reply networks. Based on 100 million tweets, we use our scaling techniques to propose a statistical characterization of the Twitter Interactome from September 2008 to November 2008. Our treatment allows us to find support for Dunbar''s hypothesis in detecting an upper threshold for the number of active social contacts that individuals maintain over the course of one week.     

Emergence,Evolution and Scaling of Online Social Networks

Online social networks have become increasingly ubiquitous and understanding their structural, dynamical, and scaling properties not only is of fundamental interest but also has a broad range of applications. Such networks can be extremely dynamic, generated almost instantaneously by, for example, breaking-news items. We investigate a common class of online social networks, the user-user retweeting networks, by analyzing the empirical data collected from Sina Weibo (a massive twitter-like microblogging social network in China) with respect to the topic of the 2011 Japan earthquake. We uncover a number of algebraic scaling relations governing the growth and structure of the network and develop a probabilistic model that captures the basic dynamical features of the system. The model is capable of reproducing all the empirical results. Our analysis not only reveals the basic mechanisms underlying the dynamics of the retweeting networks, but also provides general insights into the control of information spreading on such networks.     

Flow similarity,stochastic branching,and quarter-power scaling in plants

The origin of allometric scaling patterns that are multiples of one-fourth has long fascinated biologists. While not universal, quarter-power scaling relationships are common and have been described in all major clades. Several models have been advanced to explain the origin of such patterns, but questions regarding the discordance between model predictions and empirical data have limited their widespread acceptance. Notable among these is a fractal branching model that predicts power-law scaling of both metabolism and physical dimensions. While a power law is a useful first approximation to some data sets, nonlinear data compilations suggest the possibility of alternative mechanisms. Here, we show that quarter-power scaling can be derived using only the preservation of volume flow rate and velocity as model constraints. Applying our model to land plants, we show that incorporating biomechanical principles and allowing different parts of plant branching networks to be optimized to serve different functions predicts nonlinearity in allometric relationships and helps explain why interspecific scaling exponents covary along a fractal continuum. We also demonstrate that while branching may be a stochastic process, due to the conservation of volume, data may still be consistent with the expectations for a fractal network when one examines sub-trees within a tree. Data from numerous sources at the level of plant shoots, stems, and petioles show strong agreement with our model predictions. This theoretical framework provides an easily testable alternative to current general models of plant metabolic allometry.

A general model for the origin of quarter-power scaling in land plants predicts allometry, allometric curvature, and allometric covariation within and across land plants.     

On the long-run sensitivity of probabilistic Boolean networks

Boolean networks and, more generally, probabilistic Boolean networks, as one class of gene regulatory networks, model biological processes with the network dynamics determined by the logic-rule regulatory functions in conjunction with probabilistic parameters involved in network transitions. While there has been significant research on applying different control policies to alter network dynamics as future gene therapeutic intervention, we have seen less work on understanding the sensitivity of network dynamics with respect to perturbations to networks, including regulatory rules and the involved parameters, which is particularly critical for the design of intervention strategies. This paper studies this less investigated issue of network sensitivity in the long run. As the underlying model of probabilistic Boolean networks is a finite Markov chain, we define the network sensitivity based on the steady-state distributions of probabilistic Boolean networks and call it long-run sensitivity. The steady-state distribution reflects the long-run behavior of the network and it can give insight into the dynamics or momentum existing in a system. The change of steady-state distribution caused by possible perturbations is the key measure for intervention. This newly defined long-run sensitivity can provide insight on both network inference and intervention. We show the results for probabilistic Boolean networks generated from random Boolean networks and the results from two real biological networks illustrate preliminary applications of sensitivity in intervention for practical problems.     

Scaling of differentiation in networks: nervous systems,organisms, ant colonies,ecosystems, businesses,universities, cities,electronic circuits,and Legos

Nodes in networks are often of different types, and in this sense networks are differentiated. Here we examine the relationship between network differentiation and network size in networks under economic or natural selective pressure, such as electronic circuits (networks of electronic components), Legos (networks of Lego pieces), businesses (networks of employees), universities (networks of faculty), organisms (networks of cells), ant colonies (networks of ants), and nervous systems (networks of neurons). For each of these we find that (i) differentiation increases with network size, and (ii) the relationship is consistent with a power law. These results are explained by a hypothesis that, because nodes are costly to build and maintain in such "selected networks", network size is optimized, and from this the power-law relationship may be derived. The scaling exponent depends on the particular kind of network, and is determined by the degree to which nodes are used in a combinatorial fashion to carry out network-level functions. We find that networks under natural selection (organisms, ant colonies, and nervous systems) have much higher combinatorial abilities than the networks for which human ingenuity is involved (electronic circuits, Legos, businesses, and universities). A distinct but related optimization hypothesis may be used to explain scaling of differentiation in competitive networks (networks where the nodes themselves, rather than the entire network, are under selective pressure) such as ecosystems (networks of organisms).     

Allometric covariation: a hallmark behavior of plants and leaves

Size is one of the most important axes of variation among plants. As such, plant biologists have long searched for unifying principles that can explain how matter and energy flux and organ partitioning scale with plant size. Several recent models have proposed a universal biophysical basis for numerous scaling phenomena in plants based on vascular network geometry. Here, we review statistical analyses of several large-scale plant datasets that demonstrate that a true hallmark of plant form variability is systematic covariation among traits. This covariation is constrained by allometries that combine and trade off with one another, rather than any single universal allometric scaling exponent for a trait or suite of traits. Further, we show that covariation can be successfully modeled using network approaches that allow for species-specific designs in plants and geometric approaches that constrain relationships among economic traits in leaves. Finally, we report large-scale efforts utilizing semi-automated software tools that quantify physical networks and can inform our attempts to link vascular network structure to plant form and function. Collectively, this work highlights how the linking of morphology, biomass partitioning and the structure of physical distribution networks can improve our empirical and theoretical understanding of important drivers of plant functional diversity.     

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.