不同土地利用方式下喀斯特峰丛洼地土壤微生物群落特征

基于对喀斯特峰丛洼地6种土地利用类型(坡耕地、草丛、灌丛、人工林、次生林、原生林)的土壤微生物、养分、矿物质和植被4组变量35个指标的调查分析,研究了不同土地利用方式下土壤微生物种群数量、微生物生物量C、N、P及其分形特征,以及土壤微生物与植被、土壤养分、矿物质的关系.结果表明:不同土地利用方式下喀斯特峰丛洼地的土壤微生物种群数量及组成不同.微生物种群数量均以原生林和坡耕地最高,人工林最低;3种森林土壤的细菌比率较大,坡耕地、草丛、灌丛的放线菌比率较大,真菌的比率均很小;土壤微生物生物量C、N、P的含量均很高,其中原生林最高;土壤微生物生物量碳与土壤微生物种群数量具有良好的分形关系,而土壤微生物生物量氮、磷与种群数量不存在分形关系;土壤微生物与植被、土壤养分、土壤矿物质显著相关,其中土壤微生物生物量碳与乔木层的Shannon指数、土壤速效氮、Fe₂O₃、CaO含量显著相关.     

Multifractal analysis of wide dynamic range neuron discharge profiles in normal rats and in rats with sciatic nerve constriction

Using normal rats and rats with a chronic constriction injury of the sciatic nerve (injured, model of Bennett-Xie) we investigated the possibility of classifying, by statistical tools, the temporal sequences of neuronal discharges during different noxious and non-noxious stimuli. An analysis was made of both the distribution of the inter-spike intervals and the temporal density of spike trains, the latter being studied within the framework of stochastic universal multifractals, to allow the identification of different random processes involved in the discharge distributions through the Levy index alpha. The statistical analysis shows that the parametrization based on the Levy index seems able to discriminate between different noxious stimuli (mechanical pinching and thermal), both in normal and injured animals. Furthermore, comparing normal and injured animals, although the spontaneous basal and non-noxious stimuli (brushing) evoked activities presented different frequencies, these seem to have the same multifractal structure, while the corresponding statistics of the inter-spike intervals are quite different. This information might be relevant to the understanding of a code of neuronal firing and to the modelling of temporal patterns in acute and chronic noxious signals.     

遗传算法支持下土地利用空间分形特征尺度域的识别

针对土地利用空间分形特征只存在于有限尺度域的现象,采用无标度区内离散点拟合的离差平方和平均值最小作为目标函数,提出了一种基于遗传算法的土地利用空间分形特征尺度域的识别方法,用于准确计算分形维数的有效区间范围。以武汉市武昌区水域空间分形特征为例,利用Quickbird多光谱遥感影像提取土地利用空间信息,重点讨论了基于遗传算法识别土地利用空间分形特征尺度域范围的总体思路、适应度函数和遗传算子等环节;然后分别从测定系数、标准差和无标度区间3个角度,将其同人工判断法、相关系数法以及强化系数法进行对比讨论;并结合研究区域实际的水域空间分布格局,分析不同方法计算所得半径维数的合理性。结果表明,土地利用分形特征尺度域的范围对分形维数计算结果有较大影响;相对于传统计算方法来说,遗传算法在尺度无标度区间识别上具有更高的精度,可以为土地利用空间格局分形特征的研究提供客观指导意见。     

遥感反演植被理化参数的光谱和空间尺度效应

植被理化参数是生态系统中碳和养分等物质循环与能量交换的重要指标,利用遥感技术反演是获取区域及全球植被理化参数的重要手段,但光谱和空间尺度效应的存在,限制了源自不同遥感传感器植被理化参数产品的统一应用。阐述了遥感反演植被理化参数光谱尺度效应的概念及其产生原因,主要从光谱波段位置和波段宽度两方面对国内外相关研究进行了介绍和评述。同时,从遥感反演植被理化参数的空间尺度效应产生原因、空间异质性描述方法和空间尺度转换方法等方面对其国内外研究现状进行了归纳和评述。最后,总结了遥感反演植被理化参数光谱和空间尺度效应研究的不足之处和发展趋势,并指出光谱和空间耦合效应的研究将是一大趋势,而在生态学等领域形成的尺度效应研究的理论和方法也值得借鉴参考。     

喀斯特常绿落叶阔叶混交林植被的空间异质性

基于广西环江木论国家级自然保护区喀斯特典型峰丛洼地常绿落叶阔叶混交林2 hm2动态监测样地,选择4个多样性和5个群落结构属性变量,运用地统计学和分形几何学理论方法,分析植被的空间异质性、分形特征和分布格局,以探讨其维持机制。结果表明:(1)样地树木种类和除平均高度外的4个结构属性变量均值适中,变异系数较高(48.37%～71.01%),植物多样性丰富且稳定性强,Shannon指数、Simpson指数和均匀度指数变异系数仅在5.49%～22.64%之间。(2)除均匀度的Moran’s I系数接近0且无规律外,其他8个属性变量均有不同程度的空间自相关性,分别用球状、指数和高斯模型拟合的决定系数(R2)高达0.900～0.982,C/(C0+C)值和分维数D值分别在0.582～0.827和1.738～1.871之间,具有中等以上的空间依赖性。(3)密度、平均冠幅和高度的自相关范围和变程小于其他指标,其分布和形成过程决定了整个森林植被的空间格局。(4)森林植被的Kriging等值线图充分表征了人为干扰、地形、土壤质量的综合差异。(5)自相关、半方差模型的变程和Kriging等值线图综合分析表明,喀斯特峰丛洼地常绿落叶阔叶混交林空间异质性研究的采样间隔10 m左右较适宜,但采样范围应大于10hm2,这对确定该区域动态监测样地的面积具有一定的指导意义。     

Quantitative comparison of the diversity of landscapes with actual vs. potential natural vegetation

Abstract. In the past 20 years, several metrics have been developed to quantify various aspects of landscape structure and diversity in space and time, and most have been tested on grid‐based thematic maps. Once landscape patterns have been quantified, their effects on ecological functions can be explained if the expected pattern in the absence of specific processes is known. This type of expected pattern has been termed a neutral landscape model. In the landscape‐ecological literature, researchers traditionally adopt random and fractal computer‐generated neutral landscape models to verify the expected relationship between a given ecological process and landscape spatial heterogeneity. Conversely, little attention has been devoted to distribution patterns of potential natural vegetation (PNV) as an ecological baseline for the evaluation of pattern‐process interactions at the landscape scale. As an application for demonstration, we propose a neutral model based on PNV as a possible reference for a quantitative comparison with actual vegetation (AC V) distribution. Within this context, we introduce an evenness‐like index termed ‘actual‐to‐potential entropy ratio’ (H_A/P = H_ACV/H_PNV, where H is Shannon's entropy). Results show that, despite the hypothetical character of most PNV maps, the use of PNV distribution as a baseline for a quantitative comparison with ACV distribution may represent a first step towards a general model for the evaluation of the effects of disturbance on vegetation patterns and diversity.     

Use of fractal dimensions to quantify coral shape

A morphometrical method to quantify and characterize coral corallites using Richardson Plots and Kaye’s notion of fractal dimensions is presented. A Jurassic coral species (Aplosmilia spinosa) and five Recent coral species were compared using the Box-Counting Method. This method enables the characterization of their morphologies at calicular and septal levels by their fractal dimensions (structural and textural). Moreover, it is possible to determine differences between species of Montastraea and to tackle the high phenotypic plasticity of Montastraea annularis. The use of fractal dimensions versus conventional methods (e.g., measurements of linear dimensions with a calliper, landmarks, Fourier analyses) to explore a rugged boundary object is discussed. It appears that fractal methods have the potential to considerably simplify the morphometrical and statistical approaches, and be a valuable addition to methods based on Euclidian geometry.     

Fractal structure and conformational entropy of protein chain

The structures of 25 proteins arbitrarily chosen are investigated by fractal geometry, and their fractal dimensions (D_f) and conformational entropies S(N₀) are calculated by Havlin—Ben Avraham and Monte Carlo method, respectively. Comparison of the D_f and S(N₀) gives the relation: D_f = 1.532 - 3.00 × 10⁻⁴ S(N₀). The entropy data obtained by Monte Carlo method for the chain of random self-avoiding walks confirm the prediction of renormalization group: S(N₀) = 1.544N₀ + 0.1667 In N₀ + 0.1570 where N₀ is the number of residues in a protein chain. Both the D_f and S(N₀) reflect the conformational properties of a protein molecular chain. The idea resulting from the present communication suggests that the thermodynamic behaviours of proteins may be related to multifractals.     

放牧和刈割条件下草山草坡群落空间异质性分析

采用变异矩分析和分形方法,研究了草山草坡群落在放牧和刈割条件下的空间异质性及空间自相关性,结果表明,群落空间格局有尺度依赖性,刈割条件下空物异质性及空间相关性弱,多样性梯度即β多样性小,放牧消除地形引起的样地差异,因而使空间异质性简单化。     

Fractal Patterns of Neural Activity Exist within the Suprachiasmatic Nucleus and Require Extrinsic Network Interactions

The mammalian central circadian pacemaker (the suprachiasmatic nucleus, SCN) contains thousands of neurons that are coupled through a complex network of interactions. In addition to the established role of the SCN in generating rhythms of ∼24 hours in many physiological functions, the SCN was recently shown to be necessary for normal self-similar/fractal organization of motor activity and heart rate over a wide range of time scales—from minutes to 24 hours. To test whether the neural network within the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity of in vivo and in vitro SCNs in rodents. In vivo SCN-neural activity exhibited fractal patterns that are virtually identical in mice and rats and are similar to those in motor activity at time scales from minutes up to 10 hours. In addition, these patterns remained unchanged when the main afferent signal to the SCN, namely light, was removed. However, the fractal patterns of SCN-neural activity are not autonomous within the SCN as these patterns completely broke down in the isolated in vitro SCN despite persistence of circadian rhythmicity. Thus, SCN-neural activity is fractal in the intact organism and these fractal patterns require network interactions between the SCN and extra-SCN nodes. Such a fractal control network could underlie the fractal regulation observed in many physiological functions that involve the SCN, including motor control and heart rate regulation.     

Fractal dimension as an indicator for quantifying the effects of changing spatial scales on landscape metrics

While geographers and ecologists are well aware of the scale effects of landscape patterns, there is still a need for quantifying these effects. This paper applies the fractal method to measure the scale (grain or cell size) sensitivity of landscape metrics at both landscape and class levels using the Gold Coast City in Southeast Queensland, Australia as a case study. By transforming the original land use polygon data into raster data at eleven aggregate scales, the fractal dimensions of 57 landscape metrics as defined in FRAGSTATS were assessed. A series of linear log–log regression models were constructed based on the power law to obtain the coefficient of determination (COD or R²) of the models and the fractal dimension (FD) of the landscape metrics. The results show that most landscape metrics in the area and edge, shape and the aggregation groups exhibit a fractal law that is consistent over a range of scales. The six variations of several landscape metrics that belong to both the area/edge and shape groups show different scale behaviours and effects. However, the metrics that belong to the diversity group are scale-independent and do not accord to fractal laws. In addition, the scale effects at the class level are more complex than those at the landscape level. The quantitative assessment of the scale effect using the fractal method provides a basis for investigating landscape patterns when upscaling or downscaling as well as creating any scale-free metric to understand landscape patterns.     

Lévy Flights and Self-Similar Exploratory Behaviour of Termite Workers: Beyond Model Fitting

Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties –including Lévy flights– in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.     

Computing distribution of scale independent motifs in biological sequences

The use of Chaos Game Representation (CGR) or its generalization, Universal Sequence Maps (USM), to describe the distribution of biological sequences has been found objectionable because of the fractal structure of that coordinate system. Consequently, the investigation of distribution of symbolic motifs at multiple scales is hampered by an inexact association between distance and sequence dissimilarity. A solution to this problem could unleash the use of iterative maps as phase-state representation of sequences where its statistical properties can be conveniently investigated. In this study a family of kernel density functions is described that accommodates the fractal nature of iterative function representations of symbolic sequences and, consequently, enables the exact investigation of sequence motifs of arbitrary lengths in that scale-independent representation. Furthermore, the proposed kernel density includes both Markovian succession and currently used alignment-free sequence dissimilarity metrics as special solutions. Therefore, the fractal kernel described is in fact a generalization that provides a common framework for a diverse suite of sequence analysis techniques.     

Fractal geometry: a tool for describing spatial patterns of plant communities

Vegetation is a fractal because it exhibits variation over a continuum of scales. The spatial structure of sandrim, bryophyte, pocosin, suburban lawn, forest tree, and forest understory communities was analyzed with a combination of ordination and geostatistical methods. The results either suggest appropriate quadrat sizes and spacings for vegetation research, or they reveal that a sampling design compatible with classical statistics is impossible. The fractal dimensions obtained from these analyses are generally close to 2, implying weak spatial dependence. The fractal dimension is not a constant function of scale, implying that patterns of spatial variation at one scale cannot be extrapolated to other scales.     

Does macrophyte fractal complexity drive invertebrate diversity,biomass and body size distributions?

Habitat structure is one of the fundamental factors determining the distribution of organisms at all spatial scales, and vegetation is of primary importance in shaping the structural environment for invertebrates in many systems. In the majority of biotopes, invertebrates live within vegetation stands of mixed species composition, making estimates of structural complexity difficult to obtain. Here we use fractal indices to describe the structural complexity of mixed stands of aquatic macrophytes, and these are employed to examine the effects of habitat complexity on the composition of free-living invertebrate assemblages that utilise the habitat in three dimensions. Macrophytes and associated invertebrates were sampled from shallow ponds in southwest England, and rapid digital image analysis was used to quantify the fractal complexity of all plant species recorded, allowing the complexity of vegetation stands to be reconstructed based on their species composition. Fractal indices were found to be significantly related to both invertebrate biomass–body size scaling and overall invertebrate biomass; more complex stands of macrophytes contained a greater number of small animals. Habitat complexity was unrelated to invertebrate taxon richness and macrophyte surface area and species richness were not correlated with any of the invertebrate community parameters. The biomass–body size scaling relationship of lentic macroinvertebrates matched those predicted by models incorporating both allometric scaling of resource use and the fractal dimension of a habitat, suggesting that both habitat fractal complexity and allometry may control density–body size scaling in lentic macroinvertebrate communities.     

Multiscale patchiness of the calanoid copepod Temora longicornis in a turbulent coastal sea

We present evidence that intermittent variability in zooplanktonabundance can be characterized in terms of multifractals. A3-min-resolution time series of abundance in the calanoid copepodTemora longicornis, taken from a fixed mooring in the coastalwaters of the Eastern English Channel for 66 h, provided thedata for our analysis. The multifractal nature of the distributionof T. longicornis abundance appears to be very different fromthose of purely passive scalars (i.e. temperature and salinity),and also from phytoplankton biomass over a similar range ofscales in similar environments. Finally, we show that the multifractaldistribution of T. longicornis can be wholly described by threebasic parameters in the framework of universal multifractals,opening up very large perspectives for future modeling of pelagicecosystem structures and functions.     

A theoretical framework of ecological phase transitions for characterizing tree-grass dynamics

This paper describes a theoretical framework of ecological phase transitions for modeling tree-grass dynamics and analyzing the shifts or phase transitions from one vegetation structure to another in the southern Texas landscape. This framework implements the integration of percolation theory, fractal geometry and phase transition theory as a method for modeling the spatial patterns of tree-grass dynamics, and nonlinear Markov non-equilibrium thermodynamic stability theory as a method for characterizing temporal tree-grass dynamics and phase transition. An historical sequence of aerial photographs at a Prosopis - thornscrub savanna parkland site in southern Texas was used to determine the parameters of the models. The preliminary analytical result accords well with current understanding and field survey of vegetation dynamics in the southern Texas landscape. The potential of such approaches and other relevant theories such as self-organized criticality and synergetics to vegetation dynamics is also discussed.     

Regional vegetation mapping in Australia: a case study in the practical use of statistical modelling

Conservation evaluation of large areas ( > 10 000 km²) in Australia requires detailed mapping of vegetation types. Predicting the original vegetation cover of extensive cleared areas in an explicit, consistent and repeatable manner necessitates the use of statistical modelling. This paper describes an integrated approach to vegetation mapping in a region of New South Wales, Australia. The approach uses separate statistical models for each tree and shrub species to predict the vegetation composition in each grid cell in a geographic information system (GIS). Allocation of these grid cells to communities allows communities that no longer exist in the remaining remnants of woodland to be defined. Examples of use of this information for management are presented. This paper addresses the practical considerations which constrain the way statistical modelling can be used for vegetation mapping in an applied project. Constraints include: (1) data availability (use of sampling to fill gaps in existing data), (2) the effects of cover abundance values, (3) availability of GIS predictors, (4) data management, (5) current generalised additive model methods and (6) prediction methods. Careful attention to the practicality of all components of a vegetation mapping study is essential if modern methods are to be applied in regional studies which must provide functional products for land managers with limited resources, skills and finances at their disposal.     

Statistical evaluation of colocalization patterns in immunogold labeling experiments

The ultrastructural localization of various antigens in a cell using antibodies conjugated to gold particles is a powerful instrument in biological research. However, statistical or stereological tools for testing the observed patterns for significant clustering or colocalization are missing. The paper presents a method for the quantitative analysis of single or multiple immunogold labeling patterns using interpoint distances and tests the method using experimental data. The clustering or colocalization of gold particles was detected using various characteristics of the distribution of distances between them. Pair correlation and cross-correlation functions were used for exploratory analysis; second order reduced K (or cross-K) functions were used for testing the statistical significance of observed events. Confidence intervals of function values were estimated by Monte Carlo simulations of the Poisson process for independent particles, and results were visualized in histograms. Furthermore, a suitability of K functions modified by censoring or weighting was tested. The reliability of the method was assessed by evaluating the labeling patterns of nascent DNA and several nuclear proteins with known functions in replication foci of HeLa cells. The results demonstrate that the method is a powerful tool in biological investigations for testing the statistical significance of observed clustering or colocalization patterns in immunogold labeling experiments.