A New Methodology of Spatial Cross-Correlation Analysis

Spatial correlation modeling comprises both spatial autocorrelation and spatial cross-correlation processes. The spatial autocorrelation theory has been well-developed. It is necessary to advance the method of spatial cross-correlation analysis to supplement the autocorrelation analysis. This paper presents a set of models and analytical procedures for spatial cross-correlation analysis. By analogy with Moran’s index newly expressed in a spatial quadratic form, a theoretical framework is derived for geographical cross-correlation modeling. First, two sets of spatial cross-correlation coefficients are defined, including a global spatial cross-correlation coefficient and local spatial cross-correlation coefficients. Second, a pair of scatterplots of spatial cross-correlation is proposed, and the plots can be used to visually reveal the causality behind spatial systems. Based on the global cross-correlation coefficient, Pearson’s correlation coefficient can be decomposed into two parts: direct correlation (partial correlation) and indirect correlation (spatial cross-correlation). As an example, the methodology is applied to the relationships between China’s urbanization and economic development to illustrate how to model spatial cross-correlation phenomena. This study is an introduction to developing the theory of spatial cross-correlation, and future geographical spatial analysis might benefit from these models and indexes.     

Efficiency of using spatial analysis in first-generation coastal Douglas-fir progeny tests in the US Pacific Northwest

Single-trial and across-trial spatial analyses using autoregressive error structures were conducted for growth traits based on 1,146 data sets from 275 Douglas-fir [Pseudotsuga menziesii (Mirb.) Franco] progeny trials in 45 first-generation breeding zones in the US Pacific Northwest. The breeding zones encompassed a wide range of latitude, longitude, and elevation. Efficiency of using spatial analysis in reducing variation due to site heterogeneity, estimating genetic parameters, and increasing prediction accuracy was compared among different experimental designs, traits, assessment ages, and tree spacings. More than 97% of the data sets showed significant model improvement with spatial analysis, and height showed more improvement than diameter or volume. Spatial analysis on average removed 14~34% of residual variance due to spatial heterogeneity, which resulted in an up to 20% increase in accuracy of breeding value prediction. The coefficient of variation decreased substantially due to spatial adjustment. Rank correlation between predicted gains before and after spatial analysis was about 0.96, and spatial analysis had little effect on the average predicted gain of the top 20% of parents. We did not observe substantial geographic trends in improvements due to spatial adjustment. Across-site spatial analysis had almost no effect on genotype-by-environment interaction but tended to increase among-trial heterogeneity of residual variance. Two different methods for across-trial spatial analysis were compared and discussed.     

基于空间分析的保护生物学研究

 保护生物学家和生态学家早就认识到只有准确地辨识保护对象的空间位置、 范围、 及其相邻的关系(例如边缘)和连接度, 以及依存的地形和气候等生境条件, 才能发现生物种群和生境在空间的扩散与收缩、 增长与灭绝的动态, 揭示分布的格局, 从而系统、 全面地了解保护对象和生境的存在状态、 破碎程度和变化趋势, 进行有效的自然保护。 得益于新兴的空间分析技术, 保护生物学自20世纪90年代以来取得了很大的进步。基于空间分析的保护生物学研究是最近10年左右大力发展的新保护生物学的重要基础。 该文结合作者的研究工作,综述了基于空间分析的保护生物学项目, 探讨了保护生物学发展历史、 主要研究方法与应用、 以及今后的可能发展趋势。 在生物多样性的丰度和分布的空间解绎部分,通过综述世界保护监测中心的图解全球生物多样性的工作, 如国家尺度的生物多样性水平、 植物多样性的分布中心和维管束植物科的多样性等的空间分布 ,介绍了 Dobson等图示美国主要濒危植物、 鸟类、 鱼类和软体动物等4个主要类群在县(County) 为基本空间单位上分布的空间格局, 讨论了生物多样性空间解绎的意义。在第二部分用世界资源研究所的全球森林监测(Global forest watch)项目, 美国的国家保护缺失区分析(GAP analysis)项目, 美国林务局的无路自然区域(Roadless area)保护项目和加拿大自然审计(Nature audit)项目, 以及北美和东亚生物多样性空间分布的比较分析和生物入侵的空间分析等具体实例来说明生物多样性空间分布变化比较分析方法的应用。 过去20年来, 面向空间格局的生态学和保护生物学研究得到了快速的发展, 特别是空间格局的描述、 由地统计演变而成的空间统计、 地理信息系统、 基于个体(或栅格)的空间解绎模拟模型、 基于斑块(Patch)的种群理论及其发展(如复合种群理论, 源 汇模型等)等。在第三部分, 以美国森林破碎度空间格局分析和美国太平洋西北演替后期森林的空间格局分析为例, 介绍了空间格局分析在保护生物学中的应用。 同时介绍了澳大利亚保护生态学家Lindenmayer 和美国著名景观生态学家Franklin 2002年提出的模板(Matrix)保护理论,把保护的眼光不局限在面积不多而且分散的保护区中,应注意景观模板和保护区相邻的原生区域的综合保护, 这样将大大扩展保护的范围, 并且平衡保护与发展的关系。最后, 介绍了在保护生物学中已有一定应用的空间模型和模拟, 包括了空间解绎模型(Spatial explicit model)、 基于过程(Process-based)的空间模拟模型、 面向代理(Agent-based)的空间适应模拟模型(SWAM)以及与此有关的动态全球植被模型(DGVM)。 通过上面的讨论和综述, 预测一个新的保护生物学的分支: 空间保护生物学, 已经逐渐成熟问世, 这门基于现代信息技术和空间技术的新学科已经而且还将为全球生物多样性的研究和保育作出重大的贡献。     

Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation

Question: Are there spatial structures in the composition of plant communities? Methods: Identification and measurement of spatial structures is a topic of great interest in plant ecology. Univariate measurements of spatial autocorrelation such as Moran's I and Geary's c are widely used, but extensions to the multivariate case (i.e. multi‐species) are rare. Here, we propose a multivariate spatial analysis based on Moran's I (MULTISPATI) by introducing a row‐sum standardized spatial weight matrix in the statistical triplet notation. This analysis, which is a generalization of Wartenberg's approach to multivariate spatial correlation, would imply a compromise between the relations among many variables (multivariate analysis) and their spatial structure (autocorrelation). MULTISPATI approach is very flexible and can handle various kinds of data (quantitative and/or qualitative data, contingency tables). A study is presented to illustrate the method using a spatial version of Correspondence Analysis. Location: Territoire d'Etude et d'Expérimentation de Trois‐Fontaines (eastern France). Results: Ordination of vegetation plots by this spatial analysis is quite robust with reference to rare species and highlights spatial patterns related to soil properties.     

分形理论及其在土壤空间变异研究中的应用

土壤具有不同程度的空间变异性,土壤空间变异研究对于土壤管理有重要意义.本文简要综述了分形理论及其在土壤空间变异研究中的应用,重点讨论了利用矩方法计算土壤属性分形维,多重分形分析土壤空间变异性及基于多重分形谱参数的土壤属性尺度转换.早期研究验证了分形理论在分析土壤空间变异中的有效性和应用潜力,国内外近期研究则报道了利用分形及多重分形理论分析土壤空间变异的最新进展.分形理论可以成为量化土壤属性空间变异性及尺度转换的重要工具.     

Spatial interactions and resilience in arid ecosystems

We present a mathematical analysis of the consequences of spatial interactions between vegetation patches by means of water flow for the functioning of arid systems. Our model results suggest that spatial exchange of water improved the resilience to disturbances and increased the resistance to human-induced loss of cover. Furthermore, spatial exchange of water allowed vegetation to persist at lower rainfall levels compared to systems that lack spatial interactions. Our analysis stresses the general importance of spatial interactions for the functioning of ecological systems.     

Exploring Spatial and Multitype Assemblages of Species Abundances

The ecological theory of the existence of multiple stable states between species, or the spatial heterogeneity of some unobserved environmental factor, supports the idea of multitype interactions between species. These multitype interactions can lead to different assemblages of species abundances. An exploratory tool for the detection of these species assemblages and for their spatial analysis is presented in this article. A two‐stage analysis is proposed. First, a classification into types of species assemblages using only the species abundances at each site, regardless of their spatial location, is performed. The clustering procedure is based on multivariate normal mixtures and provides a measure of the classification uncertainty. Second, some tools for the study of the spatial structure of these types of assemblages are presented. We transfer the classification uncertainty to the spatial analysis of the classes in order to draw more accurate conclusions. This classification and spatial analysis method is used to point out a spatial gradient of infection in a host–pathogen system in the Åland Islands in Finland. It can be a useful preliminary tool for ecological studies involving the spatial distributions of several species.     

IKONOS影像景观格局特征尺度的小波与半方差分析

建立不同方向和尺度下景观格局的小波分析方法,并以IKONOS PAN 1m 影像为例,对城市景观和农田景观格局进行了实例研究,并与半方差函数的分析结果进行比较分析。试验结果发现试验区的城市景观图像表现出不同层次和方向的结构特征,主要是阴影－单个楼房－楼房与道路的组合3个尺度的特征,分别出现在2m,16m和128m以及256m分析尺度上,农田景观主要是树木行－农田2个层次和方向尺度特征组合,分别为2m,128m和256m。半方差分析结果对试验区景观结构的多层次和方向不敏感,但可发现景观结构的总体平均特征。城市景观总体结构在空间上的变程为135m,反映的是楼房与道路组合的总体平均特征;农田景观总体结构在空间上的变程为152m。通过改变半方差函数的分析范围和计算间距可以克服半方差对多尺度分析的不足,如该试验通过缩小城市景观和农田分析范围,也发现城市景观有一个在空间结构上15m的变程,与小波分析的特征尺度16m非常接近,而农田景观出现空穴效应的周期一半长度大约为2m,正好是小波分析出种植树木的行距结构特征尺度的大小。这要分析者对研究有一定的先验知识才能够做到选择合适的分析范围,而这恰是景观格局特征尺度分析服务的目的。通过试验区研究证明小波分析是一非常有应用前景的景观格局研究方法,与半方差分析相比,对在解释多尺度结构和不同方向的结构具有明显的优势,且不受分析数据统计平稳假设的约束,但由于对图像分解是基于2进制,导致分析尺度以2的幂函数变化,不像半方差分析可通过理论模型拟合,对特征尺度的估计可以是连续的。     

宏观生态学研究的特点与方法

宏观生态学是研究生态系统以上层次的生态学,研究对象为大尺度复杂系统,研究内容和方法都具有不同于传统生态学的明显特点。重视对空间异质性的研究,重视人类的生态作用,注意运用等级结构理论,其研究结果常常是非实验性和非稳定性的。遥感和地理信息系统是空间数据采集和管理、分析的主要手段,景观分析和景观模型是宏观生态研究的重要方法,定位观测试验的网络研究则是实现宏观整体研究的必由之路。     

Spatial analysis of eucalypt dieback at Coranderrk,Australia

Abstract. The cause of tree disease in any location is difficult to diagnose because of the multiplicity of potential causes. Spatial analysis provides useful evidence on the significance, scale and shape of patterns for disease diagnosis. This study explores the causes of dieback through spatial analysis of tree health at Coranderrk Reserve, an example of an important conservation reserve on the urban fringe of Melbourne, Victoria. Ca. 200 trees were sampled at two sites and measured for position, diameter and height in each of two different community types. An index of tree health was developed, and each tree was assigned a value of health. Dead trees were categorized based on state of decay. Correlograms using Moran's I found significant spatial structure at both study sites. The study employed a method of analysis that compares the spatial patterns in dead and living trees. When all dead trees were eliminated from the analysis, significant spatial pattern was found only at one site. The spatial structures obtained were compared with those expected from the different possible causes of tree dieback. Some potential explanations were eliminated. The results illustrate how spatial analysis may make useful contributions to disease diagnosis if employed systematically together with other modes of investigation.     

基于GIS的城市区域噪声空间分析

GIS技术在城市噪声管理中已经得到了广泛的应用,城市噪声监测部门在日常工作中会积累大量的数据资料,噪声地图的发展更是提供了大量的模拟噪声数据。从地学的视角来分析城市环境噪声问题,采用GIS空间分析软件Geoda支持的"箱线图"和"分层设色图"方法,通过分析现有的数据来发现噪声"热点",实施噪声评估,分析区域的环境噪声,还可轻易发现该区的噪声分布特点。这种分析方法将数据与相关的地理环境相对应,噪声数据反应的规律和噪声的空间格局得以直观地展现,分析结果可作为环境噪声研究、环境管理和政策制定的参考,是研究城市环境噪声状况的新途径。     

闽江河口湿地土壤盐分的空间分异与集聚特征

探究河口湿地土壤盐分的空间异质性,揭示分异格局下的空间集聚特征,对河口湿地的可持续发展具有重要意义。本文以福州市闽江河口湿地的Landsat 8遥感影像、数字高程模型和地面实测土壤盐分为数据源,利用相关性分析与主成分分析法选取显著性环境因子,去除变量间的共线性,分别采用支持向量机回归克里格法(SVROK)和回归克里格法(RK)分析了土壤盐分空间异质性,在基础上运用空间自相关法定量描述了土壤盐分空间集聚特征。结果表明: 通过主成分分析提取出3个主成分,可解释数据总方差的85%,反映植被覆盖、土壤属性和地形状况等综合变化信息,并保留原始变量的大部分信息;土壤盐分及其插值残差的空间变异受结构性因素和随机性因素的影响,采用主成分为自变量所建立的SVROK模型能更为精准地体现土壤盐分 “北高南低”的空间异质特征;土壤盐分的Moran I大于0.5,具有显著的空间正相关,空间集聚程度较高,呈现出“高值集聚、低值广布、低值包围高值”的空间集聚特征。     

A quantitative and statistically robust method for the determination of xylem conduit spatial distribution

? Premise of the study: Because of their limited length, xylem conduits need to connect to each other to maintain water transport from roots to leaves. Conduit spatial distribution in a cross section plays an important role in aiding this connectivity. While indices of conduit spatial distribution already exist, they are not well defined statistically. ? Methods: We used point pattern analysis to derive new spatial indices. One hundred and five cross-sectional images from different species were transformed into binary images. The resulting point patterns, based on the locations of the conduit centers-of-area, were analyzed to determine whether they departed from randomness. Conduit distribution was then modeled using a spatially explicit stochastic model. ? Key results: The presence of conduit randomness, uniformity, or aggregation depended on the spatial scale of the analysis. The large majority of the images showed patterns significantly different from randomness at least at one spatial scale. A strong phylogenetic signal was detected in the spatial variables. ? Conclusions: Conduit spatial arrangement has been largely conserved during evolution, especially at small spatial scales. Species in which conduits were aggregated in clusters had a lower conduit density compared to those with uniform distribution. Statistically sound spatial indices must be employed as an aid in the characterization of distributional patterns across species and in models of xylem water transport. Point pattern analysis is a very useful tool in identifying spatial patterns.     

Iterative kriging for removing spatial autocorrelation in analysis of forest genetic trials

Conventional analysis of spatially correlated data in inadequately blocked field genetic trials may give erroneous results that would seriously affect breeding decisions. Forest genetic trials are commonly very large and strongly heterogeneous, so adjustments for micro-environmental heterogeneity become indispensable. This study explores the use of geostatistics to account for the spatial autocorrelation in four Pinus pinaster Ait. progeny trials established on hilly and irregular terrains with a randomized complete block design and large blocks. Data of five different traits assessed at age 8 were adjusted using an iterative method based on semivariograms and kriging, and the effects on estimates of variance components, heritability, and family effects were evaluated in relation to conventional analysis. Almost all studied traits showed nonrandom spatial structures. Therefore, after the adjustments for spatial autocorrelation, the block and family × block variance components, which were extremely high in the conventional analysis, almost disappeared. The reduction of the interaction variance was recovered by the family variance component, resulting in higher heritability estimates. The removal of the spatial autocorrelation also affected the estimation of family effects, resulting in important changes in family ranks after the spatial adjustments. Comparison among families was also greatly improved due to higher accuracy of the family effect estimations. The analysis improvement was larger for growth traits, which showed the strongest spatial heterogeneity, but was also evident for other traits such as straightness or number of whorls. The present paper demonstrates how spatial autocorrelation can drastically affect the analysis of forest genetic trials with large blocks. The iterative kriging procedure presented in this paper is a promising tool to account for this spatial heterogeneity.     

Statistical and Economic Techniques for Site-specific Nematode Management

Recent advances in precision agriculture technologies and spatial statistics allow realistic, site-specific estimation of nematode damage to field crops and provide a platform for the site-specific delivery of nematicides within individual fields. This paper reviews the spatial statistical techniques that model correlations among neighboring observations and develop a spatial economic analysis to determine the potential of site-specific nematicide application. The spatial econometric methodology applied in the context of site-specific crop yield response contributes to closing the gap between data analysis and realistic site-specific nematicide recommendations and helps to provide a practical method of site-specifically controlling nematodes.     

Quantifying Landscape Spatial Pattern: What Is the State of the Art?

Landscape ecology is based on the premise that there are strong links between ecological pattern and ecological function and process. Ecological systems are spatially heterogeneous, exhibiting considerable complexity and variability in time and space. This variability is typically represented by categorical maps or by a collection of samples taken at specific spatial locations (point data). Categorical maps quantize variability by identifying patches that are relatively homogeneous and that exhibit a relatively abrupt transition to adjacent areas. Alternatively, point-data analysis (geostatistics) assumes that the system property is spatially continuous, making fewer assumptions about the nature of spatial structure. Each data model provides capabilities that the other does not, and they should be considered complementary. Although the concept of patches is intuitive and consistent with much of ecological theory, point-data analysis can answer two of the most critical questions in spatial pattern analysis: what is the appropriate scale to conduct the analysis, and what is the nature of the spatial structure? I review the techniques to evaluate categorical maps and spatial point data, and make observations about the interpretation of spatial pattern indices and the appropriate application of the techniques. Pattern analysis techniques are most useful when applied and interpreted in the context of the organism(s) and ecological processes of interest, and at appropriate scales, although some may be useful as coarse-filter indicators of ecosystem function. I suggest several important needs for future research, including continued investigation of scaling issues, development of indices that measure specific components of spatial pattern, and efforts to make point-data analysis more compatible with ecological theory.     

Genetic Analysis of Invasive Plant Populations at Different Spatial Scales

Measuring genetic diversity requires selection of a spatial scale of analysis. Different levels of genetic structuring are revealed at different spatial scales, however, and the relative importance of factors driving genetic structuring varies along the spatial scale continuum. Unequal gene flow is a major factor determining genetic structure in plant populations at the local level, while the effect of selection imposed by environmental heterogeneity increases with the spatial scale of analysis. At a continental and global scale genetic structure of invasive plant populations is significantly affected by founder effect and propagule transport via human vectors. Although genetic analysis at one spatial scale provides only partial information about the invasion process, little published research reports such data for the same species at multiple scales. A multi-faceted approach to investigating the genetic structure of invasive plant species that incorporates sampling at different spatial and temporal scales would provide a more complete picture of the role of genetic forces in invasion.     

Context dependency and metacommunity structuring in boreal headwater streams

We studied the relative importance of spatial and environmental factors as determinants of algal, bryophyte, and macroinvertebrate metacommunities in two boreal drainage basins differing in spatial extent. We used eigenfunction spatial analysis to model the spatial relationships among sites and distance‐based redundancy analysis to partition the variability in biotic communities between the spatial filters generated through spatial eigenfunction analysis and the environmental factors measured in the field. In the smaller study area, each metacommunity was structured mostly by environmental factors. This was evidenced by the fact that either the pure environmental effect was significant or environmental factors were strongly spatially structured. In the larger study area, only pure environmental effects were significant. These findings suggest that the environmental control prevails in boreal headwater streams. However, our findings also suggest that the specific details of the community‐environment and community–space relationships are dependent on the focal organism group and drainage basin.     

Zebra stripes and tiger stripes: the spatial frequency distribution of the pattern compared to that of the background is significant in display and crypsis

Some striped animals are camouflaged in their natural environment, whereas others are conspicuous. Mammals are known to have spatial frequency analysers in their visual mechanism, and it is suggested that the spatial characteristics of a striped pattern are different in camouflaged and conspicuous animals. Fourier analysis of the stripes of the zebra shows spatial frequencies in the pattern that are unlikely to be present so strongly in their natural background scene. A similar analysis of the camouflaging stripes of a tiger show that the distribution of spatial frequencies are similar to that in the background scene.     

Spatial-pattern analysis in a territorial spider: evidence for multi-scale effects

Territorial animals maintain a certain distance to neighbouring conspecifics, presumably leading to a regular spatial pattern through social spacing. Nevertheless, most animal populations are assumed to show aggregation at certain distance ranges, reflecting the scale dependency of spatial patterns. Leucorchestris arenicola (Araneae: Sparassidae) is a burrow-living spider species that shows territorial behaviour against conspecifics. A multi-scale approach in spatial analysis revealed that territory owners had fewer neighbours than expected under spatial randomness at distances up to 6 m. Behavioural field experiments showed that territory owners were able to perceive and react to burrow constructing neighbours up to at least 4 m distance from their own burrow. At larger distances individuals were often more aggregated than expected under spatial randomness. Analysing adult and immature relationships showed attraction between different development stages at small distances and avoidance at larger distances. The analysis reveals diverse spatial patterns in a territorial and cannibalistic species, showing that both behaviour and environment affect pattern development at different distances. The study outlines the importance of multi-scale approaches for spatial analysis and the need for accompanying experiments to facilitate the interpretation of results.