A review on anisotropy analysis of spatial point patterns

A major objective of plant ecology research is to determine the underlying processes responsible for the observed spatial distribution patterns of plant species. Plants can be approximated as points in space for this purpose, and thus, spatial point pattern analysis has become increasingly popular in ecological research. The basic piece of data for point pattern analysis is a point location of an ecological object in some study region. Therefore, point pattern analysis can only be performed if data can be collected. However, due to the lack of a convenient sampling method, a few previous studies have used point pattern analysis to examine the spatial patterns of grassland species. This is unfortunate because being able to explore point patterns in grassland systems has widespread implications for population dynamics, community‐level patterns, and ecological processes. In this study, we developed a new method to measure individual coordinates of species in grassland communities. This method records plant growing positions via digital picture samples that have been sub‐blocked within a geographical information system (GIS). Here, we tested out the new method by measuring the individual coordinates of Stipa grandis in grazed and ungrazed S. grandis communities in a temperate steppe ecosystem in China. Furthermore, we analyzed the pattern of S. grandis by using the pair correlation function g(r) with both a homogeneous Poisson process and a heterogeneous Poisson process. Our results showed that individuals of S. grandis were overdispersed according to the homogeneous Poisson process at 0–0.16 m in the ungrazed community, while they were clustered at 0.19 m according to the homogeneous and heterogeneous Poisson processes in the grazed community. These results suggest that competitive interactions dominated the ungrazed community, while facilitative interactions dominated the grazed community. In sum, we successfully executed a new sampling method, using digital photography and a geographical information system, to collect experimental data on the spatial point patterns for the populations in this grassland community.

In the analysis of spatial point patterns, complete spatial randomness (CSR) hypothesis,which is a restriction of a homogenous Poisson process to study region A, operates as a dividinghypothesis between “regular” and “aggregated” patterns. Meanwhile, many alternatives to CSR inaggregated patterns are extensions of homogenous Poisson processes themselves. Therefore, when theCSR hypothesis is rejected, results related to Poisson processes may be used to formulate plausiblealternatives to CSR. In this paper, we propose a new statistic for testing CSR and then by applying it inconjunction with a notion of kernels of a point pattern, we determine the “parents” of a Poisson clusterprocess when the CSR hypothesis is rejected and a Neyman-Scott process is assumed for the pointpattern under alternative hypothesis. We have made power studies for our test statistic by simulation, andhave also surveyed the performance of our method on a certain point pattern. Finally, the whole methodis carried on certain real life data.

Cox processes are natural models for point process phenomena that are environmentally driven, but much less natural for phenomena driven primarily by interactions amongst the points. The class of log-Gaussian Cox processes (LGCPs) has an elegant simplicity, and one of its attractive features is the tractability of the multivariate normal distribution carries over, to some extent, to the associated Cox process. In the statistical analysis of spatial point patterns, it is often assumed isotropy because of a simpler interpretation and ease of analysis. However, there are many cases in which the spatial structure depends on the direction. In this paper, we introduce new families of anisotropic spatial LGCPs that are useful to model spatial anisotropic point patterns that exhibit a degree of clustering. We propose classes of families consisting of elliptical and non-elliptical models. The former can be reduced to isotropic forms after some rotations, while the latter family goes beyond this property. We derive analytical forms for the covariance of the associated random field, and some second-order characteristics. A moment-based estimation procedure is followed to make inference on the parameters that control the degree of anisotropy. The estimation procedure is evaluated through a simulation study under a variety of scenarios and various degrees of anisotropy. Our methodology is illustrated on two real datasets of earthquakes in South America and the Mediterranean Europe.

There is considerable interest in cell biology in determining whether, and to what extent, the spatial arrangement of nuclear objects affects nuclear function. A common approach to address this issue involves analyzing a collection of images produced using some form of fluorescence microscopy. We assume that these images have been successfully pre-processed and a spatial point pattern representation of the objects of interest within the nuclear boundary is available. Typically in these scenarios, the number of objects per nucleus is low, which has consequences on the ability of standard analysis procedures to demonstrate the existence of spatial preference in the pattern. There are broadly two common approaches to look for structure in these spatial point patterns. First a spatial point pattern for each image is analyzed individually, or second a simple normalization is performed and the patterns are aggregated. In this paper we demonstrate using synthetic spatial point patterns drawn from predefined point processes how difficult it is to distinguish a pattern from complete spatial randomness using these techniques and hence how easy it is to miss interesting spatial preferences in the arrangement of nuclear objects. The impact of this problem is also illustrated on data related to the configuration of PML nuclear bodies in mammalian fibroblast cells.

Single tree detection is important for monitoring tree plantations in order to estimate crop yield, which can be used for assessing food and biofuels. In the field of remote sensing, there have been studies regarding single tree extraction using Light Detection and Ranging (LiDAR) point cloud data. Canopy Height Model (CHM) can be simply derived from these LiDAR data where trees can be analysed using different physical characteristics such as tree crown width, and height. However, using these physical characteristics can’t be very useful for identifying which trees are within a plantation, a forest, or a single tree. This is the motivation for developing algorithms of automated differentiation of random trees from plantation trees. Object Based Image Analysis (OBIA) was used to acquire the locations of individual trees. Trees were separated from other land cover in the image using a CHM derived from LiDAR point cloud data. Using watershed algorithm in eCognition, trees with good canopy spacing was easily distinguished. A spatial point pattern analysis was done from the extracted locations of trees to differentiate regularly patterned points from randomly distributed points. Nearest neighbour statistics was done to provide measurement of the distribution of the extracted points. The Z-Score parameter from nearest neighbor was then added to the layers in eCognition as supplement to the available height derivatives such as mean, standard deviation, and different textural parameters. Supervised type of classification was used in order to classify the trees on the image. Training samples of each tree from the image were entered in Support Vector Machine (SVM) to classify the different trees. Two sets of validation were done to compare the results of using the object parameters only, and the object parameters and Z-Score. Addition of the Z-Score from the object parameters increased the obtained accuracy on both validation sets. Classification accuracy based on validation set 1 and set 2 increased by about 20% and 6%, respectively. Additional spatial pattern analysis methods and validation can further prove the use of such layers in improving classification of trees.

PDF HTML阅读 XML下载 导出引用 引用提醒 生态学中的点格局研究概况及其在国内的应用 DOI: 10.5846/stxb201607081399 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然基金项目（31370633）。 A review of point pattern analysis in ecology and its application in China Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:点格局分析是研究生态学格局的工具之一，近年来在生态学中的应用越来越多。为深入了解点格局分析方法在国内的研究与应用情况，以所总结的研究进展、一般步骤和基本要点为背景，分析评述了1996-2015年期间以点格局为主题的国内中文核心期刊文献。结果表明，在国内生态学格局研究中，应用研究占据主导地位，研究对象广泛，包括以树木为主的乔、灌、草等不同生活型的植物，甚至包括景观；基础研究，包括概括性统计量、零模型与点过程模型等方面，以及专用软件工具包的开发等研究薄弱。在应用中存在一定问题，主要表现为：概括性统计量使用单一，且以Ripley的K-函数及其变形为主；零模型（或点过程模型）是科学问题的统计表达，但是有一半以上的研究未明确给出零模型。建议在未来应用研究中重视多种统计量的组合使用和原假设的建立，在探讨热带、亚热带森林等具有复杂空间结构系统的多样性格局时，考虑对象的不同世代和系统的不同垂直层次，并加强多变量或三维概括性统计量的开发、点格局分析方法与动态过程模型的结合研究等工作。 Abstract:Point pattern analysis, i.e., spatial point pattern analysis (SPPA) is a tool used in ecological pattern research and has recently become increasingly popular in ecology. To better understand SPPA research and its application in China, in this review we examined articles regarding SPPA published from 1996 to 2015 in China, which was based on a summary of the research progress, using steps and key points of SPPA. It was found that most articles focused on application research. Although there were extensive study objects, including forests, shrubs, grasslands, and landscapes, trees in forest communities were the main focus in all these application studies. Fundamental studies were found to be underdeveloped, such as studies regarding summary statistics and null models or point process models in SPPA, and the development of specific software packages for SPPA. Two important problems were found in SPPA applications: Firstly, although there are many alternatives, researchers preferred single summary statistics and only selected the K-function or its transformations; and secondly, although selecting null models as null hypotheses was a key step in SPPA, more than half of the research examined did not specify explicit null models. Therefore, it is recommended that different types of summary statistics are used to capture detailed spatial pattern structures, and the ecological questions or hypotheses should be clearly stated and correctly translated into statistical language, i.e., the null model and tests. Vertical layers and different generations should also be considered when studying systems with complex spatial structures, such as in tropical rainforests and subtropical evergreen broad-leaved forests. To enhance basic SPPA applications, these aspects discussed should be strengthened. 参考文献 相似文献 引证文献

Associations between two spatial processes can be due to a real dependence between the two processes or to the dependence on common underlying variables. We propose to test the existence of a real dependence by use of local tests, leading to a global test of real dependence and a map of local interactions. We present first how classical interaction tests based on random rotations between completely observed processes such as those developed by Berman (Berman. Appl. Statist. (1986) 35, 54-62), can be integrated in local analyses. For this purpose, tests are first performed locally, and the distribution of their p-values is then compared to the corresponding value under the null hypothesis. A similar approach is proposed to test non-stationarity of a point pattern by using distance statistics popularized by Diggle (Diggle. Statistical Analysis of Spatial Point Patterns. (1983) Academic Press, New York). The problem of testing the interaction between a random field and a censoring area pattern process is discussed and an approach similar to the preceding ones is then proposed. The methods are mainly applied to agricultural examples but they can be applied to any microscopical images for which one wishes to analyse the spatial structure.

To study the quantified indices for describing the distributional status of diseases in the spatial point pattern analysis, and provide the a statistic in disease prevention and control. G function, F function, J function and K function were summarized based on the inter-case distances from the view of spatial point pattern analysis. Through the introduction of the basic principles, these were used to analyze the data of acute schistosomiasis in the Guichi District, Chizhou City, Anhui province, with the study distances being from 0 to 3000 meters with 50-meter intervals. The findings were also validated by means of spatial moving scan window performed in SaTScan software. A total of 83 cases of acute schistosomiasis identified in Guichi District, and the point map showed that these cases were mainly distributed around the Yangtze and Qiupu rivers. The computational methods and characteristics of the four quantified indices were obtained. These acute schistosomiasis cases were also explored by using these indices, and the results showed that C and K functions were above 95% confidence interval. While, F and J functions were below 95% confidence interval. Ml these four indices showed that spatial clustering existed in the acute cases, which was consistent with the results of spatial moving scan window method. The latter method also found a most likely cluster, the coordinate of the circle center is (30.65 N, 117.44 E), radius is 2.69 km, and relative risk is 12.78 (DIR = 32. 80, P = 0. 0001). The quantified indices to describe the distributional status of diseases have not only solved the obstacle that spatial point pattern map which could only be analyzed qualitatively, but also supplied a theoretical foundation to deepen spatial clustering analysis. To study the quantified indices for describing the distributional status of

This study presents a massively parallel spatial computing approach that uses general-purpose graphics processing units (GPUs) to accelerate Ripley’s K function for univariate spatial point pattern analysis. Ripley’s K function is a representative spatial point pattern analysis approach that allows for quantitatively evaluating the spatial dispersion characteristics of point patterns. However, considerable computation is often required when analyzing large spatial data using Ripley’s K function. In this study, we developed a massively parallel approach of Ripley’s K function for accelerating spatial point pattern analysis. GPUs serve as a massively parallel platform that is built on many-core architecture for speeding up Ripley’s K function. Variable-grained domain decomposition and thread-level synchronization based on shared memory are parallel strategies designed to exploit concurrency in the spatial algorithm of Ripley’s K function for efficient parallelization. Experimental results demonstrate that substantial acceleration is obtained for Ripley’s K function parallelized within GPU environments.

In making inference on Spatial Point Processes often there it is the problem of knowing (or estimating) the distribution of relevant statistics. In the present paper it is proposed a method for estimating the distribution function of any strongly convergent statistic in a large class of Spatial Point Processes. The method is based on conditional simulation and doesn't depend on process' distribution. Asymptotically the statistics generated by this method of "autosimulation" have the same distribution as those generated by Montecarlo methods when the probability structure of the Process is completely known.

Machine Learning Classification of Spatial Patterns of Malignant Cells Reveals Implications in Prognosis and Tumor Microenvironment Composition in Lymphoma

The altered proportion of Korean pine to broadleaved tree species following selective logging strongly affected post-harvest regeneration and species coexistence pattern in a temperate mixed broadleaved/Korean pine forest in eastern Eurasian. Species interaction should be considered when implementing selective logging schemes. It has been documented widely that selective logging can exert varied influences on post-harvested forest structure and dynamics via different logging intensity and rotation. However, few studies have been extended to evaluate the effects of the tree species selected for removal, which is also a critical component in prescribing a selective harvest plan. To clarify the effects and underlying mechanisms of logged tree species selection on species coexistence and regeneration pattern in post-harvested mixed broadleaved/Korean pine (Pinus koraiensis Siebold & Zucc.) forest in Changbai Mountains, China. Four types of plots were established based on different selection of logged tree species. Stand structure, spatial distribution pattern and spatial association of major tree species were analyzed using spatial point pattern (SPP) analysis. The effect of soil nitrogen concentration on forest regeneration was also examined through a Pearson correlation analysis. Sapling density of both Korean pine and commercially valuable broadleaved tree species was significantly greater on plots where Korean pines were logged than on plots where only commercial broadleaved trees were removed. Soil N and density of saplings were not correlated. SPP analysis showed strong negative spatial association between mature Korean pine and saplings of most tree species in most sampling plots. The proportion of Korean pine to broadleaved tree species selected for removal can lead to different stand structure and spatial distribution patterns of tree locations. Due to species–specific competition effects, such variations in spatial association of tree locations can exert varied effects on regeneration in this pine-dominated Eurasian temperate forest. To promote post-harvest tree regeneration and species coexistence, forest managers in this region should consider controlling the density of competition-superior trees such as large-size Korean pines when implementing a selective logging scheme.

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matern covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Approximations are derived for some simple properties of a Strauss-type spatial point process with two types of point, on the assumption that the interactions between points are fairly weak and that boundary effects are negligible. In particular, expansions are obtained of the reduced second moment measure Kij used in the statistical analysis of spatial point patterns. It is found that these expansions may be useful in the estimation of the inter-point interactions and their ranges.

The potential offered by the increasing availability of micro-geographic data is tremendous and still largely not exploited. In this paper, we propose a new methodology to study the spatial dynamics of firm demography making use of such rich source of information. Exploiting the techniques of stochastic spatial point processes (Diggle, Statistical analysis of spatial point patterns, 2003), it is indeed possible to model the firm birth, growth and death explaining the behavior of the individual economic agent. We consider the spatial distribution of the economic activities as the result of a dynamic process occurring in space and time, and we model the micro-spatial patterns as single realizations of marked space–time survival point processes (Rathbun and Cressie, J Am Stat Assoc 89:1164–1174, 1994). Within such a methodological framework firms are created at some random location and some point of time and then operate, grow, and attract (or repulse) the localization of other firms in their neighborhood. The proposed model is fitted to some empirical data on firms’ locations sourced from the ASIA harmonised archive of the Italian National Institute of Statistics. The empirical analysis reveals the presence of local competition behavior in firm creation among small retail food stores, thus shedding light on the phenomena of firm demography.