Ripley's K函数方法修正与估计方法比较

Algorithm Modification and Estimation Comparison of Ripley's K-function

深入研究空间点格局分析方法,探讨Ripley’s K函数应用问题,梳理其边界效应改正的定义,综合考虑随机模拟动态性、参数定义合意性和算法可靠性,详细分析各种边界改正算法的优缺点,避免函数的误用。以中国云南省某柑橘种植园为例,采用Ripley’s K函数修正的各种方法,对柑橘植株营养分布的空间点格局进行估计与比较。研究发现,蒙特卡洛模拟次数越多,空间点格局估计结果越准确,建议模拟次数大于2000次;受困于动态性难题,基于商业软件的算法会导致空间点格局分析结论具有一定的不确定性,建议先构建一组虚拟的空间点格局,再做蒙特卡洛模拟;推荐使用基于GIS技术的边界效应改正算法,可将一般的矩形研究区推广至任意多边形,能够提高Ripley’s K函数估计结果的可靠性。

Objectives The Ripley's K-function has been widely applied to test for spatial point patterns in many fields such as economic geography,plant geography,and epidemiology.Because of the mathematical confusion of spatial point processes,there are many errors in measuring the distributions of spatial point objects in the corresponding published papers.Methods This paper discusses Monte Carlo simulation method in the application of Ripley's K-function from perspectives of dynamics of random point patterns,suitability of parameter definition,and reliability of edge correction algorithms.First,we introduce the estimation methods of spatial point pattern analysis based on Ripley's K-function.Second,the formula of Ripley's K-function is corrected by various edge effect correction methods and compared in the applications.Finally,the modified algorithm is employed for spatial point pattern analysis of the nutrient concentrations of orange plants in Xinping County,Yunnan Province,China.Results The preliminary results indicated that the number of Monte Carlo simulations has a great influence on the analysis of the observed spatial point patterns.The significance tests of the observed spatial point patterns change in the process of running ArcGIS Ripley's K-function software package,showing some degree of uncertainty of the observed results.The edge effect correction of Ripley's K-function based on GIS techniques is greatly recommended due to its extension to an arbitrary polygon from a common rectangular shape.Conclusions Considering the popularity of Monte Carlo simulation in statistics and spatial data analysis,this paper provides important insights on edge correction and significance tests in other spatial clustering methods.