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

  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.