Comparison of Ripley's K-, pair correlation, and O-ring functions in spatial pattern analysis of Christ's thorn jujube trees (Ziziphus spina-christi) in Fars province

Understanding the underlying processes in spatial pattern of trees is an important goal in forest ecology. The first step in characterizing these spatial patterns is to use appropriate summary statistics. This study was aimed to compare four univariate second-order summary statistics (Ripley's K-, L-, pair correlation and O-ring functions) in spatial pattern analysis of Christ's thorn jujube trees (Ziziphus spina-christi) in Fars province. All individual trees with height more than 1 m were mapped in a 200 × 200 m2 plot. Two other point patterns were also generated with similar density and different spatial distributions from the true pattern. The observed pattern of trees showed no spatial heterogeneity as compared to homogeneous Poisson process. The results showed that K- and L-functions did not reveal the clustering of Christ's thorn jujube trees in different spatial scales as shown by pair correlation function and O-ring statistic because of their cumulative structure. The range of dispersion resulted from K- and L-functions (20 m) did not conform the results of pair correlation function and O-ring statistic (11 m). Comparison of mean squared error also showed that O-ring function had the least amount compared to pair correlation, L- and K-functions in all three plots. In general, pair correlation function and O-ring statistic were more precise and efficient than K- and L-functions in analyzing the pattern of Christ's thorn jujube trees in this study.