Efficiency of different summary statistics in modelling spatial point patterns of Christ's thorn jujube trees (Ziziphus spina-christi (L.) Wild.)

Abstract

Understanding the ecological processes underlying the spatial distribution of trees is enabled by simulation of their spatial structure within stands. Summary statistics enable modelling the spatial point patterns of trees and provide an efficient representation of the link between point patterns and ecological processes. In this study, five summary statistics, i.e. first-order (intensity function 𝜆(x)), second-order (pair correlation function g(r)), higher-order (T-function T(r)), nearest neighbor (nearest neighbor distribution function D(r)), and morphological (spherical contact distribution function Hs(r)) were used to model the spatial pattern of Christ thorn jujube trees (Ziziphus spina-christi (L.) Wild.) in the south of Fars Province. One real and two simulated homogeneous, 200 × 200 m2 sample plots were selected to investigate the performance of those functions. The results showed that 𝜆(x) significantly followed the homogeneous Poisson process and identified different spatial distributions of Christ thorn jujube trees in three plots. The results also indicated that g(r) was non-cumulative and sensitive to tree patterns in different scales. Although T(r) described the dispersion, randomness, and clustering of trees in the plots, its power to indicate fine structural patterns was not obvious due to low densities of the trees in the plots. The distances to nearest tree were quantified by D(r), which were located about 20 m from each other in all three plots. Finally, the amount of Hs(r) clearly showed the non-randomness patterns of trees in the plots. All in all, it was concluded that different summary statistics characterize different statistical properties of spatial point patterns across the study area.

Keywords

• Summary statistic
• point pattern
• spatial analysis
• Christ’s thorn jujube
• modelling