Reconstructing spatial tree point patterns from nearest neighbour summary statistics measured in small subwindows

Abstract

Spatial tree data are required for the development of spatially explicit models and for the estimation of summary statistics such as Ripley’s K function. Such data are rare and expensive to gather. This paper presents an efficient method of synthesizing spatial tree point patterns from nearest neighbour summary statistics (NNSS) sampled in small circular subwindows, which uses a stochastic optimization technique based on simulated annealing and conditional simulation. This nonparametric method was tested by comparing tree point patterns, reconstructed from sample data, with the original woodland patterns of three structurally different tree populations. Analysis and validation show that complex spatial woodland structures, including long-range tree interactions, can be successfully reconstructed from NNSS despite the limited range of the subwindows and statistics. The influence of the NNSS varies depending on the woodland under study. In some cases, the sampling results can be improved by reconstruction. Furthermore, it is clearly shown that it is possible to estimate second-order characteristics such as Ripley’s K function from small circular subwindows through the reconstruction technique. The results offer new opportunities for adding value to woodland surveys by making raw data available for further work such as growth projections, visualization, and modelling.