A permutation test of spatial randomness: application to nearest neighbour indices in forest stands

The ability to precisely describe forest spatial structures, and their modifications through timber harvesting, is of prime importance for sustainable management of complex forest ecosystems, especially regarding uneven-aged, multi-species forests. For this purpose, forest managers require statistical indices that are meaningful descriptors of the spatial structure of a given forest ecosystem. This paper presents a new sensitive permutation test of spatial randomness for solving the classification problem of three nearest neighbour-based indices. The test enables a categorisation of a spatial pattern as a whole into one of three groups: regular, random or cluster, with a sensitivity comparable to that of Ripley's L test, at finer scales. The examples illustrate how the Clark and Evans, the uniform angle, and the mean directional indices can be used for precise detection of departure from spatial randomness. The results show that these three indices should be used simultaneously because they are sensitive to slightly different types of processes.