Adapting the pair-correlation function for analysing the spatial distribution of canopy gaps

Forestry around the world has been experiencing a paradigm shift towards more nature-oriented forest management leading foresters to emulate natural disturbances by their silvicultural treatments. Important characteristics of all disturbances are their size, severity, temporal and spatial distribution. This study focuses on the spatial distribution of gaps in the forest canopy which are typically caused by small-scale, low intensity disturbances. The considerable spatial extent and irregular shape of canopy gaps are obvious obstacles to the application of classical point pattern analysis. The approximation of objects by their centroids does not lead to reasonable results, since the objects are at the same scale as the expected effects. By dividing the study area in grid cells and analysing all cells covered by an object, the size and the shape of the objects is accounted for. Nevertheless, both methods show undesirable effects. Thus we propose a new approach using the boundary polygons of the objects and construct the adapted pair-correlation function from the shortest distances between polygons. The adapted pair-correlation function is presented using simulated data and mapped canopy gaps of a near natural forest reserve. The results of our proposed method are compared to the grid-based approach and the classical point pattern analysis. The presented method provides meaningful results and even reveals the relationship of objects at short distances, which is not possible using the classical point pattern analysis or the grid-based approach. With regard to the analysis of the spatial distribution of canopy gaps, the adapted pair-correlation function proves to be a useful analytical tool.