Toward a better understanding of forest spatial patterns:A generalisation of the uniform angle index

Spatial structure is important for characterizing a forest ecosystem. Among a myriad of spatial structure indices, the Uniform Angle Index (UAI) is rather special. The UAI quantifies a spatial pattern based on angles between neighbouring trees, thereby offering new insights into close range tree arrangements, competition, and stand dynamics. However, previous theoretical studies of the UAI have primarily relied on simulation stand and hence the uncertainty associated with them since its inception. Therefore, a mathematical derivation is still lacking. In this study, we present a theoretical framework for the UAI with the aim of broadening its applicability in quantifying the intensity of interactions among trees. Our theory is developed at two levels, the individual tree level and the stand level. The objective is to eliminate any simulation-induced uncertainty and bias and to enrich the theoretical foundation and applicability. We present a significant improvement of the UAI for estimating interaction strength among trees by the distance between an ideal and a real stand. This research highlights the opportunities for point pattern research in a new multidisciplinary science of forest ecology by growing knowledge and information along scientifically meaningful lines.