Analysis of single tree productivity and growing space on long term trial plots - Methods, program development and initial results

Are trees with larger crowns more productive than those with smaller ones? How is the productivity of single trees related to stand productivity? These questions are of significance as forest management, increasingly focuses on the single tree. In this paper, results from longterm trial plots are presented which provide interesting insights into the relationship between growth and growing space. Of particular importance for this investigation is the fact that crown radii measurements and stem position on the plots were carried out some time ago. A new method is presented and discussed to assign a certain. ground area to each tree. The method is based on Voronoi-diagrams and uses crown size and the distance between neighboring trees to determine the space occupied by a particular tree in the entire stand area. The method requires a two-step procedure. First, non-overlapping crown projection areas are isolated from the crown radii measurements. These areas serve as polygonal operators. Then, the rest of the crown projection area and the uncovered ground area are distributed evenly between the trees involved. The relationship between the available ground area and tree growth are presented for 5 trial plots, including the species oak (Quercus petrea), spruce (Picea abies) and beech (Fagus sylvatica). It is apparent that single tree growth increases initially-with decreasing stand density but approaches a saturation point after which the increasing growing space has no further effect on individual growth. Thus, tree growth per related ground area decreases with increasing crown size, particularly if the crowns are already large. The results can be used to estimate the optimal stem number per hectare for maximum single tree growth or maximum stand productivity, respectively.