Fig. 1.

Cumulative probability distribution of the range of influence r_i for the BCI dataset (1995) (24). is the fraction of trees whose minimum distance to a tree of bigger size is > r_i (measured in meters). The solid line is a power law with exponent -2, equivalent to an exponent of -3 for the PDF. Surprisingly, the power law behavior holds up to the size of the forest that is much larger than the largest crown size and there is little need for the scaling function to provide the expected cutoff of pure power law behavior. This fact and that this exponent is independent of H has a simple interpretation. Indeed by assuming a random distribution of trees within the forest, which ought to be true for trees separated by a large distance, one can prove that the PDF of r_i is a power law with the same decay exponent of 3. It is this harmonious matching of exponent values at short length scales (where the tree shape and the width of the crown matter) and the long length scale behavior (where one may apply random distribution considerations), which leads to an almost perfect power law relationship extending over a wide range of r_i.