Using nonlinear quantile regression to estimate the self-thinning boundary curveThis article is part of a larger document. View the larger document here.
The relationship between tree size (quadratic mean diameter) and tree density (number of trees per unit area) has been a topic of research and discussion for many decades. Starting with Reineke in 1933, the maximum size-density relationship, on a log-log scale, has been assumed to be linear. Several techniques, including linear quantile regression, have been employed to obtain parameters of the self-thinning line. Some authors recently considered that restriction on the maximum diameter at lower spatial densities resulted in a curvilinear relationship. In this study, a nonlinear quantile regression based on the 99th quantile was used to characterize this upper boundary. The resulting self-thinning curve fit the curvilinear boundary much better than did the Reineke’s self-thinning line