Modelling outer- and inner-crown profiles based on tree status and cardinal directions in relation to competition for Larix kaempferi plantations in northeastern China

Using the branch data from 90 sample trees, we developed novel models of outer- and inner-crown profiles for the northern, eastern, southern, and western sides of planted Larix kaempferi (Lam.) Carriere trees in northeastern China via the integration of competition indices (CIs) based on nonlinear marginal regression (NMR). We also used nonparametric boundary regression (NBR) to model the crown-profile boundary. The largest crown radius and inflection points of sample trees were calculated using NBR and NMR. We determined that the CIs of the ratio of the diameter of the subject tree to the quadratic mean diameter (CI3) and ratio of the basal area of the subject tree to the mean basal area of the stand (CI5) were the best distance-independent CIs for incorporation into the models of outer- and inner-crown profiles, respectively. The CIs showed a significant effect on the outer-crown profile in all four directions for dominant, intermediate, and suppressed trees but did not show a significant effect on inner-crown profile. The outer-crown radius increased and inner-crown radius decreased with increasing CI3 and CI5, respectively. The crown profile on the northern side was the largest, which conformed to the regularity in the mean current increment of the sampled branches.