[Crown shape model for planted greening tree species Pinus tabuliformis in Shenyang based on marginal regression.]

Developing outer crown profile prediction models of typical urban greening tree species will lay a foundation for the spatial allocation optimization of urban greening. In this study, Pinus tabuliformis, a typical greening tree species in Shenyang, was selected as the research object. Based on the Crown Window device, a total of 60 sample trees were selected to measure the crown shape, with power equation, segmented polynomial equation, and modified Kozak equation as the basic models. By introducing crown structure variables (the maximum crown radius) and neighbour competition variables (mean tree height, mean diameter at breast height, mean crown width, number for the neighbour trees, and mean crown contact height between sample trees and neighbour trees) through reparameterization, we constructed an outer crown shape model of P. tabuliformis that incorporates neighbour tree competition and maximum crown radius. The results showed that modified Kozak equation had the largest R_a² and the smallest RMSE, as well as good stability. After introducing the maximum crown radius and the mean DBH of neighbour trees into the basic model through reparameterization, the R_a² of the model increased by 0.0693 and the MSER was 14.4%. The maximum crown radius had a great influence on the crown shape, while the crown radius increased with the increases of the maximum crown radius. The influence of mean DBH of neighbour trees on crown shape was weaker than that of maximum crown radius. The upper part of crown increased and the lower part of crown decreased with increasing neighbour tree competition. In this study, the marginal regression outer crown profile model of P. tabuliformis coupled with neighbour tree competition and the maximum crown radius showed good goodness of fit and could reasonably simulate and predict the crown shape of planted P. tabuliformis.