Abstract: [Objective] The maximum outer and inner (defoliation part) crown shape predicted models for Larix olgensis plantation were developed based on the easily measurable individual tree variables to provide suitable approach to estimate crown surface area, crown volume and crown biomass for L. olgensis plantation.[Method] Using branch analysis data of 49 trees from Mengjiagang forest farm in Heilongjiang Province, the models of maximum outer crown and inner shape were developed. Outer crown shape predicted model constructed the continuous segmented equation with constraints and biological reasoning by employing the segmented regression technology. The outer crown radius equaled "0" at the tree tip and the inflection point where crown radius got maximum value was unique. Different from outer model, the straight line was used to model the inner crown shape. The relationships between the estimated parameters and tree variables were analyzed and the most intimate variable or variables combination were included in the models. The best models were selected as the basic model to develop the one level mixed effect model for the outer and inner crown shape. Based on the fixed effect of models, the outer and inner crown shapes were simulated.[Result] Diameter at breast height (DBH), tree height to diameter ratio (HD), crown length (CL) combined with crown ratio (CR) would predict the outer crown shape with the high accuracy. While the inner crown shape was modeled as DBH, HD and CL. The predicted accuracy was significantly increased by using 1 level (plot) mixed effect models compared with the basic models based on the goodness-of-fit and validation criteria. The coefficients of determination (R²), RMSE and average bias (Bias) of outer crown shape predicted model were 0.914 2,0.232 7 m,0.001 2 m respectively and 0.723 5,0.147 0 m,-0.000 034 m for the inner crown shape predicted model,respectively. Compared to the basic model, R² increased,while RMSE and Bias decreased for the mixed effect model. The segmented polynomial can reflect the variation regularity of the inflection point within the entire crown. The radii of the outer crown shape increased with the increase of DBH and CL, and decreased with HD and CL while other variables kept constant. The radii of inner crown shape increased with DBH, HD and CL.[Conclusion] The segmented polynomial equation with biological reasoning and linear model could effectively reflect the outer and inner crown shape. The models which possessed the random effect have improved the prediction accuracy and heteroscedasticity features of the models. Based on the fixed effect, the model could give reasonable simulation to the outer and inner crown shape. The segmented polynomial equation was flexible to describe the movement regularity of inflection points within the entire crown. Singular linear model performed well in modeling inner crown shape.

Key words: larch (Larix olgensis) plantation, outer crown shape, inner crown shape, nonlinear mixed effect model