Abstract: [Objective] Based on the modification for the Kozak equation, the easily measurable individual tree variables were used as the independent variables to develop the maximum outer crown profile model for Pinus sylvestris var. mongolica plantation. The purposes were to provide reference to study tree physiology, competition and crown surface area and volume of individual tree.[Method] The data of 907 largest branches which were selected from 70 sample trees of Pinus sylvestris var. mongolica by established 14 permanent sample plots in Heilongjiang Province were used. The Kozak model was modified to be used as the basic model to describe the crown profile of Pinus sylvestris var. mongolica, and the best model was selected to construct the nonlinear mixed effect model. The plot effect, tree effect and the effect of plot and tree were considered separately and two level nonlinear mixed effect techniques were used to develop the crown profile model. The package of nlme from R package was used to estimate the parameters of the model. AIC,BIC and -2LL were used to evaluate and compare models with different random parameters combinations, different variance-covariance structure and variance function. The best model was selected and the relationships between crown profile and tree variables were also studied. The dummy variable crown profile model for Pinus sylvestris var. mongolica was developed using forest density as the indicator.[Result] The results showed that the finial crown profile model of Pinus sylvestris var. mongolica included DBH, CR and HD. Compared with the basic model, the nonlinear mixed effect model included only plot effect or tree effect, showed significantly increased the fitting effect and the difference mainly sourced from individual tree. For the model employing only sample tree as the 1 level mixed effect, the model taking a₂, a₆ as the random parameters, diagonal matrix as the variance-covariance matrix, ARMA(1, 1) to explain the variance of within-group, power function to eliminate the heteroscedasticity was selected as the best model. The model with 2 level mixed effect had significantly increased the fitting efficiency compared to the 1 level mixed effect model. Using the two level mixed effect model, the relationship between the outer crown profile and tree variables were analyzed. The analysis was done under the situation where the other two variables were kept fixed and the crown radius increased with the increasing of DBH and CR. The crown radius of the upper and lower crown profile increased and decreased with the increasing of HD, respectively. The range of inflection points of outer crown profile was 0.625 0-0.917 0 and averaging 0.841 3. With the increase of suppress intensity, the inflection points moved to the crown base. The crown profile for the stand with the density less than 1 000 trees·hm^-2 was different from those between 1 000 and 2 000 trees·hm^-2 and larger than 2 000 trees·hm^-2.[Conclusion] The modified Kozak model which satisfied the biological reasoning, such that the crown radius equals to 0 at the tree tip and the inflection point was unique along the entire crown, has powerful advantages to simulate the outer crown profile of Pinus sylvestris var. mongolica plantation. 2 level nonlinear mixed effect model significantly increased the fitting efficiency of the model, and it can be applied into the maximum outer crown profile construction.

Key words: Pinus sylvestris var, mongolica plantation, live crown, outer crown profile, Kozak model, nonlinear mixed effect model