Objective To study the effects of stand spatial structure on individual diameter growth of natural Larix gmelinii stand so as to provide reference and support for the effective recovery of secondary forests in the region.

Method Based on 50 sample trees of L. gmelinii collected from the secondary forests in Pangu Forest Farm of Tahe Forestry Bureau, eight commonly used forest growth models were compared and evaluated using NLS function in S-Plus software, and the best basic model was determined. Then, the effects of commonly used stand factors, individual tree factors, species diversity, and stand spatial structure on the diameter growth were quantified using the parameterized method. Finally, the optimal mixed-effect model of growth for L. gmelinii trees were developed using NLME function, and the goodness-of-fit of different models were systematically evaluated.

Result Mitscherlich equation was proved to be the optimal basic model of diameter growth for natural L. gmelinii stand, in which the coefficient of determination (R_a²) of the function was 0.6285. The parameter a highly related with the DBH of individual trees, and the mean tree height, the mingling and the uniform of the stand, while the parameter b mainly related with the mean DBH and the competition index of stand. The generalized diameter growth model could improve the value of R_a² by about 31% (R_a² = 0.8264) when comparing with the basic model. However, the technique of mixed-effect model could further improve the value of R_a² by about 17% (R_a² = 0.9710) when the random parameters (a₁), heteroscedasticity function (varPower), and autocorrelation structure (corGaussian) were introduced. The results of 5-fold cross-validation showed that the coefficient of determination, average absolute error and root mean square of the estimated mixed-effect model were 0.9838, 0.56 cm and 0.72 cm respectively, indicating the outstanding prediction accuracy of the model. The simulation results showed that the amount of diameter growth increased significantly with the increase of the DBH of individual tree, the mingling and the uniform values (the closer to 0.5, the better), but decreased dramatically with the increases of the average DBH, the average tree height, and the Heygi's competition index. The corresponding amount of diameter growth would be: +0.45 cm, +3.62 cm, +4.71 cm, −0.34 cm, −0.21 cm and −0.73 cm, respectively, if the value of each variable increased by ten percent, however it highly depended on the stand characteristics and growth stages.

Conclusion The levels of stand uniform and competition will affect the diameter growth of natural Larix gmelinii stand significantly, thus decreasing the competition levels of forest and creating (or maintaining) the random distributions and higher mingling degrees of the trees by appropriately cutting are highly recommended for the forest management in the near future.