Based on data from 83 sample plots (30 m × 30 m) of Larix principis?rupprechtii and Betula platyphylla in the Saihanba mechanical forest farm, the optimal position indices of the different tree species were determined based on six basic site index models (Richards, Log-Logistic, Logistic, Power, Weibull and Korf models) with biological significance. The basic models for the different tree species were fitted and evaluated using the least square method. The best basic model of the different tree species was selected based on the model evaluation index. A nonlinear mixed effect position index model for each tree species was constructed using the Gauss-Newton method. Then, the geometrical linear regression method was used to construct the position index conversion equation between the different tree species based on a nonlinear mixed effect model.

Of the six candidate basic site index models, the Richards and Logistic models were the optimal models for Larix principis?rupprechtii and Betula platyphylla, respectively. In the study, when a site index model with two random effects was constructed, the nonlinear mixed effect model of the different species could not converge, so only one random effect parameter was inclu?ded in the site index model of the different species. When the asymptotic and shape parameters were applied, the nonlinear mixed effect position index model of Larix principis?rupprechtii and Betula platyphylla had a higher fitting precision. Based on the analysis of the prediction of the residuals of the nonlinear mixed effect model, it was determined that there was no heteroscedasticity in the distribution of the residuals of the different tree species, which shows that the nonlinear mixed effect site index model of the different tree species has better prediction and practicability accuracies.The parameters and evaluation indices of the site index conversion equation for Larix principis?rupprechtii and Betula platyphylla were constructed using a geometric linear regression algorithm. The transformation coefficients of the different tree species were determined to be 0.88 and 0.91, respectively, indicating that the prediction accuracy of the site index conversion equations for the different tree species was higher.

In this study, based on the biological significance of the site index prediction model, Richards and Logistic models were determined as the optimal site index models of Larixprincipis?rupprechtii and Betula platyphylla, respectively. Based on the optimal model, the nonlinear mixed effect site index prediction model of the different tree species was constructed using nonlinear mixed effect modeling technology. When the random effect parameters act on the asymptote and shape parameters, the fitting accuracy of the parameters is high. In addition, the transformation equation for the site index of the different species was established using a geometric regression algorithm, which could provide a scientific basis for site quality evaluations and production potential predictions of mixed forests.