Abstract: [Objective] This paper established the nonlinear mixed effects model for height-diameter relationship in multi-storied and multi-species mixed forests. The purpose of this study was to provide some references for the further study on growth rule in mixed forests. [Method] A total of 87 temporary plots were used in Larix principis-rupprechtii and Betula platyphylla mixed forest of Saihanba National Forest Park, Hebei Province, China. Plot size was 20 m × 30 m. A total of 4953 individuals of Larix principis-rupprechtii and 3 608 individuals of Betula platyphylla were investigated. 13 typical models were selected to fit height-diameter relationship. The best-fit model was chose as the basis for building mixed-effects models. Both fixed-and random-effects parameters expressed in terms of high species strengths and stand basal area were considered to establish height-diameter relationships. Furthermore, dummy variables were added to the mixed-effects models in order to solve intra-plot variability resulting from species difference. The goodness-of-fit criteria used were the coefficient of determination (R²), the absolute error of estimate (Bias) and the root mean square error (RMSE). [Result] 1) Among the 13 pieces of height-diameter candidate models, model 13 (M13) provided the most accurate prediction of height with the highest R²(0.9157), the lowest Bias (1.200 6) and RMSE (0.129 1). 2) For Larix principis-rupprechtii and Betula platyphylla, mixed effects models were established based on M13, respectively. Both models had the best fits with the fit statistics values (R²=0.926 4; AIC=319.7; Bias=0.084 1; RMSE=1.070 8) for Larix principis-rupprechtii and values (R²=0.918 7; AIC=297.6; Bias=0.070 5; RMSE=1.1022) for Betula platyphylla. 3) To further evaluate mixed-effects models for two species, trees from the validation data were divided into different DBH classes with every 2 cm interval. The average values of height prediction bias (observed-predicted) were small for both species. The above results indicated that mixed-effects models including species dummy variable provided in a better fit to the data and improved prediction accuracy. [Conclusion] The mixed-effects models with dummy variables solved the negative effects of species differences between plots and within plot on height-diameter relationships in mixed forests. It was proved able to provide better model fitting, more applicability and more precise estimations than the basic generalized model.

Key words: nonlinear mixed model, Larix principis-rupprechtii, Betula platyphylla, height-diameter, mixed forest