[目的]建立多树种、多层次混交林的树高 -胸径生长关系非线性混合效应模型,为研究混交林多树种生长规律提供参考依据.[方法]以河北省塞罕坝国家森林公园华北落叶松 -白桦针阔混交林为研究对象,基于87 块标准地(20 m × 30 m)的4 953 株华北落叶松和3 608 株白桦单木数据,选取13 个具有代表性且具有生物学意义的树高 -胸径模型进行拟合,从中筛选出拟合优度较高的模型作为构建混合效应模型的基础模型,并在混合效应模型中加入哑变量以解决样地内不同树种带来的差异.[结果]1) 在13 个树高 -胸径候选模型中,模型13 的确定系数最大(R2 =0. 915 7),绝对误差(Bias =1. 200 6)、均方根误差(RMSE =0. 129 1) 最小,其拟合效果较好.2) 以模型13 为基础模型建立华北落叶松 -白桦混交林树高 -胸径关系混合效应模型,华北落叶松混合模型确定系数(R2)为0. 926 4,AIC值为319. 7,均方根误差(RMSE)值1. 070 8,绝对误差(Bias)为0. 084 1; 白桦混合模型确定系数(R2)为0. 918 7,AIC值为297. 6,均方根误差(RMSE)为1. 102 2,绝对误差(Bias)为0. 070 5,表明模型拟合效果较好.3 ) 利用所构建的混合效应模型,以2 cm为一个径阶对华北落叶松和白桦树高进行预测,其树高预测结果与测量值分布一致,表明包含树种哑变量混合效应模型中的参数充分反映出相同径级树高的变异趋势,提高了混交林树高 -胸径模型预估精度.[结论]包含哑变量的混合效应生长模型可解决混交林中样地间及样地内树种对树高 -胸径生长关系的影响,提高模型精度及适用性,为该地区提高针阔混交林经营水平及经营效果提供科学支撑.%[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 4 953 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. 915 7),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. 102 2 ) 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.
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