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Scientia Silvae Sinicae ›› 2019, Vol. 55 ›› Issue (11): 85-94.doi: 10.11707/j.1001-7488.20191110

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Height-Diameter Relationship for Conifer Mixed Forest Based on Bayesian Nonlinear Mixed-Effects Model

Wang Dongzhi1,2, Zhang Dongyan3, Li Yongning1,2, Zhang Zhidong1,2, Li Dayong4, Huang Xuanrui1,2   

  1. 1. Forestry College, Agricultural University of Hebei Baoding 071000;
    2. Forest Resources Innovation and Protection Laboratory of Hebei Baoding 071000;
    3. Business College, Agricultural University of Hebei Baoding 071000;
    4. Mulan Weichang State-Owned Forest Farm Administration Bureau of Hebei Province Weichang 068450
  • Received:2019-02-26 Revised:2019-07-12 Online:2019-11-25 Published:2019-12-21

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Abstract: [Objective] This paper established the nonlinear mixed effects model for height-diameter relationship based on Bayesian statistics in multi-storied and multi-species mixed forests. The purpose of this study was to provide some references for growth regularity of multiple tree species, differences in resource allocation and precision improvement of forest quality.[Method] A total of 112 temporary plots were established in Larix principis-rupprechtii and Betula platyphylla mixed forest of Saihanba national forest park, Hebei Province, China. Plot size was 30 m×30 m. We selected 6 typical models including different stand factors to fit height-diameter relationship. And the best-fit model was chose as the basis for building mixed-effects models by the method of Bayesian and nonlinear mixed models. We also added dummy variables 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] Richards equation including dominant height and basal area of stand provided the most accurate prediction of height with the highest R2(0.849 5), the lowest Bias(2.378 6)and RMSE(0.365 4).The fitting accuracy of Bayesian non-linear mixed effect method was slightly higher than that of traditional non-linear mixed effects model method. Parameter estimation method of traditional non-linear mixed effect model had the best fits with the fit statistics values(RMSE=0.930 4; Bias=0.103 4)for L. principis-rupprechtii and values(RMSE=0.982 7; Bias=0.112 6)for B. platyphylla. Parameter estimation method of Bayesian nonlinear mixed effect model had the best fits with the fit statistics values(RMSE=0.910 5; Bias=0.096 8)for L. principis-rupprechtii and values(RMSE=0.963 3; Bias=0.100 2)for B. platyphylla.[Conclusion] The non-linear mixed effect model based on Bayesian theory considered the uncertainties of parameters in the model of tree height-diameter relationship of multi-species. The prediction results have better reliability and stability.

Key words: Bayesian statistics, nonlinear mixed-effects model, dummy variable, height-diameter, mixed forest

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