基于分位数回归的长白落叶松人工林最大密度线

Maximum density-size line for Larix olgensis plantations based on quantile regression

基于东北地区378块固定样地和415块临时样地的调查数据和Reineke方程,利用线性分位数回归技术建立了不同分位点(τ=0.90、0.95、0.99)下的长白落叶松人工林最大林分密度与林木平均胸径的关系模型,选出拟合长白落叶松人工林最大密度线的最优模型.利用人为选取最大的拟合数据,采用最小二乘(OLS)和最大似然(ML)回归同时建立最大密度线模型.采用极值统计理论的广义Pareto模型推算现实林分特定径阶的极限最大株数,进一步建立极限密度线模型.将线性分位数回归模型与其他方法进行对比.结果表明:在全部径阶范围内选取5个最大数据点拟合的方法能够得到现实林分的最大密度线,选取的样点过多会使模拟结果偏离最大密度线,且ML法要优于OLS法.分位点为0.99的线性分位数回归模型能够取得与ML接近的拟合结果,但分位数回归模型参数的估计结果更稳定.人为选取拟合数据具有一定的人为性,最终选取分位点为0.99的分位数回归模型为拟合最大密度线的最优模型,参数估计结果为k=11.790、β=-1.586,极限密度线模型的参数估计结果为k=11.820、β=-1.594.所确定的极限密度线位置略高于最大密度线,但二者差异不明显.由固定样地数据的验证结果可知,所建立的最大林分密度线及极限密度线能够对现实林分的最大密度及极限密度进行预测,为长白落叶松人工林的合理经营提供依据.

Based on 378 permanent and 415 temporary plots from Northeast China, the relationship of maximum stand density and quadratic mean diameter at breast height of trees for Larix olgensis plantation was developed. Linear quantile regression model with different quantiles （ τ = 0.90, 0.95, 0.99） was used and the optimal model for the maximum density-size line model was selected. The ordinary least square （OLS） and maximum likelihood （ML） regression were also employed to de- velop the maximum density-size line by using the arbitrary selected data. Generalized Pareto model of extreme value theory was used to calculate the number of limited maximum trees based on the current stands so that the limited density-size line was developed. The linear quantile regression model was compared with the other methods. The results showed that selecting 5 points within the whole diameter class for the maximum density-size line model development would get the satisfying prediction model. The fitting line would deviate from the maximum density-size line with the increas- ing points selected. The method of ML was superior to OLS in parameter estimation. The linear quantile regression model with the quantile of 0.99 achieved similar fitting results compared with ML regression and the estimation results was much stable. Traditional approach that selecting fittng data was considered arbitrary so that linear quantile regression with quantile of 0.99 was selected as the best model to construct the maximum density-size line with the estimates for the parameters as k = 11.790 andβ= - 1.586, and k = 11.820 and β= - 1.594 for the limited density-size line model. The determined limited density-size line was above the maximum density-size line but the difference was not pronounced. The validation results by using the data of permanent sample plots showed the models were suitable to predict the maximum and limited density line of the current forest stands, which would provide basis for the sustainable management of L. olgensis plantation.