基于空间结构参数的大兴安岭天然落叶松单木直径生长模型

目的 研究林分空间结构对兴安落叶松单木直径生长的影响，为大兴安岭天然落叶松次生林的有效恢复提供理论依据和技术支撑。 方法 以大兴安岭天然落叶松次生林为研究对象，基于塔河林业局盘古林场50株兴安落叶松解析木数据，采用S-Plus软件中的NLS函数对8种常用的林木生长模型进行拟合优度评价，进而确定最优基础模型；通过再参数化方法，考虑常用林分因子、单木因子、物种多样性以及林分空间结构等参数对林木直径生长的影响；最终，采用NLME函数构建兴安落叶松单木直径生长的最优混合效应模型，并系统评价不同模型的拟合优度。 结果 兴安落叶松单木直径生长的最优基础模型为Mitscherlich方程（调整系数Ra2 = 0.6285），其参数a分别与林分平均树高、单木胸径、混交度和角尺度显著相关，而参数b则与林分平均胸径和竞争指数显著相关；据此，建立的兴安落叶松广义直径生长模型的Ra2值相较基础模型提升约31%（Ra2 = 0.8264）；通过引入随机参数（参数a1）、异方差函数（幂函数varPower）、时间序列函数（高斯结构corGaussian），单木水平的混合效应模型进一步将Ra2值提升约17%（Ra2 = 0.9710）；五折交叉检验结果表明，混合模型的调整系数、平均绝对误差和均方根误差分别为0.9838、0.56 cm和0.72 cm，能够满足单木直径生长预测的需要。模型模拟结果表明，单木直径生长量随着单木胸径、角尺度和混交度的增加而增加，但随着林分平均胸径、平均树高和竞争指数的增加而减小；当各变量数值每增加10%时，其对应的胸径生长量依次为：+0.45 cm、+3.62 cm、+4.71 cm、−0.34 cm、−0.21 cm和−0.73 cm，但取决于不同的林分特征和生长阶段。 结论 林分角尺度、混交度和竞争水平对兴安落叶松单木直径生长具有显著作用，在后续森林经营中应通过合理的采伐来降低林木的竞争水平，并注重创建和维护林木的随机分布格局和混交程度。

Diameter Growth Model Using Spatial Structure Parameters of Natural Larix gmelinii Stand in Daxing'anling Mountains,Northeast China

Objective To study the effects of stand spatial structure on individual diameter growth of natural Larix gmelinii stand so as to provide reference and support for the effective recovery of secondary forests in the region. Method Based on 50 sample trees of L. gmelinii collected from the secondary forests in Pangu Forest Farm of Tahe Forestry Bureau, eight commonly used forest growth models were compared and evaluated using NLS function in S-Plus software, and the best basic model was determined. Then, the effects of commonly used stand factors, individual tree factors, species diversity, and stand spatial structure on the diameter growth were quantified using the parameterized method. Finally, the optimal mixed-effect model of growth for L. gmelinii trees were developed using NLME function, and the goodness-of-fit of different models were systematically evaluated. Result Mitscherlich equation was proved to be the optimal basic model of diameter growth for natural L. gmelinii stand, in which the coefficient of determination (Ra2) of the function was 0.6285. The parameter a highly related with the DBH of individual trees, and the mean tree height, the mingling and the uniform of the stand, while the parameter b mainly related with the mean DBH and the competition index of stand. The generalized diameter growth model could improve the value of Ra2 by about 31% (Ra2 = 0.8264) when comparing with the basic model. However, the technique of mixed-effect model could further improve the value of Ra2 by about 17% (Ra2 = 0.9710) when the random parameters (a1), heteroscedasticity function (varPower), and autocorrelation structure (corGaussian) were introduced. The results of 5-fold cross-validation showed that the coefficient of determination, average absolute error and root mean square of the estimated mixed-effect model were 0.9838, 0.56 cm and 0.72 cm respectively, indicating the outstanding prediction accuracy of the model. The simulation results showed that the amount of diameter growth increased significantly with the increase of the DBH of individual tree, the mingling and the uniform values (the closer to 0.5, the better), but decreased dramatically with the increases of the average DBH, the average tree height, and the Heygi's competition index. The corresponding amount of diameter growth would be: +0.45 cm, +3.62 cm, +4.71 cm, −0.34 cm, −0.21 cm and −0.73 cm, respectively, if the value of each variable increased by ten percent, however it highly depended on the stand characteristics and growth stages. Conclusion The levels of stand uniform and competition will affect the diameter growth of natural Larix gmelinii stand significantly, thus decreasing the competition levels of forest and creating (or maintaining) the random distributions and higher mingling degrees of the trees by appropriately cutting are highly recommended for the forest management in the near future.