基于广义线性混合效应模型的森林树木死亡研究

Studying forest tree mortality based on a generalized linear mixed-effects model

基于计数模型方法,同时考虑样地的随机效应,构建林分水平死亡模型,探究影响树木死亡的因素,以期为森林资源的监测与管理提供参考依据。以美国德州东部森林连续清查的样地数据为数据源,按4∶1的比例将其进行随机抽样,划分为训练集和验证集数据,将立地因子、林分因子和气候因子作为模型的自变量,林木死亡株数则作为模型的因变量,运用计数模型和混合效应模型方法进行模型的构建,并分析影响林木死亡株数的因子。使用赤池信息准则(AIC)、贝叶斯信息准则(BIC)和-2倍对数似然函数值(-2logL)3种模型评价指标评估各模型间的拟合效果;采用平均绝对误差(MAE)和均方根误差(RMSE)2种评价指标评估其预测效果,以便筛选出最佳的林分水平死亡模型。结果表明:立地因子方面,林木死亡株数与海拔(P<0.01)呈显著的负效应,与坡度(P<0.05)呈显著的正效应,说明林木死亡株数随海拔的升高而减少,随坡度的增加而增多;林分因子方面,林木死亡株数与林分年龄(P<0.001)和树木基面积(P<0.001)呈显著的正效应,与林分平方平均胸径(P<0.001)和林分密度(P<0.05)呈显著的负效应,说明林木死亡株数随林分年龄的增加和树木基面积的增大而增加,随林分平方平均胸径和林分密度的增大而减少;气候因子方面,林木死亡株数与SPEI(P<0.05)、干旱长度(P<0.001)、年平均温度(P<0.001)和夏季平均降雨量(P<0.05)均呈显著的负效应,与夏季平均温度(P<0.001)呈显著的正效应,说明林木死亡株数随干旱强度和夏季平均温度的增加而增多,随干旱长度、年平均温度和夏季平均降雨量的增加而减少。在基础计数模型中,零膨胀负二项(ZINB)模型的拟合效果最好。而加入样地随机效应后,混合效应模型的拟合精度明显有所提高。基于所有模型模拟结果的比较,得出德州东部森林的林分水平死亡模型以ZINB-mixed模型为最优模型。

This study used count-data model,combined with random effects of the survey plots,to develop forest stand level tree mortality models and to investigate the factors influencing tree mortality.The aim of the study was to provide a baseline for forest health monitoring and resource management.The data were consists of forest inventory plots from the continuous inventory of the eastern Texas forests,USA.The data were randomly divided into a ratio of 4∶1 for training and validation.The generalized linear models were developed using count-data method with a mixed-effect model to analyze the factors affecting tree mortality,used site factors,stand factors,and climate factors as independent variables,with the number of dead trees as dependent variable.Three model evaluation metrics,including Akaike information criterion(AIC),Bayesian information criterion(BIC),and-2-fold log-likelihood function value(-2logL),were used to assess the fitting effect among models.Two more evaluation metrics,mean absolute error(MAE)and root mean squared error(RMSE),were used to assess the prediction effect in order to screen out the optimal forest stand level mortality models.The results showed significantly negative correlation with elevation(P<0.01)and positive correlation with slope(P<0.05)between site factors and the number of dead trees.This indicates that the number of dead trees decreases with increasing elevation and increases with increasing slope.For the stand factors,the number of dead trees was significantly positively correlated with both stand age(P<0.001)and tree basal area(P<0.001),while it was significantly negatively correlated with stand squared mean diameter at breast height(P<0.001)and stand density(P<0.05).This suggests that the number of dead trees increases with the increase in stand age and tree basal area,while decreases with an increase in stand squared mean diameter at breast height and stand density.As for climate factors,the number of dead trees had significantly negative correlation with standardized precipitation evapotranspiration index(P<0.05),drought length(P<0.001),mean annual temperature(P<0.001),and the mean summer precipitation(P<0.05),but showed significantly positive correlation with mean summer temperature(P<0.001).This implies that the number of dead trees increases as drought intensity and mean summer temperature rise,whereas the numbers decrease as drought length,mean annual temperature,and mean summer precipitation increase.Among all base-count models,the zero-inflated negative binomial(ZINB)model had the best fit.The fitting accuracy of the mixed-effects model was significantly improved by adding the sample random effect.Based on the comparison of all model simulation results,we concluded that the ZINB-mixed model was the optimal model for the standlevel mortality model in the east of Texas forests.