Ingrowth Model Of Larix Gmelinii—Betula Platyphylla Mixed Forest In Eastern Daxing’an Mountains

As an important process of stand dynamic change,ingrowth plays an important role in the study of stand development of multi-layered forest.Ingrowth model,together with reserved wood model and mortality model,make up growth and yield models for uneven-aged forest.Based on the retest data of 368 Larix gmelinii-Betula platyphylla mixed forest in Eastern Daxing’an Mountains,the stand and single tree factors which affecting the ingrowth were analyzed.Also,ingrowth probability model,ingrowth number model and ingrowth volume growth rate model were established.The results were as follows:Stand age(age group t),stand average diameter at breast height(d),stand average height(H),stand density index(SDI)and other factors affect the ingrowth of forest.Due to the less species produced when trees are older and the fierce competition caused by the high stand density,these factors are negatively correlated with the number of ingrowth trees and ingrowth volume growth rate.But there is a positive correlation between current ingrowth volume per hectare and ingrowth situation in the future,because it can reflect ingrowth potential of the stand in the next few years.Two-stage estimating method can solve the problem of zero-inflation and discrete data.The specific method is as follows:first,establish the probability model to predict whether the sample plot has ingrowth,for the sample plot with ingrowth,establish the number model or growth rate model to predict ingrowth situation.In this paper,ingrowth probability model is established in the form of logit of logistic model.After the model is established,the ROC curve of the model is diagnosed.The AUC value was 0.761,which was of good diagnostic value,and could be used to accurately estimate whether the sample plot had ingrowth.Two methods were used to predict the number of ingrowth,and the differences between them are small.The first method was two-stage estimating method,which used ingrowth probability model to predict the sample plots which have ingrowth,and then used logarithmic model to fit the relationship between the number of ingrowth trees and the related factors.The second method was based on possion model and negative binomial model,zero-inflation model and hurdle model were established.The results showed that negative binomial model was better than possion model.Zero-inflation negative binomial model(ZINB)and hurdle negative binomial model(hurdle-NB)were better than ordinary negative binomial model.From the predicting results of ZINB,Hurdle-NB and two-stage estimating model,it can be seen that the two-stage estimating model is slightly better than ZINB and hurdle-NB on the basis of the higher accuracy of the probability model.But if the accuracy of ingrowth probability model is low,ZINB model and hurdle-NB model are better.Two-stage estimating method is used in the study of ingrowth volume growth rate model.The first stage model is the probability model.In the second stage,the basic model,dummy variable model and mixed-effect model were used respectively.Firstly,five equations were used to fit the growth rate,and the Radj2 of them were between 0.204 and 0.547.After comparing the fitting results,it is determined that the exponential equation is the best,which is transformed into logarithmic form as the basic model.Then,all plots were divided into five regions and five age groups,and three dummy variable models were constructed respectively.After comparing the goodness of fit,the regional dummy variable model was determined as the optimal form.Then,mixed-effect models based on regional level and age group level were established to better analyze the group level and individual level data.After comparing AIC value,BIC value and LL value of several mixed-effect models,mixed-effect model of regional level was determined as optimal model.Radj2 of the mixed-effect model is 0.636,which is higher than that of the basic model and the dummy variable model,and root mean square error(RMSE)is 0.860,which is lower than that of basic model and dummy variable model.It is proved that the mixed-effect model is the best,followed by the dummy variable model.The results of dummy variable model and mixed-effect model show that the differences of regions can evidently affect ingrowth volume growth rate.Through the independent sample test of the three optimal models,it is found that the mean error(ME)of the mixed-effect model is-0.0173,which is closer to 0 than that of the basic model and the dummy variable model;the mean absolute error(MAE)is 0.719,and the mean percentage of prediction error(MPSE)is 73.8%,which is less than that of the basic model and the dummy variable model.Therefore,the mixed-effect model not only improves the accuracy of the model,but also improves the prediction ability of the model.