| Forests are the mainstay of terrestrial ecosystems and the material basis for the survival of human society.Larch(Larix olgensis)is one of the main coniferous tree species of plantation construction in northeast China.Modelling the branch attributes and branch dynamic quantitatively is the basic to study the wood quality,crown structure and crown biomass.It is also the foundation to evaluate tree competitive ability and forest productivity.And it provides a reference to simulate the crown,tree and forest dynamic growth,to finally formulate scientific and rational management decisions for Larch(Larix olgensis).In this study,based on the branch analysis data and branch growth data of 4,679 branches in 818 pseudo-whorls from 77 destructively sampled trees in 11 sample plots of Larch plantation in Heilongjiang Province,the generalized linear models,nonlinear models,the quantile regression technology,mixed-effects models are used to construct a model system including the branch characteristic factor,i.e.,the branch number,branch size,branch angle and dynamic simulation for the growth of branch diameter and length.The specific results and main conclusions of this study are as follows:(1)Based on seven common count data models,i.e.,Poisson,negative binomial(i.e.NB,including NB-1,NB-2,and NB-P)and generalized Poisson(i.e.GP,including GP-1,GP-2,and GP-P)regression models,models for the number of first-order and second-order branches were constructed respectively.Further,the generalized linear mixed-models(GLMM)were applied to those models using the sampled trees as the random effects,and the jackknifing technique was utilized to evaluate the model validation and prediction performance.The results showed that the Poisson regression was preferred for modeling the number of the first-order branches and the GP-1 regression was considered the optimal model for modeling the number of the second-order branches,and the significant predictor variables included tree height increment,branch position,relative tree size,average dominant height,and tree age.The GLMM models significantly improved both modeling fitting and prediction performance,and the prediction accuracy of the GLMM models increased gradually with the increasing number of sample sizes.Sampling strategies also affect the prediction accuracy,and the improving effect of prediction accuracy for different sampling strategies varies in the upside crown and low part of crown.Relatively small sample size with an appropriate sampling strategy would be adequate to provide a good estimation at a specific crown section.(2)Based on simple linear model,quadratic polynomial equation,segmented polynomial equation,segmented power equation,segmented Mitscherlich equation,Rолясрfunction,modified Kozak function and modified Weibull function,the quantile regression technique was used for different quantile points(q=0.05,0.10,0.20,......,0.90,0.95 for 11 quantile points)to fit the branch diameter and branch length vertical distribution models,to select the model form that performed optimally at the high,medium,and low quantile points,and then reparametrized them t with tree level and stand level variables.The best quantile values of branch minimum and maximum diameter and length vertical distribution were selected from multiple low quantile points(i.e.,q=0.01,0.05,0.10,0.15,0.20,0.25,0.30)and high quantile(i.e.,q=0.99,0.95,0.90,0.85,0.80,0.75,0.70)respectively,to establish the maximum and minimum branch diameter and length vertical distribution models.In the meanwhile,based on the vertical distribution modeled of branch diameter and length of multiple intermediate quartiles,combined with linear interpolation method,the diameter and length of all the whorl branches were calculated.The results showed that the modified Weibull function could model the vertical distribution of branch diameter and branch length better at each quantile point after introducing the variables of diameter at breast height,height to diameter ratio,crown length,crown length ratio,stand basal area and mean height of dominant wood;q=0.20 and q=0.85 were the best quantile points for the vertical distribution of branch minimum and maximum diameter,q=0.20 and q=0.80 were the best quantile points for the vertical distribution of branch minimum and maximum length,respectively.The best quantile points selected were closely related to the number of branches in each pseudo-whorl.The values of the quantile points corresponding to each branch in the pseudo-whorl were calculated,and the vertical distribution of branch diameter and branch length at q=0.30,0.40,0.50,0.60,0.70,and 0.80 quantile points were modeled with quantile regression and calculated using linear interpolation.The accuracy of fitting the branch diameter and branch length vertical distribution models reached~2=0.8816,=1.9292 and~2=0.8572,=21.5263,respectively.And the prediction accuracy of branch diameter and branch length vertical distribution models reached%=-5.6926,%=19.4562 and%=-8.5424,%=22.9040 based on jackknifing technique.(3)Based on the nonlinear model form,the branch insertion angle model was established with the variables of branch,tree and stand level,and the nonlinear mixed-effects model of branch angle was established by taking the tree level as the random effect,and the jackknifing technique was utilized to evaluate the model validation and prediction performance.The results showed that the nonlinear model form could simulate the variation of branch angle well,and the relative branch depth,branch diameter,branch length,branch age,height-to-diameter ratio and stand index had significant effects on branch angle.The mixed-effects model at tree level could significantly improve the fitting and prediction accuracy of the model,and the prediction accuracy of the model improved gradually with the increase of the number of sample branches.The effects of different sampling strategies on the branch angle were different at different locations of crown.The prediction accuracy of the model improved significantly as the number of branches was increased to 10.(4)Based on the Mitscherlich equation,branch height and tree height growth were introduced as independent variables to construct the branch diameter and length growth model within the crown.And the nonlinear mixed-effects model(NLME)and quantile regression(QR)model were used to predict branch growth,and the prediction accuracy of the mixed-effects model was compared with the quantile regression combined prediction method based on three(QR3),five(QR5)and nine(QR9)quantile regression curves.The results showed that the mixed-effects model and quantile regression method could significantly improve the prediction accuracy of branch diameter and length,and the prediction ability of the mixed-effects model was better than the quantile regression method in general.However,the quantile regression models still had the irreplaceable advantage for describing the growth process of branches in different sizes,and the quantile regression method had higher accuracy in predicting the growth of branches in the upside crown.The prediction accuracy of the mixed-effects model and quantile regression model increased gradually with the increasing number of sample sizes,especially when five sample branches per tree is taken,both methods obtained higher prediction accuracy.There is little difference between three sampling strategies on the prediction accuracy of the branch growth model.And since the method of taking sample branches from the bottom of crown is simpler and has less impact on tree growth,we recommend applying this sampling strategy and taking five sample branches to calibrate the branch growth mixed-effects model and quantile regression model.(5)Based on the established branch number vertical distribution model,branch diameter and length prediction model,and branch angle model,the number,diameter,and length of branches within all pseudo-whorls in crown can be accurately predicted,indirectly showing the shape and internal structural characteristics of crown.The established branch growth prediction model combined with the branch number vertical distribution model can dynamically simulate the dynamic change process of the number and size of branches as the tree height growth. |
PDF Full Text Request