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

Abstract

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 treesfor 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 develop 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 increasing 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 and β=-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.