A suitable self‐thinning model is fundamental to effective density control and management. Using data from 265 plot measurements in oak mixed forests in central China, we demonstrated how to estimate a suitable self‐thinning line for oak mixed forests from three aspects, i.e., self‐thinning models (Reineke's model and the variable density model), statistical methods (quantile regression and stochastic frontier analysis), and the variables affecting stands (topography and stand structure factors). The proposed variable density model, which is based on the quadratic mean diameter and dominant height, exhibited a better goodness of fit and biological relevance than Reineke's model for modeling the self‐thinning line for mixed oak forests. In addition, the normal‐truncated normal stochastic frontier model was superior to quantile regression for modeling the self‐thinning line. The altitude, Simpson index, and dominant height–diameter ratio (Hd$$ {H}_{\mathrm{d}} $$/D) also had significant effects on the density of mixed forests. Overall, a variable density self‐thinning model may be constructed using stochastic frontier analysis for oak mixed forests while considering the effects of site quality and stand structure on density. The findings may contribute to a more accurate density management map for mixed forests.

Diameter at breast height (DBH) and height (H) of trees are two important variables used in forest management plans. However, collecting the measurements of H is time-consuming and costly. Instead, the H-DBH relationship is modeled and used to estimate H. But, ignoring the effects of slope, aspect and tree competition on the H-DBH relationship often impedes the improvement of H predictions. In this study, to improve predictions of (Thunb.) Oerst. tree H in mixed forests, we compared eleven H-DBH models and examined the influence of slope and aspect on the H-DBH relationship using 426 trees. We then improved Hegyi competition index and explored its effect on the H predictions by including it in the selected models. Results showed 1) There were statistically significant effects of slope and aspect on the H-DBH relationship; 2) The log transformation and exponential model performed best for sunny- and shady-steep, respectively, and the Gompertz’s model was optimal for both sunny- and shady-gentle; 3) Compared with the whole dataset, the division of the data into the slope and aspect sub-datasets significantly reduced the RMSE of H predictions; 4) Compared with the selected models without competition index, adding the original Hegyi and improved Hegyi_I into the models improved the H predictions but only the models containing the improved Hegyi_I significantly increased the prediction accuracy at the significant level of 0.1. This study implied that modeling the H-DBH relationship under different slopes and aspects and including the improved Hegyi_I provided the great potential to improve the H predictions.Cyclobalanopsis glauca

The parameters of the probability density function (PDF) may be estimated using the parameter prediction method (PPM) and the parameter recovery method (PRM). However, these methods can suffer from accuracy issues. We developed and evaluated the prediction accuracy of two PPMs (stepwise regression model and dummy variable model) and an artificial neural network (ANN) to predict diameter distribution using data collected from 188 oak forest plots. The results demonstrated that the Weibull distribution performed well in fitting the diameter distribution. Compared with the stepwise regression model, the PPM model with stand type as a dummy variable reduced the predictional errors in estimating the parameters b and c of the Weibull distribution, but the prediction accuracy of the diameter distribution showed no significant improvement. Compared with the two PPM models, the ANN model with diameter class (C), average diameter (D) and stand type (T) as input variables decreased the RRMSE by 2.9% and 4.33% in estimating diameter distribution, respectively. The satisfactory prediction accuracy and simple model structure indicated that an ANN worked well for the prediction of the diameter distribution with few requirements and high practicality.

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