Abstract:The self-thinning rule is regarded as one of the most important principles in plantation management. This rule, involving the assumption of a constant slope coefficient, has been universally applied when regulating stand density. In this study, we hypothesized that the slope coefficient can change significantly with changes in site quality. To test this hypothesis, we first grouped forest plots into 5 categories based on site index. Second, we produced the self-thinning line represented by the Reineke function for each of the 5 site categories, selecting fully stocked plots using reduced major axis regression. Third, the slope coefficients for the different categories were tested for significant differences. The results indicated that in general, the slope was significantly different with different site quality. In addition, we observed that the slope of the self-thinning line exhibited a steeper trend for sites of lower quality, which indicated increased self-thinning or reduced self-tolerance. Finally, we concluded that it is imperative to produce specific self-thinning lines for different site quality categories.

Key message Including individual-tree competition indices as predictor variables could significantly improve the performance of crown width and length models for Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). Moreover, distance-dependent competition indices are superior to distance-independent ones when modeling crown width and length. Compared with crown width and length basic models with optimum competition indices, the performance of the two-level nonlinear mixed-effects models improved. Context Crown width (CW) and crown length (CL) are two important variables widely included as the predictors in growth and yield models that contribute to forest management strategies. Aims Individual-tree crown width and length models were developed with data from 1498 Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) trees in 16 sample plots located at Jiangle County, Fujian Province, southeastern China. Two hypotheses were proposed: (1) including individual-tree competition indices as predictor variables could significantly improve performance of both the CW-DBH and CL-DBH models; and (2) the distance-dependent competition indices would perform better than distance-independent ones. Methods The models were fitted using generalized linear least squares or generalized nonlinear least squares methods. In addition, to prevent correlations between observations from the same sampling unit, we introduced age classes and sample plots as random effects to develop the two-level nonlinear mixed-effects models. ResultsWe found introduction of competition indices could significantly improve the performance of the CW-DBH and CL-DBH models. The distance-dependent competition index (i.e., competitor to subject tree distance) performed best in modeling the crown width and length models. Compared with crown width and length basic models with optimum competition indices, the performance of the two-level nonlinear mixed-effects models was significantly better. Conclusion The two hypotheses were accepted. We hope these models will contribute to scientific management of Chinese fir plantations.