Stand density regulation considering multi-objective benefits in a Platycladus orientalis plantation in hilly areas of Taihang Mountains

Taking the Platycladus orientalis plantation in hilly areas of the Taihang Mountains as the research object, plot surveys and the envelope analysis were employed to establish functional relationships between stand density and indicators such as tree biomass, tree damage and mortality scores, seedling and sapling density, and the Simpson index of shrubs and herbs. Based on the results of indicator standardization, the trade-offs among production, health, sustainability, and diversity objectives were analyzed. A coupling function for multi-objective benefits was constructed, and the optimal stand density was calculated. Results indicated that the tree biomass varied from 0.46 to 94.21 t/hm², with an average of 40.42 t/hm²; the tree damage and mortality scores ranged from 0 to 1700 points, with an average of 267 points; the density of saplings and seedlings varied from 200 to 4600 plants/hm², with an average of 1450 plants/hm²; and the Simpson index of shrubs and herbs ranged from 0.13 to 0.88, with an average of 0.59. With increasing density, tree biomass increased rapidly at first and then tended to level off when density exceeded 3300 plants/hm²; tree damage and mortality scores increased continuously in a linear manner; the density of saplings and seedlings and the Simpson index of shrubs and herbs both showed a unimodal pattern, with peaks at 2000 and 2500 plants/hm², respectively. When stand density ranged from 100 to 2500 plants/hm², a synergistic relationship existed among the benefits of productivity, sustainability, and diversity, while a trade-off relationship with the benefit of health; when stand density ranged from 2500 to 3600 plants/hm², productivity and diversity benefits were synergistic, and health and sustainability benefits were synergistic, but the former two were not correlated with the latter two. The multi-objective comprehensive benefit value first increased and then decreased with increasing density, showing a unimodal variation, with a maximum value corresponding to an optimal density of 2500 plants/hm². The relevant methods can provide a reference for multi-objective forest management in similar areas.