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Bivariate distribution is an effective approach to spatial structure analysis. Combined with two of the three structure parameters (uniform angle index (W), dominance (U) and mingling (M)), the structural bivariate characteristics of five different Pinus massoniana forests were explored in this study. Our objective was to provide a theoretical direction for structure-based and detailed management in P. massoniana forests. The bivariate traits showed that mixed artificial or secondary forests predominated by P. massoniana trees do not typically achieve the highest mingling level. Trees under extreme mingling conditions were rare and typically comprised of non-dominant species instead of dominant ones in P. massoniana forests; these trees were generally overtopped and randomly distributed. Management implications can be extracted comparing the bivariate traits between all species and dominant species. The original community structure, development stage, and mixed-tree species number affect the univariate M and, furthermore, the two bivariate U-M and W-M distributions in mixed forests. Forest type has little effect on all-species W-U traits compared to those of the dominant species. U-M traits should be adjusted first if the random frequency values are highest in W-U and W-M bivariate distribution, and it is necessary to determine whether these two bivariate traits shade the W univariate. Adjustments made based on bivariate distribution can reveal poor frequency combinations for foresters to target; this allows the simultaneous adjustment of dual aspects of forest structure based on one bivariate index. Our results show that bivariate distribution may provide very useful information for the management of P. massoniana and other forests.

Bivariate distribution characteristics of spatial structure in five different Pinus massoniana forests