Abstract: Whether the gravitational model can be used to analyze tree competition in forest community is a valuable question. A tree relative vitality circle based on the gravitational model can illustrate the magnitude of competitive tree vitality. A gravitational competition index based on the relative vitality circle of competitive trees can accurately depict the relationship between growth and competition. This study was conducted in the coniferous and broadleaf mixed forest of Tianmu Mountain National Nature Reserve in Zhejiang Province. We carried out correlation analyses between the V_Hegyi competition index and diameter at breast height (DBH), between the gravitational competition index and DBH, and between the two competition indices and the basal area increment. We further analyzed the correlation between the growth rate of DBH and the ratio of the two-phase gravitational competition index, that is, the ratio of the 2021 gravitational competition index to that of 2006. In addition, the correlation analysis was applied between the relative vitality circle diameter and DBH. We also compared the magnitudes of the competition indices between the living standing trees and the dead trees. The results showed that both competition indices were negatively correlated with DBH, and followed a power function relationship. The basal area increment was negatively correlated with each of the two competition indices. However, the gravitational competition index was better than V_Hegyi competition index for indicating the relationship between tree growth and tree competition. Compared with the ratio of the V_Hegyi competition indices, the ratio of the two-phase gravitational competition indices could better demonstrate the relationship between tree growth and tree competition. In the coniferous and broadleaved mixed forests, the correlation coefficient between the growth and competition of broadleaved species was greater than that of coniferous species. The dead trees were significantly influenced by competition. Tree relative vitality circle size was negatively correlated with DBH. The gravitational model was one of the critical models that reflect spatial interactions and could be applied to examine forest competition. The gravitational competition index could be used as a spatially structured indicator to evaluate tree competition and tree vitality, which could better indicate the relationship between tree growth and tree competition than the V_Hegyi competition index.

Key words: gravitational competition index, V_Hegyi competition index, tree relative vitality circle