Abstract:

【Objective】To solve the problem that the existing mingling can't distinguish the isolation of a single tree species in different mixed ways by row, we put forward the mingling of adjacent trees considering k-order(M_k). 【Method】According to the adjacent relationship of features to subdividing space, regarding individual tree as a planar point, we establish the k-order adjacent relation of objective tree based on Voronoi diagram.When k= 1, the calculation formulas and results of M_k and other mingling are exactly same, When k >2, M_k uses 1/k weighted, using similar calculation method with M_g, M_v, M_p, and M_c.【Result】Taking Cunninghamia lanceolata pure forest in Hunan Fushou farm as the research object, in order to optimize and adjust the spatial structure, we replanted the Tsoongiodendron odorum and Liriodendron chinense taking two different spatial configurations schemes of plots replantion and cross replantion in young pure forest, comparing five minglings(M_g, M_v, M_p, M_c and M_k), which showed thatin the structure unit of"1+n"space, M_g and M_p can not distinguish the mingling of Tsoongiodendron odorum and Liriodendron chinense in two replanting schemes, M_g of two tree species is all equal to 1, and M_p is all equal to 0.539, M_v and M_c can distinguish the mingling of Cunninghamia lanceolata forest of different replanting schemes, which is respectively 0.027, 0.039 in plots replantingand 0.043, 0.045 in cross replanting, but can not discriminate the mingling of single tree planting tree species. M_k makes spatial structure unit extending from"1 + n"to"1 + n₁ + n₂ +…+ n_k", k is set to 2 in this paper, namely, spatial structure unit is"1 + n₁ + n₂", M_k can distinguish the mingling of Cunninghamia lanceolata plantation and replanting trees in two kinds of replanting schemes.The calculation method using M_g (M_kg), M_kg of Cunninghamia lanceolata, Tsoongiodendron odorum and Liriodendron chinense is 0.098, 0.641, 0.645 in the plots replanting scheme, and 0.101, 0.652, 0.655 in the cross replanting scheme respectively. The mingling of three tree species in the cross replanting scheme were larger than in the plots replanting scheme, The use of M_kv, M_kp and M_kc can get the same rules.【Conclusion】This paper put forward M_k that the spatial structure unit is"1 + n"to"1 + n₁ + n₂ +…+ n_k", the forms of spatial structure unit is more diverse, however, the calculation method of mingling is more complex, distinguish degree is higher, and it improves the discrimination of a single tree mingling, solves the mixed ways that first order nearby can't distinguish, reflects the actual mingling condition of single tree and stand, provides theoretical basis for optimizing the space structure and accurately quantifying the mingling on the adjustment, and reflect the more accurate isolation condition of different varieties of trees in forest community.

Key words: mingling, k-order nearby, Voronoi diagram, spatial structure unit