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(Mk).[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 Mk and other mingling are exactly same,When k >2,Mk 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(Mg,Mv,Mp,Mc and Mk),which showed thatin the structure unit of“1 +n”space,Mg 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. Mk makes spatial structure unit extending from“1 + n”to“1 + n1 + n2 +… + nk”,k is set to 2 in this paper,namely,spatial structure unit is“1 + n1 + n2”,Mk can distinguish the mingling of Cunninghamia lanceolata plantation and replanting trees in two kinds of replanting schemes. The calculation method using Mg ( Mkg ),Mkg 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 Mkv,Mkp and Mkc can get the same rules.[Conclusion]This paper put forward Mk that the spatial structure unit is“1 + n”to“1 + n1 + n2 +… + nk”,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.%【目的】为了解决现有混交度不能区分单一树种在不同行间混交方式中的隔离程度问题，提出考虑 k阶邻近林木的混交度( M k)。【方法】依据地物的邻近关系对空间进行剖分，以单株木视为平面点构建 Voronoi图，基于Voronoi图建立对象木的k阶邻近关系。当k取1时，M k 与其他混交度的计算公式及计算结果完全一样；当k取2或更大值时，Mk 采用1/k加权，与 Mg，Mv，Mp 和 Mc 采用相同的计算方法。以湖南福寿林场杉木人工纯林为研究对象，为了进行空间结构优化与调整，在幼龄林林分内补植了观光木和鹅掌楸，采取成片补植与2个树种交叉补植2种不同的空间配置补植方案，对比分析5种不同的混交度(Mg，Mv，Mp，Mc 和Mk)。【结果】在“1+n”空间结构单元中，Mg 和 Mp 不能区分观光木和鹅掌楸补植树种在不同补植方案中的混交度，其中 Mg 2种补植树种的混交度均为1，Mp 2种补植树种的混交度均为0.539； Mv 与 Mc能够区分不同补植方案杉木林的混交度，成片补植方案中杉木的混交度依次为0.027和0.039，交叉补植方案中杉木的混交度为0.043和0.045，但不能区分补植树种的单木混交度。考虑 k阶邻近林木的混交度把空间结构单元从“1+n”扩展到“1+n1+n2+…+ nk”，本文 k取2，即空间结构单元为“1+n1+n2”，Mk 能够区分2种补植方案杉木林与补植树种的混交度，使用 Mg 的计算方法(Mkg)，Mkg在成片补植方案中杉木、观光木和鹅掌楸的混交度为0.098，0.641，0.645，Mkg在交叉补植方案中杉木、观光木和鹅掌楸的混交度为0.101，0.652，0.655，交叉补植方案中杉木、观光木和鹅掌楸的混交度均大于成片补植方案中的混交度，使用 Mkv，Mkp，Mkc计算方法，能够得到同样的规律。【结论】本文提出考虑 k 阶邻近林木的混交度 Mk，其空间结构单元为“1+n1+n2+…+ nk”，空间结构单元的形式更多样，但混交度的计算更加复杂，区分度也更高，提高了单一树种混交度的区分度，能够解决1阶邻近不能区分的混交方式，可反映单木与林分的实际混交状况，为空间结构优化与调整时准确量化混交度提供了理论依据，能够更加准确地反映森林群落中树种相互隔离状况。
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