A Novel Model to evaluate Spatial Structure in Thinned Conifer-Broadleaved Mixed Natural Forests

This study aimed to establish a management strategy for forest structures in Xiaoxing'an Mountains, China. We investigated the non-spatial structure factors affecting the spatial structure units of conifer-broadleaved mixed natural secondary forests via thinning and further quanti�ed the spatial structure characteristics. Six forest plots (100 m×100 m) of similar stand conditions located in the Xiaoxing'an Mountains were used for the study. The thinning intensities were 10%, 15%, 20%, 25%, 30%, and 35% for plots A-F respectively. The structure units were constructed using Voronoi diagrams in ArcGIS and constrained by non-spatial structure indexes. Seven stand spatial structure parameters were selected, and each was quanti�ed by the optimal distance model (TOPSIS and combination weight methods), which was directly used to evaluate and compare the spatial structure disparity of the structural units and re�ect the degree of the spatial structure of tending and thinning. The effects of crown width and crown length on the spatial structure unit of a stand were respectively higher than that of diameter at breast height and tree height. Nine possible values for the number of trees adjacent to a central tree in the spatial structure unit were obtained via weighted Voronoi diagrams, and the distribution frequency of 3–8 adjacent trees accounted for 90–96%. The spatial structure parameters derived from weighted Voronoi diagrams were analyzed using the optimal distance model. The mingling intensity and levels of competition in the tended and thinned plots differed from the control. The spatial structure evaluation index of natural mixed forests was B (0.488) > C (0.487) > E (0.480) > D (0.479) > A (0.475) > Control (0.442) > F (0.433). Plot B had a higher proportion of trees at the medium open level (41.18%), with medium and upper stand variation (72.94%), and higher levels of competition (55.29%) than plot F. This indicated that the 35% interval caused a less than ideal stand spatial structure. For the unique properties of mixed coniferous natural forests, crown length had a greater in�uence on structure units than tree height. Thus, the spatial structure evaluation index based on the optimal distance model offers


Introduction
The Xiaoxing'an Mountains, one of the three major forest areas in northeast China, largely contribute to climate change mitigation Yin et al., 2011), forest carbon sequestration, biodiversity conservation (Ma, 2015), water containment, and soil microbiology. Different nascent forest management methods now meet the demands for sustainable development of forest ecosystems, among which domestic and foreign mixed thinning is the most common (Fulé et al., 2012;Hartley, 2002;Huuskonen et al., 2021;Kolström et al., 2011;Spathelf P, 2015). This management method not only maintains stable forest diversity, reduces pests and diseases, maintains forest self-regulation, enhances self-recovery (Knoke et al., 2008), improves the forest environment (Li et al., 2021), but also affects forest non-spatial structure (Horner et al., 2010), forest spatial structure (Duchateau et al., 2021;Ye et al., 2018), species diversity in the forest understory, and understory plant regeneration. These complementary effects optimize the functioning of the forest ecosystem.
Thinning is mainly used to adjust the structure and function of the forest stand -the function of the forest depends largely on how reasonable the structure of the forest is (Pommerening, 2006;Song & Dong, 2014). Single-tree-based structured forest management is a current research focus, which would possibly be developed into another forest management method (Ghalandarayeshi et al., 2017;Hui et al., 2018;. When studying forest carbon sink function in single-tree microbial environments, it is important to quantify structure units and the integrated spatial structure of forest stands. Thus, either the "1 + 4" adjacent tree method or the spatial structure unit composed of regular Voronoi diagrams to calculate the spatial structure index of forest stands (Cherubini et al., 2002;Daniels et al., 1986) when selecting adjacent trees are used. Both methods have shortcomings which are compensated for by using the non-spatial structure parameters of the stand as weights. The in uence of the diameter at breast height is strong and is thus used to weight the spatial structure units (Aakala et al., 2013;Li et al., 2015), and this has developed into a weighting analysis using tree height, diameter at breast height, and crown (Abellanas et al., 2016b;. This study modi es this weighting analysis by not only adding the crown length attribute to those of diameter at breast height, height, and crown spacing but also making reasonable usage of the crown and stand spacing factors that are related to stand density based on the characteristics of the species in the mixed forests. Thus, this study had two objectives. First, analysis of a weighted Voronoi diagram constructed by tree height, diameter at breast height, crown length, and crown width factors because the degree of mingling and stand characteristics of conifer-broadleaved mixed forests may have different effects on structure units. Second, quantitatively analysis of each spatial structure unit using an optimal distance model, and further analysis of the overall pro le of the stand using its homogenization. The grey correlation method was used to determine the weights of non-spatial structure parameters affecting the extent of spatial structure units in conifer-broadleaved mixed forests, and the spatial structure index derived from the multiplication and division method was used to analyze the importance of each spatial structure parameter. The spatial structure of the stand was quanti ed by combining it with the optimal distance model, and the spatial structure of natural conifer-broadleaved mixed forests was analyzed by the intensity of thinning. We hypothesized that crown width has a stronger in uence on the structure units than the diameter at breast height, and crown length has a stronger correlation with height than crown width. Moreover, the spatial structure of thinned coniferous broad-leaved mixed forests can be directly evaluated through an optimal distance model. This method has recently been applied in the supply chain, environment, energy, business, and healthcare systems (dos Santos  The study area was located in Dailing Forestry Experimental Bureau, Dongfang Hong Forestry Field, Xiaoxing'an Region (128°37'46″ to 129°17'50″E, 46°50'8″ to 47°21'32″N), with an average elevation of 600 m. In 2011, within conifer-broadleaved mixed natural forests, six forest plots (A, B, C, D, E, F) of area 1 hm 2 (100 m×100 m) were established according to the ratio of harvested to total stockpile. Six continuous monitoring plots (A, B, C, D, E, and F) were set up with the thinning intensities of 10%, 15%, 20%, 25%, 30%, and 35% respectively, whereas a control plot with 0% thinning intensity(CK) was set up. Each tree was checked annually. The forest community was a conifer-broad mixed secondary forest, and the main tree species were Pinus koraiensis Sieb.et Zucc, Picea koraiensis Nakai, Abies fabri (Mast.) Craib, Tilia tuan Szyszyl, Betula platyphylla Suk, Fraxinus mandshurica Rupr, et al.
The average age, diameter at breast height, and tree height of the trees in the study sites were 70 a, 13.5 cm, and 10.5 m, respectively, and the stand densities were above 0.8 before thinning -in 2011. The trees were non-target species, partially over-dense trees. There were also harmful species, including diseased and decayed, stressed, dying trees, and trees with poor stem shape. In 2021, we recorded the elevation, slope, and other stand factors of each forest plot. We determined the location and recorded the species, height, diameter at breast height (≥ 5 cm), live branch height, crown width, crown length, and other factors of each tree in the forest plots; there were more than 800 trees in total. These characteristics are summarized in Table 1. According to the nearest neighbor property of Voronoi diagrams, we let P i (i = 1,2,...,n) be n points on a twodimensional Euclidean space and λ i (i = 1,2,...,n) be a given n positive real numbers. The regular Voronoi diagram is a special case of the weighted Voronoi diagram when all weights are equal i.e., λ i = λ 2 = ... = λ n .
However, the actual central tree differed from the surrounding adjacent trees due to its stand properties (diameter at breast height, tree height, crown length, and crown width), and the effects, i.e., the competitive range, likewise differed. For example, stand 82 of the conventional Voronoi diagram in Fig. 2-b is hexagonal without weighting, whereas stand 82 is pentagonal after weighting (as in Fig. 2-c), -central tree 82 has ve adjacent trees, 81, 84, 83, 79, and 77T. Each weighted Voronoi diagram was a polygon, and each edge of the polygon corresponded to a tree that was adjacent to the central tree. The number of edges of the weighted Voronoi polygon corresponded to the number of neighbors of the central tree. Thus, the blank part connected with 82 was the in uence range of the central tree 82.
When using the weighted Voronoi diagram to determine adjacent trees, the area where all four edges of the original forest plot widened horizontally by 2 m was used as the outer boundary of the Voronoi polygon, and the distance buffer method was used to eliminate the in uence of edges. Voronoi diagrams generated from corrected forest plots were complete, taking the weighted Voronoi diagram of the control forest plot as an example ( Fig. 2-a). The trees in the corrected forest plots were used as the central trees to calculate each spatial structure index, and the trees in the buffer zone were only used as adjacent trees in the calculation.
Based on the characteristics of natural conifer-broadleaved forests, the crown length characteristic factor was added to determine the competitive unit of the stand. We used the entropy-grey correlation method to analyze the intrinsic relationship between the number of convex edges in the Voronoi diagram and the corresponding diameter at breast height, height, crown width, and crown length of the trees and assigned weights to the diameter at breast height, height, crown width, and crown length. Grey correlation analysis was used to not only consider the number of tree stems adjacent to the central tree and the characteristics of the stand's attributes as a gray system but also to analyze the in uence of each stand's attributes on the number of adjacent tree stems. The number of trees adjacent to the central tree was used as the reference series . The factors in uencing the number of trees adjacent to the central tree, i.e., diameter at breast height, height, crown length, and average crown width of the central tree, were used as the comparator series. and and , and , and is the number of stems of the central tree, then its correlation coe cient formula is as follows: is a sequence of numbers numerical series at the absolute difference at the point; , and denote the minimum and maximum absolute differences at each moment of all comparator series, respectively; is the discriminant coe cient to weaken the distortion caused by the maximum absolute difference, which is taken as [0,1] to increase the signi cance of the difference between the correlation coe cients, and is usually taken as = 0.5 (Sun, 2007). To facilitate comparison, we use the critic method to weight each characteristic factor, i.e., to obtain the weighted correlation degree. The critical grey method can not only evaluate the differences within a single indicator but also measure the correlation ρ ρ between indicators and subsequently discriminate each factor's importance. The weighted grey correlation is obtained as follows.
The correlation between four factors -tree height, diameter at breast height, crown length, and average crown width-and the number of trees adjacent to the central tree was then calculated. The combined weights of the four factors were calculated . The weighted Voronoi diagram was generated using the Weighted Voronoi Diagram tool in ArcGIS to determine the stand spatial structure units and calculate the stand spatial structure index.

Selection of spatial structure parameters of forest stands
Seven spatial structure parameters representing three aspects based on single tree mingling, uniform angle, openness ratio, neighborhood comparison, competition, crowding, and forest layer difference were selected for structure analysis and evaluation. Among them, the degree of species mingling ( ) described the degree of spatial isolation of the stand ( Table 2, and the range of each parameter is divided into ve intervals 0.00, (0.00,0.25], (0.25, 0.50], (0.50, 0.75], (0.75, 1.00]. Among them, the forest layer was divided into six levels based on GB/T 26424 − 2010, and trees within the 2 m buffer zone were used as reference trees to determine the spatial structure parameters. ; represented the rst diversity index of all tree species within the basic spatial structure unit wherein the central tree was. The central tree was represented by , represented the number of forest layers in the spatial structure unit represented the angle between the line of two directly adjacent trees and the central tree. represented the standard angle of the structural unit. , , , represented the height of the central tree, the height of adjacent trees the horizontal distance between the central tree and adjacent trees, the number of adjacent trees in the spatial structure unit the central tree, the adjacent trees respectively. is the number of tree species in the structure unit was denoted by , whereas represented the number of the jth tree species in the structure unit where the ith central tree is located.
2.3 Evaluation of the optimal distance model for the spatial structure of forest stands 2.3.1 Importance of spatial structure parameters We apply the theory of landscape ecology, which requires homogeneity within patches and has essentially different characteristics from adjacent patches, to understand patch homogeneity as the homogeneity of stand structure by drawing on the existing research results of natural forest stand structure at home and abroad (Paluch, 2021;Weintraub & Cholaky, 1991). MIC (Reshef et al., 2011) (maximum mutual information coe cient) data mining and analysis were conducted using the spatial structure index derived by the multiplication and division method with each parameter to not only analyze the correlation and importance of each parameter affecting the spatial structure of conifer-broadleaved mixed forests but to also determine the priority and weight of each parameter, and to provide a theoretical basis for quantifying the factors affecting the spatial structure of natural conifer-broadleaved mixed forests in intending and thinning.
The homogeneity index was derived by multiplication and division method as follows.
When calculating the distance, we defaulted to the same weight for each index, but in the actual problem, the importance of different indexes varied. We use the homogeneity spatial structure index with the importance of each parameter for the improved fuzzy hierarchy method analysis, which was combined with the entropy weight method for the combined weight analysis to determine the importance of each parameter.

Quantifying spatial structure parameters
The TOPSIS (technique for order preference by similarity to an ideal solution) method was used (Behzadian et al., 2012; Çelikbilek & Tüysüz, 2020) to evaluate the combined distance of the spatial structure parameters from the optimal and the worst solutions of the structure parameters in any structure unit through certain calculations. A characteristic of the optimal distance model is that it uses the ideal optimal solution and the worst solution as the basis for judging the solution, which is then evaluated within the system of the solution, and such an evaluation tool better expresses the disparity between the solutions in the system, fully utilizing all the data. The optimal distance model realizes a comprehensive multi-indicator evaluation of forest spatial structure, and the ideal values can be set as very large, very small, intermediate, and interval (Chai, 2016), and we thus divide the ideal values of indicators into three categories as shown in Table 3.

Use of weighted grey correlation method to determine the spatial structure unit
The raw data of each characteristic factor for the 821 trees in the forest plot were processed without dimensions. The number of convex edges (number of adjacent trees) in the Voronoi diagram generated based on the tree point information for the corresponding 821 trees was analyzed in terms of diameter at breast height, height, crown length, and average crown width to obtain the weighted grey correlation for the spatial extent of tree competition.
Except for plot C, the forest plots had a similar correlation trend -mean crown width > diameter at breast height > crown length > tree height. Moreover, the weighted correlation of mean crown width in each thinned forest plot was no less than 0.30, and the weighted correlation of diameter at breast height was between 0.21 and 0.31, indicating that among the four factors, in almost all thinned forest plots, crown width had the greatest in uence on the competitive range of trees. Relatedly, crown length was strongly correlated with the diameter at breast height, and this correlation was second only to tree height (Table 4).

Determination of the number of adjacent trees via weighted Voronoi diagrams
The number of adjacent trees in each spatial structure unit was determined within the corrected forest plots based on weighted Voronoi diagrams, with a maximum of nine values for all forest plots, ranging from 2 to 10 trees (Fig. 3) corroborating previous studies. The distribution frequency of 3-8 adjacent trees in each plot was high, ranging from 90-96%; the distribution frequency of 2-3 adjacent trees did not exceed 14%; 9-10 adjacent trees accounted for 4-6.6% in each inter-logging plot, which was lower than the control.
This may have been due to the high sparseness and large distance between trees from the forest plot thinning -the number of adjacent trees in the forest sites was reduced due to the distance between the trees and the sparseness of the forest sites. Although the stand density of forest plot A was greater than that of forest plot C, the frequency distribution of stands with more than 8 trees was smaller than that of forest plot C, which was due to the distribution of trees. The distance between the central and adjacent tree was predominantly found within the interval of the average crown width, and this demonstrated the applicability of the weighted Voronoi diagram for analysis of thinned forest plots.
3.3 Analysis of spatial structure parameters of forest stands

Degree of tree species segregation
The median mingling degree value for the CK forest site was 0.488, whereas those for plots A-F were 0.609, 0.601, 0.589, 0.639, 0.512, and 0.675, respectively (Fig. 4). Except for the CK forest plot, the mean mingling degree values were all greater than 0.5. This suggests that the spatial con guration of tree species in the non-thinned stands was simpler, with a lower degree of species mingling than that of the control. In particular, the mean mingling degree value for the F forest plot was 0.636-this plot was highly mixed. In The average competition index of the forest plots was ca. 0.5, and most of the trees were in a moderate or strong competition state, except for the forest plots of E and F. The average competition index of these forest plots was lower than that of the control. This may be due to weak competition between trees due to the reduction of stand density by moderate thinning. The competition index of the forest plot was between 0.323-0.778, with an average value of 0.507. This indicates that forest plot C had high space utilization.

Spatial distribution pattern
The median and mean values of the openness ratio of forest plot C were 0.500 and 0.488, respectivelythese were the highest (Fig. 7). Moreover, the IQRs of A, B, and C were 0.250, 0.300, and 0.334, respectively.
These were smaller than those of CK, indicating that the dispersion of A, B, and C was smaller, and the median and mean values of C were higher than those of CK. Thus, the openness of forest plot C was the highest. However, the spatial allocation of the openness ratio should be optimized for the forest plots that have been logged, such as forest plot D. The frequency of distribution of trees in very open conditions was between 2.5-10.61%, and the lowest percentage was from the control forest plot. The openness ratio proportion was (OPv=(0.25,0.5])31-44%, indicating that most of the tree units in the stand were in a moderately open condition -they were not shaded. The openness ratio of forest plot C was higher than the other forest plots, indicating that its light conditions and transmissions were better than the other forest plots. Moreover, the number of spatial units with openness was highest in forest plot C, and its frequency of shaded and fully shaded units in the stand was lowest -the percentage of fully shaded units was 4.55%. This indicated that the growing space in the stand was su cient, and the light environment was good.
The greater the stand variation, the more complex the vertical strati cation structure of the stand. The stand variance index was distributed between 0.00-0.75, and the vertical strati cation complexity of the stand was medium (Fig. 8). About 20% of trees adjacent to central trees were not in the same stratum as the central tree. There were mostly only two or three stands in each spatial structure unit, and they were mainly concentrated in the middle layer (Figs. S3, S4). In comparison, the median and mean values in the D data were located slightly above the box, with a good degree of concentration; the full distance (0.750) and inter-quartile range (0.200) were small, with a low degree of dispersion. The lengths of the upper and lower tentacles were similar and as were the distances from the box, showing a clear symmetry of the in uencing factor. Box of D < box of CK < box of A = B < F < the length of A tentacles < B tentacles < C tentacles. The length of the upper and lower tentacles of C varied, and they also were asymmetrical as per normal distribution. Except for B and D, the mean value of the difference in stand strati cation was lower than that of the control forest, and the mean value was ca. 0.400. This indicated that the stand strati cation structure was simple, and the spatial utilization of the forest was low. From the distribution of the frequency of different values of the stand index, those below 0.5 were more than those above.
From the variation of angular scales in the thinned forest plots, the mean angular scales were between 0.381-0.423 (Fig. 9). In the thinned forest plots, 55.67-66.33% of the stands had a random distribution in the thinned forest plot was lower than that of the control and was lowest in forest plot F(6.40%). This re ects the relative reasonableness of the stand distribution pattern in this forest site. Plots A and F had a better stand distribution pattern compared to other thinned forest plots, but further optimization is needed to achieve the ideal condition. Currently, the clustered stands can be harvested to reduce the frequency of clustered distribution, so that the stand distribution can develop in the direction of random distribution. The mean value of the F angular scale was ca. 0.5, but the proportion of random distribution was signi cantly smaller than that of B and E forest plots, and the proportion of aggregated distribution was higher than that of B-E forest plots (Fig. 9). Although the mean value of the angular scale was larger, this higher mean value was probably due to the higher percentage of the aggregated distribution. Thus, the situation described by the mean value cannot represent that of the whole forest area.
The means of crowding degree -0.780, 0.631, 0.692, 0.719, and 0.702-were lower than that of the control expect for plot A. Here, the average crowding degree in the forest plot was higher than that in the control, and it was consequently denser than the control. As crowding class increased so did the proportion of trees in the forest plots (Fig. 10). Most of the trees in forest A were very dense, reaching 85.33%, and there were no sparse trees in forest A. Appropriate thinning intensity could reduce the average crowding degree of trees and increase the proportion of very sparse and relatively sparse trees.
3.4 Evaluation of integrated spatial structure indexes based on the optimal distance model 3.4.1 Parameter importance of spatial structure The importance analysis using homogeneity spatial structure indexes with each structure parameter yielded an importance ranking of Uv > aCIv > Wv > Mcv > OP > Hv > Cv. According to the consistency test, CR = 0.025 < 0.1 and CI = 0.03; these were acceptable (Alanís-Anaya et al., 2017). The entropy weighting method analysis yielded objective weights for each structure parameter (Table 5), and the nal combined weights were 0.29, 0.14, 0.11, 0.08, 0.12, 0.06, and 0.20. Table 5: Consistency test and weight of spatial structure parameters of natural conifer-broadleaved and broad-leaved mixed forest 3.4.2 Comprehensive evaluation of the spatial structure of forest stands The ranking according to the optimal distance method was B (0. The evaluation index value of forest plot F was the lowest, differing by 0.009 from that of the control plot. Individual trees (51.67%) in the control plot had moderate or less than moderate mingling, and those that had weak mingling were 20.83%, which was the highest among all forest plots. Very dense tree crowns were 71.67%, and 63.33%-this was the highest-of trees had a strong competition level. Trees in the absolute inferior state were 34.17%, and those with a moderately inferior level of forest layer difference were 68.33%. The proportion of randomly distributed trees was 57.50%. Plot F had 4.26% of its trees with weak mingling. However, 57.45% of its stands were above the poor state level, and 30% of their trees had dense tree crowns. The open ratio of stands was 38.30% for shade level 60.64% for strong competition, 67.02% for moderate to low level of forest layer, and 61.70% for randomly distributed stands, which was not signi cantly different from the control. The spatial structure of the above two forest stands was the poorest and therefore should be the focus of future improvement measures. In terms of optimal spatial structure, 65% of the trees in forest plot B were in a random distribution pattern, and 30% of trees were above the subdominant level, which was the highest. Trees above the moderate state were ca. 71%, whereas 65% of trees were above the strong mingling level. For the randomly distributed trees in plot C, 61% had an absolute uniform distribution pattern -this was 4% higher than plot B-62% were above the strong mingling level-this was 3% lower than B. Moreover, 17% were above the subdominant level, like plot B. In terms of openness ratios, plot B was less open than C, but its distribution of forest layer differences was better than C. Although the percentage of trees in plot B at the very intensive level (58.82%) was higher than in C (40.91%), the percentage of trees in C above the strong competition level (46.97%) was lower than that of plot B (62.35%). Although plot F was very open ( 7.45%), had strong forest layer variation (8.51%), and a high level of competition (9.57%) -these were higher than those of forest B-their ranks accounted for a lower proportion of the total ranks than plot B. Plot B not only had a higher proportion of moderate openness (41.18%), moderate and upper forest layer variation (72.94%), and higher levels of strong competition(55.29%) than plot F but also had a higher proportion of ranks in the forest. In terms of levels of mingling, the distribution of very intense levels of mingling was better in forest plot F than B, but the proportion of randomly distributed stands, subdominant and dominant ranks (U = [0, 0.25]), and moderately mingled stands was lower in plot F than B.
The evaluation indicators of different plots corroborated the Topsis value rankings, which had a better evaluation effect. Moreover, it better expressed the disparity between the plots and fully utilized all data. In a comprehensive analysis, the optimal solution distance model combined the optimal distance and the dominance of each parameter, which in uenced the comprehensive evaluation of the spatial structure of forest stands. The maximum value of the index was in the forest plot B with 15% of the thinning intensity The best spatial structure and average neighborhood comparison based on DBH were from 15% intensity of thinning (Fig. 9). This indicated that the spatial structure of natural conifer-broadleaved mixed forests was mainly related to the size ratio at DBH. After performing standardizations to facilitate comparisons among spatial structure indicators and evaluating the structure unit composition of each forest tree, we attained a closer to the ideal optimal solution, suggesting that this scheme better achieved accurate analysis of spatial structure indicators.

Discussion And Conclusion
Page 15/32 The determination of the stand spatial structure unit is a prerequisite for forest spatial structure analysis.
The traditional "1 + 4" adjacent tree method (1 central tree, 4 adjacent trees) or the conventional Voronoi diagram to analyze the spatial structure may exclude competing (= adjacent) trees or include noncompeting trees in a real stand . Based on the shortcomings of "1 + 4" which often excludes adjacent trees, Mengping Tang and others (Smith, 1987;Tang et al., 2007) in their study of competition indexes, used the conventional Voronoi diagram to determine the basis of stand structure units, which ensured the maximum correlation between the central and adjacent trees and improved the accuracy of the results. However, the conventional Voronoi diagram only considered the spatial location of the forest trees when determining the adjacent trees and regarded all the forest trees as stands with identical competitiveness, without considering the factors of the forest trees themselves, and often included non-competing trees. Thus, the constructed structure units could not truly re ect the actual range of in uence of forest trees (Aakala et al., 2013). As the most common physical impediments to interactions between stands are crowding of growing space and shading from above, such interactions, in previous studies of pure stands, were mainly dependent on the differences in breast height, tree height, and crown width of adjacent stands. In this study -considering the differences of tree species in conifer-broadleaved mixed natural forests-the Voronoi diagram method was modi ed to determine the structure unit of the forest based on the position information of the forest trees, combined with the four most critical factors affecting the competitive dynamics of the forest trees: crown width, DBH, crown length, and height.
The results of grey correlation analyses of the number of trees adjacent to the central tree and its key in uencing factors showed that the average crown width of conifer-broadleaved mixed forests at each thinning intensity (10%, 15%, 20%, 25%, 30%, 35%) had a greater in uence on the spatial extent of structure units when compared to the control forest plot; the crown length factor had higher in uence than the tree height. It has been shown that the allocation of tree organs is strongly related to spatial partitioning and Based on the results of the determination of spatial units via weighted Voronoi diagrams, seven spatial structure parameters -mingling, uniform angle, openness ratio, neighborhood comparison, competition, crowding, and forest layer difference-were used to analyze the spatial structure in the study area after 10a of natural conifer-broadleaved mixed forests. The spatial distribution pattern of trees in each plot was uniform, and the proportion of uneven and very uneven distribution of adjacent trees around the six thinned forest plots was smaller than that of the control plot. However, the selection of one or two trees should within the structure unit to make the distribution more balanced is a recommended improvement. The compound forest structure is hypothesized as the most reasonable structure for the rational use of space and forest stability, and the closer the stand is to its natural state, the more complex the structure of the forest layer is. From the ndings on the forest layer difference index, the best stand structure was in the forest plot with 25% thinning intensity, and the distribution of trees in the upper, middle, and lower stands was even. The stand index was low, the vertical spatial structure of the stand was poor, and the trees did not make enough use of the vertical space. The average openness ratio of the six forests under varying thinning intensities was between 0.358-0.488, with medium openness and su cient space for tree growth. The more open the space in the stand, the more permeable the stand is, which then meets the demand for growing space and resources of trees. The average degree of crown intersection in conifer-broadleaved mixed natural forests was as high as 80%, and this degree was higher in low thinning intensity plots (10% and 15%); plots with 10% thinning intensity of the tree crown crowding had a higher than the control plot. All six plots under various thinning intensities were very dense (C=(0.75, 1]), demonstrating that 41%-85% of the crown can be pruned to ensure the growing space between trees. The simple structure and low strati cation of each forest plot re ected poor regeneration. Thus, reforestation plans should broaden the duration for the formation of a heterogeneous stand and increase the structure diversity in the vertical dimension (3). From the competition, the mean size ratio distribution of each plot was ca. 0.5. Plot F was appropriately replanted with native species to increase the diversity of stand species composition and increase the stand diameter class and span of the trees, rationalize the distribution of the DBH ratios, and improve the vertical strati cation of the stand. Compared with the control plot, the competitive pressure of the stands was reduced, but the competition intensity of each forest plot was generally higher, indicating a strong ecological vigor.
To clarify the strength of in uence of each parameter on spatial structure, the spatial structure index (homogeneity structure index) obtained by the multiplication and division method was correlated with each parameter, and the importance ranking of each factor of spatial structure in mixed forest stands was determined as Ui > aCIi > Wi > Mci > OP > Hi > Ci. The optimal distance model was used to rank the size of the spatial structure. The proposed optimal distance model-based evaluation of stand spatial structure not only solves the importance and priority in calculating structure parameters but is also a method for quantitative evaluation of stand spatial structure. The size ranking of the spatial structure index of the thinned forest plots was B (0.488) > C (0.487) > E (0.480) > D (0.479) > A (0.475) > CK (0.442) > F (0.433).According to the combined score of the optimal distance model, the spatial structure of the stand was optimal in B. The proportion of trees at the moderately open level (41.18%), with moderate and upper stand variation (72.94%), and a strong level of competition (55.29%) was high in plot B. In terms of the degree of mingling, the distribution of very intense mingling classes was better in forest plot F than in B, but its share of randomly distributed stands, subdominant and dominant classes (U=[0, 0.25]), and those with a moderate degree of mingling were lower than of forest plot B. Forest plots with better stand structure were those with under 15% and 20% thinning intensities, which were more ecologically vigorous due to the large degree of mingling, suitable size differentiation, and competition. Moreover, the whole stand was more ecologically vigorous, whereas the plots under 35% thinning had weak mingling, a simple structure in the vertical direction, lacked young trees in the lower layer, and had poor overall stability. For the forest plots with unclear differentiation of the forest layers, replanting or thinning based on tree height at a later stage would reasonably increase the differentiation and improve the spatial structure of the forest stand. Thinning priority is determined according to the health of the stand, and thinning mainly aims to strengthen the stand difference and reduce the density, which is supplemented by the adjustment of single trees. Therefore, after investigating and evaluating the spatial structure of mixed conifer-broadleaved natural forests, we recommend careful consideration of the thinning intensity of stand variation, increasing the openness of the stand, determination of the priority of stand adjustment according to the grade, and then replanting or thinning according to the speci c conditions of a plot.
Structured management has become a common forest management model in the last decade, and stand structure plays a decisive role in the development of forest functions. Conversely, natural secondary forests are prone to over-depression and rely only on the natural thinning of the stand, which has a very slow growth rate, an unreasonable structure, and is unfavorable to the growth of light-loving tree species . The appropriate harvesting intensity is very important for spatial structure adjustment and optimization. The spatial structure of forest stands varies with region and stand type. The crown crowding in the area we studied was large, thus speci c management measures such as post-harvesting were used to adjust the crown and promote natural forest regeneration. Studies on the spatial structure of forest stands now tend towards comprehensive evaluation. However, the forest structure is highly complex. The comprehensive evaluation method of optimal distance demonstrated in this study had certain evaluation effects on the spatial structure, but lacked uniformity in the degree of difference of its quantitative indexes. This was achieved only through the comprehensive analysis of each structure parameter with the comprehensive evaluation index. Therefore, further research is needed for the subsequent comprehensive quantitative degree characterization.