Research method of stability of tropical coastal shelterbelt trees based on growth game relationship

Abstract

The application discloses a kind of tropical coastal shelter forest tree stability research methods based on growth game relation, belong to coastal shelter forest research technical field, including test area setting and tree species configuration, obtain growth index and material property index, construct allometric growth relation model, game relation and the influence analysis of spatial structure to tree stability and tree resistance stability measurement step.The application method proposes the tree height-diameter relationship model construction method containing competition effect and spatial structure random effect from the angle of game theory, constructs the game relationship of tree height and diameter with spatial structure parameter as random variable, divides the relationship of tree height-diameter into six types such as mutual benefit, partial benefit, competition and parasitism, and quantitatively characterizes through regression coefficient positive and negative and significance, breaks through the limitation that traditional competition index only reflects one-way pressure, and can realize the scientific expression of game relationship of different tree species in mixed forest.

Description

Technical Field

[0001] This invention belongs to the field of coastal shelterbelt research technology, specifically involving a research method for the stability of trees in tropical coastal shelterbelts based on growth game theory. Background Technology

[0002] In multi-species mixed afforestation based on the near-natural concept, the spatial structure of trees after multi-species mixed afforestation is heterogeneous and random due to the differences in height and diameter growth rate among different tree species. The game relationship between tree height and diameter at breast height cannot be fully explained by competition alone (Hegyi, Bella).

[0003] Traditional allometric growth models only consider the tree's own genetic characteristics, reflecting information such as tree height and diameter at breast height (DBH), while neglecting the competitive and mutually beneficial relationships between trees and their neighbors, as well as the spatial structure information of the growth unit in which the tree is located. These factors all influence the height-to-diameter ratio (HBR). Furthermore, existing studies often use fixed competition indices (such as the Hegyi index) to characterize the neighbor effect, but these indices only reflect unidirectional competitive pressure and cannot quantify the dynamic trade-offs of mutual promotion or inhibition between tree species or between different growth indicators (height and diameter) of the same species. In reality, in the allocation of resources, there is a game-like strategy between tree height growth and DBH growth in ecology—they can benefit each other (mutual benefit), or one may benefit while the other suffers (parasitism), or they may inhibit each other (competition). This game-like relationship directly affects the wind resistance and overall stability of trees, especially in tropical coastal areas where typhoons are frequent; the tree configuration (height-to-diameter ratio) is one of the key factors determining whether a tree will fall over. However, no studies have yet systematically constructed an allometric growth model with spatial structure stochastic effects from a game theory perspective, nor have they incorporated the interaction effects of game relations and spatial structure parameters into the forest stability assessment system.

[0004] Therefore, it is essential to develop a research method for the stability of tropical coastal shelterbelts based on growth game theory that can solve the above problems. Summary of the Invention

[0005] To address the problem that existing methods cannot accurately explain the differences in growth variation and wind resistance stability of different tree species in mixed forests under typhoon disturbance, the present invention aims to provide a research method for the stability of trees in tropical coastal shelterbelts based on growth game theory relationships. By fusing backpack lidar point cloud data, the method accurately obtains the three-dimensional morphology of trees, constructs a system of simultaneous equations containing game strategies and random parameters of spatial structure, quantifies the game type of growth indicators of different tree species and their interaction with spatial structure, and then evaluates the resistance stability of trees, providing a scientific basis for the mixed configuration of coastal shelterbelts.

[0006] The objective of this invention is achieved by including the following steps:

[0007] S1. Experimental area setup and tree species configuration: Experimental areas were set up at different distances from the sea, and each experimental area was used to establish mixed forest experimental plots with different densities and tree species configurations, as well as pure forest experimental plots.

[0008] S2. Obtain growth indicators, wood properties and spatial structure parameters: Obtain growth indicators, wood properties and spatial structure parameters of different tree species in each experimental plot. Growth indicators include tree height, diameter at breast height and crown information. Wood properties include microfibril angle, fiber characteristics and mechanical properties. Spatial structure parameters include size ratio, angular scale, degree of mixing and density.

[0009] S3. Constructing an allometric growth relationship model: Taking different tree species in the experimental plot as the object, and using the structural information of the spatial unit composed of the object tree and four adjacent trees, an allometric growth relationship model of tree height and diameter at breast height (DBH) of tree species is established based on game theory. The differences in the game relationship of tree height and DBH of tree species with different biological characteristics and the influence of the spatial structure on the game relationship are compared. The stability mechanism of tropical coastal shelterbelt trees is revealed from the perspective of tree growth game.

[0010] S4. Analysis of the impact of game relations and spatial structure on forest stability: Comparative analysis of the game relations (mutualism, symbiotic relationship, competition, primitive cooperation, etc.) of tree height and diameter at breast height, and the differences in growth stability and wood properties of different tree species by spatial structure (size ratio, angular scale, degree of mixing, density, etc.), analyze the interaction effect of game relations and spatial structure, and reveal the formation mechanism of forest stability from the perspective of game theory.

[0011] S5. Measurement of tree resistance stability: Calculate the coefficient of variation of tree height, diameter at breast height, crown volume, and crown surface area before and after typhoon disturbance to assess the resistance stability of trees.

[0012] Traditional forest surveys can generally obtain relatively accurate diameter at breast height (DBH) information. For tree height, an error of 1 meter is generally acceptable. For the crown, only parameters such as crown width and crown length can be obtained, which cannot accurately describe the three-dimensional morphology of the canopy. Traditional survey methods cannot meet the project's requirements for accurately obtaining short-term variability in tree height and DBH growth and canopy dynamics data. Therefore, this invention develops a method for calculating tree height and crown information, as detailed below.

[0013] Preferably, in step S2, the tree height is determined by acquiring forest laser point cloud data using a backpack lidar, coloring the laser point clouds collected from the two backpacks separately, and then superimposing them to calculate the tree height using the height difference between the point clouds.

[0014] Preferably, the calculation process of the canopy information in step S2 is as follows:

[0015] (1) Use backpack lidar to obtain the absolute spatial location of trees and the lidar morphology features of trees using lidar;

[0016] (2) Extract the crown data of a single tree from the point cloud data and remove the part below the first main branch or the first branch;

[0017] (3) Divide the crown of the tree in step (2) into several equal-height segments along the vertical direction. That is, regard the entire crown of a single tree as a solid composed of a cone at the top and n frustums below. The volume of the crown is the sum of the volumes of the cone and the n frustums.

[0018] (4) Project the tree canopy data from step (2) onto the XY coordinate plane to construct an irregular shape with closed edges. Divide the irregular circle into n equal-width intervals using vertical lines parallel to the Y-axis and perpendicular to the X-axis. The width of each interval is j. s If an irregular shape is considered to be composed of two triangles at the beginning and end and n-2 trapezoids, then the area of ​​the irregular circle is the sum of the areas of the two triangles at the beginning and end and the areas of the n-2 trapezoids.

[0019] Preferably, the process of constructing the allometric growth relationship model between tree height and diameter at breast height in step S3 is as follows:

[0020] 1) Construct game strategies for tree species diameter at breast height (DBH) and tree height, resulting in 6 interactions, of which 3 are positive interactions:

[0021] Mutually beneficial, tree height and diameter at breast height both benefit from each other;

[0022] In the original cooperative model, there was no obvious mutual benefit between tree height and diameter at breast height;

[0023] In a symbiotic relationship, one of the tree's height and diameter at breast height (DBH) benefits while the other remains unaffected.

[0024] The three negative interactions are:

[0025] Competition hinders both tree height and diameter at breast height;

[0026] In a parasitic relationship, the tree's height and diameter at breast height both benefit from the growth while the other is hindered.

[0027] Symbiotic relationship where one tree's height or diameter at breast height is obstructed while the other remains unaffected;

[0028] 2) For a given tree species, select its four nearest neighbor trees and analyze their relationship with the target tree. Based on game theory and considering the randomness of the spatial structure of the target tree, construct a tree height-diameter-at-breast-width allometric growth relationship model containing spatial structure information:

[0029]

[0030] In the formula, and These represent the individual tree height and diameter at breast height (DBH) of a specific tree species, respectively. This represents the weighted average distance between the i-th type of tree species and the individual target tree; This represents the weighted average diameter at breast height (DBH) of the i-th tree species. This represents the weighted average tree height of the i-th tree species; and These represent the intercept terms for tree height and diameter at breast height, respectively. and These represent random parameters of the spatial structure in which the object is located; , , , , , , and The regression coefficients represent the rates of influence of the weighted distance, diameter at breast height (DBH), and tree height of the target tree and the n competing tree types on the tree height and DBH of the target tree, respectively. The random error in the tree height and diameter at breast height equations in the system of simultaneous equations follows a set rule. ~ (0, ) ,in = , For deviation The error structure matrix, The variance of the random error;

[0031] 3) Decompose equation (1) into two parts:

[0032]

[0033] In the formula, and This indicates the relative growth of a single tree's height and diameter at breast height in an independent environment; and This indicates that competing trees in a competitive environment affect the growth of the single tree.

[0034] 4) Write equation (2) as follows:

[0035]

[0036] in,

[0037]

[0038] 5) Use least squares (OLS) and seemingly uncorrelated regression (SUR) to estimate the parameters of model (2); use error bias ( ), error variance ( ), root mean square error (RMSE), total relative error (TRE), and coefficient of determination ( The model is evaluated.

[0039] Compared with the prior art, the present invention has the following technical effects:

[0040] 1. This invention uses backpack lidar to accurately acquire point cloud data of individual trees, and uses methods such as fusion and overlay of multiple phases of lidar point clouds to obtain the differences in tree height and crown morphology at different time periods;

[0041] 2. This invention proposes a method for constructing a tree height-diameter relationship model from the perspective of game theory, incorporating competition effects and spatial structure random effects. It uses spatial structure parameters as random variables to construct the game relationship between tree height and diameter, classifying the tree height-diameter relationship into six types: mutually beneficial, pejorative, competitive, and parasitic. Through quantitative characterization using the positive and negative values ​​and significance of regression coefficients, it overcomes the limitation of traditional competition indices that only reflect unidirectional pressure, enabling a scientific expression of the game relationship between different tree species in mixed forests. This invention will combine the game relationship of tree growth to analyze the influence of different spatial structure parameters on tree growth variation and wood properties, clarifying the spatial structure effect that contributes to the stability of trees in mixed forests. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the test cell for Example 1;

[0043] Figure 2 Example 1: Point cloud of a single tree;

[0044] Figure 3 A schematic diagram illustrating the differentiation of tree canopy volume;

[0045] Figure 4 A schematic diagram showing the cross-section of the tree crown. Detailed Implementation

[0046] The present invention will be further described below with reference to the embodiments and accompanying drawings, but this does not limit the present invention in any way. Any changes or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0047] Example 1

[0048] This embodiment uses a method based on growth game theory to study the stability of tropical coastal shelterbelt trees, including the following steps:

[0049] S1. Experimental area setup and tree species configuration: A comprehensive experimental field of a forest ecological positioning station in Hainan Province selected 1 non-native tree species, 2 relatively fast-growing native tree species, and 2 slow-growing native tree species, for a total of 5 species (see Table 1).

[0050] Table 1. Tree species and characteristics of near-natural regeneration afforestation

[0051]

[0052] To analyze the effects of mixed afforestation, native tree species were replanted in the experimental field. Four tree species were selected: Chinaberry (a), Hainan Bean Tree (b), Malus yunnanensis (c), and Litsea cubeba (d), and planted according to different initial planting densities (see Table 2).

[0053] Table 2 Afforestation Design Units for Near-Natural Regeneration Afforestation

[0054]

[0055] Density experimental design: ① and ④ plots retained 3333 plants / hm2; ② and ⑤ plots retained 1667 plants / hm2; ③ and ⑥ plots retained 2500 plants / hm2.

[0056] Among them, communities ①, ②, and ③ are close to the coastline (5km), while communities ④, ⑤, and ⑥ are far from the coastline (20km).

[0057] Each afforestation unit consisted of 6 experimental plots (as shown in Figure 1). Ultimately, a total of 9 afforestation units (Table 2) were formed, comprising 54 experimental plots: A, B, C, D, E, a, b, c, and d.

[0058] S2. Acquisition of growth and wood property indicators: In order to understand the variability of forest growth indicators before and after environmental disturbance, according to the natural disturbance pattern in the study area, growth indicators, wood property indicators and spatial structure parameters of different tree species in each experimental plot were acquired in April and October of each year. Growth indicators include tree height, diameter at breast height and crown information; wood property indicators include microfibril angle, fiber characteristics and mechanical properties; spatial structure parameters include size ratio, angular scale, mixing degree and density.

[0059] Tree height is calculated by using backpack lidar to acquire forest laser point cloud data, coloring the laser point clouds collected by the backpack twice, and then superimposing them, using the height difference of the point clouds to calculate the height of the trees.

[0060] The diameter at breast height was obtained by measuring the diameters in two perpendicular directions using vernier calipers, and then the average value was calculated.

[0061] Microfibril angle: One of the main determinants of the mechanical properties of wood; a small microfibril angle indicates high tensile strength, while a large microfibril angle indicates high elasticity. Its determination methods include three main categories: microscopic techniques, X-ray diffraction, and near-infrared spectroscopy. This study used electron microscopy to observe the characteristics of the alignment between the longitudinal surface of the sample or the orientation of individual fibers and microfibrils, and used computer image processing technology to obtain the microfibril angle.

[0062] Wood Fiber: Wood fiber quality was determined using an LDA02 fiber quality analyzer. The specific material treatment method was as follows: 1-2 cm segments of material were cut and placed in a test tube. A 1:1 mixture of glacial acetic acid and 30% H2O2 (prepared fresh) was added, ensuring the reagent completely covered the wood core. The test tube containing the wood core and reagent was placed in an 80°C water bath and heated until the wood core turned completely white. The treated wood core was then broken down into individual fibers using a dispersant. A small amount of the fiber solution was poured into a special beaker for measurement. Due to the minimal difference between heartwood and sapwood during the seedling stage, this study only sampled and analyzed the wood fiber characteristics from the xylem and phloem.

[0063] Mechanical properties: The mechanical properties of the wood were determined using a MW-4 universal wood testing machine. The modulus of elasticity in bending and the bending strength were measured using the same specimen. First, test specimens were prepared and the modulus of elasticity in bending was measured according to the national standard GB1936.2-91 "Method for Determination of Modulus of Elasticity in Bending of Wood". Then, the bending strength was measured according to the national standard GB1936.1-91 "Method for Test of Bending Strength of Wood". Considering the workload of the above research and the differences in our own expertise, the testing of the timber properties was outsourced to an external institution.

[0064] To quantify the spatial structure of the target trees, the following four commonly used forest stand spatial structure parameters need to be calculated:

[0065] Size ratio (U): Reflects the comparison of the diameter at breast height (DBH) of the target tree with that of its neighboring trees. It takes the value [0,1] and is calculated by dividing the number of neighboring trees with a DBH greater than that of the target tree by the total number of neighboring trees.

[0066] Angular scale (W): describes the uniformity of adjacent trees around the object tree. It is obtained by measuring the angle between adjacent trees and comparing it with the standard angle (72°). The value is [0,1].

[0067] Mixing degree (M): represents the proportion of different tree species between the object tree and its neighboring trees, with a value of [0,1]. It is the number of dissimilar trees in the neighboring group divided by the total number of neighboring groups.

[0068] Density (C): Reflects the density of the surrounding trees of an object tree, usually expressed as the proportion of trees in the surrounding trees whose distance is less than a certain threshold;

[0069] All the above parameters are calculated using the target tree and its four nearest neighbors as the unit of calculation, and the specific calculation method refers to the conventional definition in forest management (standard literature can be cited). In this invention, these parameters will be included as random variables in θ of the allometric growth model (Equation 1). h And θᵈ.

[0070] The specific process for calculating tree canopy information is as follows:

[0071] (1) Use backpack lidar to obtain the absolute spatial location of trees and the lidar morphology features of trees using lidar;

[0072] (2) Use FARO SCENE to extract the crown data of individual trees from the collected point cloud data and remove the part below the first main branch or the first branch;

[0073] (3) Divide the canopy from step (2) vertically into several segments of equal height. That is, consider the entire canopy of a single tree as a solid composed of a cone at the top and n frustums below. When n approaches infinity, the height of a single frustum (cone) becomes infinitesimally small, and the volume of the canopy is the sum of the volumes of the cone and the n frustums. See Figure 3 As shown;

[0074] (4) Project the tree canopy data from step (2) onto the XY coordinate plane to construct an irregular shape with closed edges. Divide the irregular circle into n equal-width intervals using vertical lines parallel to the Y-axis and perpendicular to the X-axis. The width of each interval is j. s The irregular shape can be considered as consisting of two triangles at the beginning and end and n-2 trapezoids. When n is infinite, the width j of the interval segment is... s If it is infinitesimal, then the area of ​​the irregular circle is the sum of the areas of the two triangles at the beginning and end and the areas of n-2 trapezoids, see... Figure 4 As shown;

[0075] L i To divide the interval segments, let L0 be the length of the first edge of the first interval segment, L0=0, and L1, L2, ..., L n-1 The lengths of the 2nd, 3rd, ..., nth edges are L respectively. n The length of the last edge of the last interval segment;

[0076] S3. Construct an allometric growth relationship model: Taking different tree species in the experimental plot as the object, and using the structural information of the spatial unit composed of the object tree and its four neighboring trees, an allometric growth relationship model of tree height and diameter at breast height (DBH) is established based on game theory. The differences in the game relationship of tree height and DBH of tree species with different biological characteristics and the influence of the spatial structure on the game relationship are compared.

[0077] The specific process for constructing the allometric growth relationship model between tree species, tree height, and diameter at breast height is as follows:

[0078] 1) Construct game strategies for tree species diameter at breast height (DBH) and tree height, resulting in 6 interactions, of which 3 are positive interactions:

[0079] Mutually beneficial, tree height and diameter at breast height both benefit from each other;

[0080] In the original cooperative model, there was no obvious mutual benefit between tree height and diameter at breast height;

[0081] In a symbiotic relationship, one of the tree's height and diameter at breast height (DBH) benefits while the other remains unaffected.

[0082] The three negative interactions are:

[0083] Competition hinders both tree height and diameter at breast height;

[0084] In a parasitic relationship, the tree's height and diameter at breast height both benefit from the growth while the other is hindered.

[0085] Symbiotic relationship where one tree's height or diameter at breast height is obstructed while the other remains unaffected;

[0086] The interactions are shown in Table 3;

[0087] Table 3 Game strategies for tree species' diameter at breast height (DBH) and tree height.

[0088]

[0089] 2) For a given tree species (the target tree), select its four nearest neighbor trees and analyze their relationship with the target tree. Based on game theory and considering the randomness of the spatial structure of the target tree, construct a tree height-diameter-at-breast-width allometric growth relationship model containing spatial structure information:

[0090]

[0091] In the formula, and These represent the individual tree height and diameter at breast height (DBH) of specific tree species (Casuarina equisetifolia, Chinaberry, Litsea cubeba, etc.). (I = 1, ..., n) represents the weighted average distance between the i-th type of tree species and the target tree; (i = 1, ..., n) represents the weighted average diameter at breast height (DBH) of the i-th tree species; (i = 1, ..., 4) represents the weighted average tree height of the i-th type of tree species; i = 1 indicates that the competing trees are the same species, and i = 2...n indicates that the competing trees are respectively Chinaberry, Hainan Bean Tree, Hainan Crabapple, and Litsea cubeba. and These represent the intercept terms for tree height and diameter at breast height, respectively. and These represent the random parameters of the spatial structure in which the object is located. , , , , , , and (i = 1, 2, 3, 4, 5) are regression coefficients, representing the rate of influence of the weighted distance, diameter at breast height (DBH), and tree height of the target tree and the n types of competing trees on the tree height and DBH of the single tree, respectively. The random error in the tree height and diameter at breast height equations in the system of simultaneous equations follows a set rule. ~ (0, ) ,in = , For deviation The error structure matrix, The variance of the random error;

[0092] 3) Decompose equation (1) into two parts:

[0093]

[0094] In the formula, and This indicates the relative growth of a single tree's height and diameter at breast height in an independent environment; and This indicates that competing trees in a competitive environment affect the growth of the single tree.

[0095] 4) Write equation (2) as follows:

[0096]

[0097] in,

[0098]

[0099] The parameter estimates in Equation (1) quantify the degree of each interaction, thereby measuring the growth status of the target tree species under the influence of its own genetic factors or the external environment. The positive or negative sign of the parameter value indicates whether the interaction strengthens or weakens the growth ability of the target tree species D or H. If the parameter value is not significant, it indicates that the interaction does not affect the growth of the target tree species D or H. Therefore, Equation (1) can effectively reflect the growth allocation strategy of the target tree species in terms of tree height (H) or diameter at breast height (D) under the influence of its own internal mechanisms and external environmental disturbances.

[0100] 5) Use least squares (OLS) and seemingly uncorrelated regression (SUR) to estimate the parameters of model (2); use error bias ( ), error variance ( ), root mean square error (RMSE), total relative error (TRE), and coefficient of determination ( Evaluate the model;

[0101] S4. Analysis of the impact of game theory relationships and spatial structure on forest stability: Compare and analyze the game theory relationships between tree height and diameter at breast height (DBH), and between crown information and DBH, as well as the differences in the impact of spatial structure on the growth stability and wood properties of different tree species, and analyze the interaction effect between game theory relationships and spatial structure.

[0102] S5. Measurement of Tree Resistance Stability: Based on the growth process information (height, diameter at breast height, crown volume, crown surface area) of the stand in the year prior to the typhoon disturbance period (July-September), four surveys were conducted in October, June of the following year, October of the following year, and June of the third year. October of the current year to June of the following year is considered the pre-disturbance growth period, and October of the following year to June of the fourth year is considered the post-disturbance growth period. The coefficients of variation of tree height, diameter at breast height, crown volume, and crown surface area before and after typhoon disturbance were calculated to assess the stability of tree resistance. The smaller the coefficient of variation after disturbance, the stronger the tree resistance stability. The formula is as follows:

[0103]

[0104] In the formula, CV is the coefficient of variation. The standard deviation is... This is the average value;

[0105] Using multivariate analysis of variance and repeated measures data, we compared and analyzed the differences in height and diameter growth of different tree species under different stand densities, tree species compositions and disturbance levels during a period before and after the typhoon season (July-September), and compared the variability of forest growth indicators under different scenarios.

[0106] The above analysis was performed using SPSS 16.0, R, Frostat and other relevant statistical software.

Claims

1. A method for studying the stability of tropical coastal shelterbelt trees based on growth game theory, characterized in that... Includes the following steps: S1. Experimental area setup and tree species configuration: Experimental areas were set up at different distances from the sea, and each experimental area was used to establish mixed forest experimental plots with different densities and tree species configurations, as well as pure forest experimental plots. S2. Obtain growth indicators, wood properties and spatial structure parameters: Obtain growth indicators, wood properties and spatial structure parameters of different tree species in each experimental plot. Growth indicators include tree height, diameter at breast height and crown information. Wood properties include microfibril angle, fiber characteristics and mechanical properties. Spatial structure parameters include size ratio, angular scale, degree of mixing and density. S3. Construct an allometric growth relationship model: Taking different tree species in the experimental plot as the object, and using the structural information of the spatial unit composed of the object tree and its four neighboring trees, an allometric growth relationship model of tree height and diameter at breast height (DBH) is established based on game theory. The differences in the game relationship of tree height and DBH of tree species with different biological characteristics and the influence of the spatial structure on the game relationship are compared. S4. Analysis of the impact of game theory relationships and spatial structure on forest stability: Comparative analysis of the game theory relationship between tree height and diameter at breast height, and the differences in the impact of spatial structure on the growth stability and wood properties of different tree species, and analysis of the interaction effect between game theory relationships and spatial structure. S5. Measurement of tree resistance stability: Calculate the coefficient of variation of tree height, diameter at breast height, crown volume, and crown surface area before and after typhoon disturbance to assess the resistance stability of trees.

2. The method for studying the stability of tropical coastal shelterbelt trees based on growth game theory as described in claim 1, characterized in that... The S2 step tree height is calculated by using backpack lidar to acquire forest laser point cloud data, coloring the laser point clouds collected from the two backpacks separately and then superimposing them, and using the height difference of the point clouds to calculate the height of the trees.

3. The method for studying the stability of tropical coastal shelterbelt trees based on growth game theory as described in claim 1, characterized in that... The specific calculation process for tree canopy information in step S2 is as follows: (1) Use backpack lidar to obtain the absolute spatial location of trees and the lidar morphology features of trees using lidar; (2) Extract the crown data of a single tree from the point cloud data and remove the part below the first main branch or the first branch; (3) Divide the crown of the tree in step (2) into several equal-height segments along the vertical direction. That is, regard the entire crown of a single tree as a solid composed of a cone at the top and n frustums below. The volume of the crown is the sum of the volumes of the cone and the n frustums. (4) Project the tree canopy data from step (2) onto the XY coordinate plane to construct an irregular shape with closed edges. Divide the irregular circle into n equal-width intervals using vertical lines parallel to the Y-axis and perpendicular to the X-axis. The width of each interval is j. s If an irregular shape is considered to be composed of two triangles at the beginning and end and n-2 trapezoids, then the area of ​​the irregular circle is the sum of the areas of the two triangles at the beginning and end and the areas of the n-2 trapezoids.

4. The method for studying the stability of tropical coastal shelterbelt trees based on growth game theory as described in claim 1, characterized in that... The specific process of constructing the allometric growth relationship model between tree species height and diameter at breast height in step S3 is as follows: 1) Construct game strategies for tree species diameter at breast height (DBH) and tree height, resulting in 6 interactions, of which 3 are positive interactions: Mutually beneficial, tree height and diameter at breast height both benefit from each other; In the original cooperative model, there was no obvious mutual benefit between tree height and diameter at breast height; In a symbiotic relationship, one of the tree's height and diameter at breast height (DBH) benefits while the other remains unaffected. The three negative interactions are: Competition hinders both tree height and diameter at breast height; In a parasitic relationship, the tree's height and diameter at breast height both benefit from the growth while the other is hindered. Symbiotic relationship where one tree's height or diameter at breast height is obstructed while the other remains unaffected; 2) For a given tree species, select its four nearest neighbor trees and analyze their relationship with the target tree. Based on game theory and considering the randomness of the spatial structure of the target tree, construct a tree height-diameter-at-breast-width allometric growth relationship model containing spatial structure information: ； In the formula, and These represent the individual tree height and diameter at breast height (DBH) of a specific tree species, respectively. This represents the weighted average distance between the i-th type of tree species and the individual target tree; This represents the weighted average diameter at breast height (DBH) of the i-th tree species. This represents the weighted average tree height of the i-th tree species; and These represent the intercept terms for tree height and diameter at breast height, respectively. and These represent random parameters of the spatial structure in which the object is located; , , , , , , and The regression coefficients represent the rates of influence of the weighted distance, diameter at breast height (DBH), and tree height of the target tree and the n competing tree types on the tree height and DBH of the target tree, respectively. The random error in the tree height and diameter at breast height equations in the system of simultaneous equations follows a set rule. ~ (0, ) ,in = , For deviation The error structure matrix, The variance of the random error; 3) Decompose equation (1) into two parts: ； In the formula, and This indicates the relative growth of a single tree's height and diameter at breast height in an isolated environment; and This indicates that competing trees in a competitive environment affect the growth of the single tree. 4) Write equation (2) as follows: ； in, ； 5) The least squares method and seemingly uncorrelated regression method are used to estimate the parameters of model (2); the error deviation, error variance, root mean square error, total relative error and coefficient of determination are used to evaluate the model.

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