地统计学在害虫生物防治中的应用与决策支持

doi:10.3864/j.issn.0578-1752.2026.18.010

Abstract

Abstract:

The spatial distribution of natural enemy populations as well as their spatio-temporal relationships with pests directly determines the performance of agricultural ecosystems’ natural pest suppression function, and acts as a critical foundation for research on green and precision pest management. Traditional research continues to follow the analytical paradigm of “population monitoring - average assessment - uniform intervention”, focusing on the temporal dynamics of pest density. This confines many studies to merely descriptive analysis of spatial patterns, leaving them unable to underpin practices of pesticide reduction & efficiency improvement and green pest control in terms of spatial heterogeneity identification, pest-natural enemy spatial relationship dissection, and management decision support. By integrating spatial location data and population observation values, geostatistics can effectively characterize the spatial structure of pest and natural enemy populations, identify pest high-density aggregation hotspots and natural enemy dominant distribution zones, and further quantitatively diagnose their spatial overlap zones, tracking relationships and spatial mismatch zones. It thus provides an innovative analytical approach to break through the limitations of traditional methods. We provide a systematic review of research progress and applications of geostatistics in biological pest control, focusing on how it has advanced from describing average pest populations to recognizing spatial heterogeneity, from describing the distribution of single populations to diagnosing natural enemy-pest relationships, and further from analyzing spatial patterns to supporting precision pest control decision-making. We summarize differentiated geostatistical application modes marked by “rapid response” and “stable persistence” in annual field crops and perennial horticultural systems. A pest control decision-making pathway of “data capture - spatial diagnosis - management decision - feedback optimization” is proposed, which systematically converts spatial evidence including pest hotspots, natural enemy coverage and spatial mismatches into implementable management measures such as zoned management, targeted natural enemy release and control efficacy evaluation. In the future, multi-source spatial data integration, cross-scale dynamic modeling, ecological mechanism embedding and intelligent decision-making platform construction should be further strengthened to elevate the interpretive capacity, decision-making ability and application potential of geostatistics in biological pest control.

Key words: geostatistics, pest-natural enemy interaction, spatial heterogeneity, spatial overlap, precision control, biological control

LI Shu, MA Chi, WANG JiaJia, XIAO Da, MI YingYing, YUE YanLi, WANG Su. Application of Geostatistics in Insect Biological Control and Its Support for Precision Pest Management Decisions[J].Scientia Agricultura Sinica, 2026, 59(18): 4076-4091.

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Table 1

Key geostatistical methods and their applicable conditions for data-driven decision-making"

计算类别Category	方法名称 Method name	核心公式 Core formula	适用场景 Applicable scenario	应用逻辑 Application logic
克里金插值类 Kriging interpolation methods	普通克里金 Ordinary Kriging^[10,12]	$\hat{Z}\left(s_{0}\right)=\sum_{i=1}^{n} \lambda_{i} Z\left(s_{i}\right)$ 约束条件Constraint：$\sum_{i=1}^{n} \lambda_{i}=1$ $\hat{Z}\left(s_{0}\right)$：位置s₀处的预测值Predicted value at location s₀；Z(s_i)：采样点i的观测值Observed value at sampling site i；λ_i：权重系数Weight coefficient；n：样本点数量Number of sample points	棉铃虫等害虫种群密度空间插值；害虫低密度区域精准预测；害虫空间分布制图；害虫种群密度空间制图 Spatial interpolation of pest population density, e.g., cotton bollworm; Precise prediction of low-density pest areas; Spatial distribution mapping of pests occurrence; Spatial distribution mapping of pests population density	基于半方差函数建模，假设未知常数均值，通过空间权重优化实现最优线性无偏估计；适用于二阶平稳的害虫种群数据 Based on semi-variogram modeling, assuming unknown constant means, achieving the best linear unbiased prediction through spatial weight optimization; Applicable to second- order stationary pest population data
	简单克里金 Simple Kriging^[60]	$\hat{Z}\left(s_{0}\right)=\mu+\sum_{i=1}^{n} \lambda_{i}\left[Z\left(s_{i}\right)-\mu\right]$ μ：已知的总体均值Known global mean，其他参数同普通克里金Other parameters are the same as Ordinary Kriging	已知平均密度的空间插值；病虫害历史发生区预测 Spatial interpolation with known mean density; Prediction of historical pest and disease occurrence areas	假设总体均值已知且恒定，通过残差项加权估计未知位置的值；适用于长期监测数据充足的害虫预测Assuming the global mean is known and constant, estimating values at unknown locations by weighting residual terms; Applicable to pest prediction with sufficient long- term monitoring data
	泛克里金 Universal Kriging^[61]	Z(s)=m(s)+∈(s)； $m(s)={\displaystyle \sum _{k=0}^{p}\beta kfk(s)}$ m(s)：趋势项Trend term；∈(s)：残差项Residual term；β_k：漂移系数Drift coefficient；f_k(s)：趋势函数Trend function	环境变量影响下的害虫分布预测；存在明显空间趋势的病虫害扩散 Prediction of pest distribution under environmental factors; Pest and disease spread with distinct spatial trends	处理非平稳空间数据，可纳入环境协变量（海拔、温度等）作为趋势项；适用于病虫害发生受地理因素显著影响的场景 Handles non-stationary spatial data by incorporating environmental covariates, e.g., elevation and temperature, as trend terms; Applicable to scenarios where pest and disease outbreaks are significantly influenced by geographical factors
	协同克里金 Cokriging^[62]	${\widehat{Z}}_{1}({s}_{0})={\displaystyle \sum _{i=1}^{{n}_{1}}{{\displaystyle \lambda }}_{i}^{1}{Z}_{1}({s}_{i})}+{\displaystyle \sum _{j=1}^{{n}_{2}}{{\displaystyle \lambda }}_{j}^{2}{Z}_{2}({s}_{j})}$ Z₁：主要变量（害虫密度）Primary variables, e.g., pest density；Z₂：辅助变量（植被指数/土壤湿度）Auxiliary variables, e.g., vegetation index/soil moisture；λ¹、λ²：各变量权重Weights for each variable	引入环境协变量的害虫分布预测 Pest distribution prediction incorporating environmental covariate	利用多个相关变量的空间相关性提高估计精度；适用于辅助数据采样密度高于目标害虫数据的情况 Improve estimation accuracy by utilizing spatial correlation of multiple related variables; Applicable when the sampling density of secondary data is higher than that of the target pest data
	指示克里金 Indicator Kriging^[63]	$I\left(s ; z_{c}\right)=\left\{\begin{array}{l} 1, Z(s) \leq z_{c} \\ 0, Z(s)>z_{c} \end{array}\right.$ $P\left[Z\left(s_{0}\right) \leq z_{c}\right]=\sum_{i=1}^{n} \lambda_{i} I\left(s_{i} ; z_{c}\right)$ z_c：阈值（如防治指标）Threshold value, e.g., prevention Indicators；I(s; z_c)：指示函数，在位置s处，若实测值低于或等于阈值z_c，则赋值为1，否则为0 Indicate function, at position s, to be assigned a value of 1 if the actual measured value is less than or equal to the threshold z_c, otherwise 0；P：超过阈值的概率Probability of surpassing threshold	害虫密度超过防治阈值的概率制图；病害发生风险区域划分 Probability mapping of pest density exceeding control thresholds; Risk zoning of disease and pest outbreaks	将连续变量转换为二元指示变量，估计超过防治阈值的概率，支持精准施药决策 Converts continuous variables into binary indicator variables to estimate the probability of exceeding prevention and treatment thresholds, supporting accurate drug administration decisions
确定性插值类Deterministic interpolation	反距离加权 Inverse distance weighting^[64-65]	$\hat{Z}\left(s_{0}\right)=\frac{\sum_{i=1}^{n} w_{i} Z\left(s_{i}\right)}{\sum_{i=1}^{n} w_{i}} \quad w_{i}=\frac{1}{d_{i 0}^{p}}$ d_i₀：样本点到预测点的距离Distance from sample point to the predicted point；p：距离幂次（通常取2）Distance power, typically set to 2；w_i：距离权重Distance weight	害虫调查数据快速制图；实时监测数据的空间插值 Rapid mapping of pest survey data; Spatial interpolation of real-time monitoring data	计算简便，无需建模，距离越近权重越大；适用于大规模实时监测和快速决策场景，用于样本点密集且分布均匀的场景，进行害虫密度的快速插值，为精准施药提供即时地图，但无法提供预测误差 Simplicity of calculation, no need for modeling, greater weight at closer distances; Appropriate for large-scale real-time monitoring and quick decision- making scenarios, for samples densely packed and evenly distributed scenarios, for rapid interpolation of pest density, providing an instant map for accurate drug administration but unable to provide prediction errors
空间自相关类 Spatial autoocorrelation	全局莫兰指数Global Moran’s I^[21]	$I=\frac{n}{{\sum }_{i}{\sum }_{j}{w}_{ij}}\frac{{\sum }_{i}{\sum }_{j}{w}_{ij}(x{}_{i}-\overline{x})({x}_{j}-\overline{x})}{{\sum }_{i}{(x{}_{i}-\overline{x})}^{2}}$ n：样本单元数Number of spatial units；x_i、x_j：单元i、j的观测值Observed values of units i and j；$\bar{x}$：均值Mean value；w_ij：空间权重矩阵元素Elements of the spatial weight matrix	害虫种群整体聚集性检验；病害空间自相关强度评估；监测网点优化布局 Global clustering test of pest populations; Strength evaluation of disease spatial auto correlation; Optimal layout of monitoring networks	值域[-1，1]，正值表示聚集，负值表示离散，0表示随机分布；判断害虫是否呈聚集分布，指导采样策略 The value range is [-1,1], with positive values for aggregation, negative values for dispersion, and 0 for random distribution; Use to determine whether the pests are clustered or not, and guide the sampling strategy
空间自相关类 Spatial autoocorrelation	局部莫兰指数Local Moran’s I^[66]	${I}_{i}=\frac{x{}_{i}-\overline{x}}{{\sigma }^{2}}{\displaystyle \sum _{j}{w}_{ij}({x}_{j}-\overline{x})}$ I_i：单元i的局部莫兰指数Local Moran’s I for unit i；σ²：方差Variance。其他参数同全局莫兰指数Other parameters are the same as Global Moran’s I	识别害虫高密度热点区域；天敌-害虫空间关联分析；局部聚集区精准防治 Identifying high-density pest hotspots; Spatial association analysis between pests and natural enemies; Precision management of local clustered zones	识别HH（高-高）、LL（低-低）、HL（高-低）、LH（低-高）4种局部空间模式，定位热点和冷点区域，用于发现病虫害暴发中心，实施分区管理 Identify four local spatial modes: HH (high-high), LL (low-low), HL (high-low), and LH (low-high). Locate hot and cold areas for the discovery of disease and pest outbreak centers and implement partition management
热点分析类 Hotspot analysis	Getis-Ord Gi统计量Getis-Ord Gi*^[67]	${G}_{i}^{}=\frac{{\sum }_{j}{w}_{ij}x{}_{j}-\overline{x}{\sum }_{j}{w}_{ij}}{S\sqrt{\frac{n{\sum }_{j}{w}_{ij}^{2}-{({\sum }_{j}{w}_{ij})}^{2}}{n-1}}}$ $\bar{x}$：全局均值Global mean；S：标准差Standard deviation；G_i^：标准化统计量Standardized statistics	害虫暴发热点识别；冷点区域（天敌优势区）定位；时空热点追踪 Identification of pest outbreak hotspots; Localization of cold spots, i.e., natural enemy dominant zones; Spatio-temporal hotspot tracking	相比于局部莫兰指数，G_i^能更纯粹地识别具有统计显著性的高值（热点）和低值（冷点）空间聚类（Z>1.96为显著热点，Z<-1.96为冷点），识别高值和低值空间聚集，常用于害虫密度热点区识别，支持靶向施药和天敌保护 Compared to the local Morland index, G_i^ can more purely identify high-value (hot spots) and low-value (cold spots) spatial clustering with statistical significance (Z>1.96 for significant hot spots, Z<-1.96 for cold spots), identify high-value and low-value spatial clustering, commonly used for pest density hot spot area identification, support for targeted drug administration and nemesis protection
空间关联可视化Spatial association visualization	Moran散点图 Moran scatterplot^[68]	横轴x axis：$z_{i}=\frac{x_{i}-\bar{x}}{\sigma}$ 纵轴y axis：Wz_i=∑_jw_ijz_j z_i：标准化值Standardized value；Wz_i：空间滞后的标准化值Standardized value of spatial lag	识别空间异常值；可视化空间关联模式；检测边缘效应 Identification of spatial outliers; Visualization of spatial association patterns; Detection of edge effects	四象限分类：HH（热点）、LL（冷点）、HL/LH（空间异常值）。直观展示空间聚集模式，辅助决策 Four quadrant categories: HH (hot spots), LL (cold spots), HL/LH (spatial anomaly value). Visualize spatial clustering patterns to assist in decision making
聚集度指数类 Aggregation indices	负二项分布指标K Negative binomial K^[69]	$K=\frac{{\overline{x}}^{2}}{{s}^{2}-\overline{x}}$ $\bar{x}$：样方均值Mean square of a sample；s²：样方方差Variance of the sample。K越小聚集越强The smaller K, the stronger the cluster	样方调查数据聚集度量化；田间害虫空间格局判定 Aggregation measurement of sample survey data; Determination of field pest spatial patterns	K<0高度聚集，K→∞趋于随机分布。常用于昆虫种群空间格局的基本判定 K<0 is highly clustered, and K→∞ tends to be randomly distributed. A basic determination often used for the spatial layout of insect populations
聚集度指数类 Aggregation indices	平均拥挤度 Mean crowding^[70]	${M}^{}=\overline{x}+\frac{{s}^{2}}{\overline{x}}-1$ M^：平均拥挤度，值越大个体间拥挤程度越高Mean crowding index, higher values indicate higher crowding among individuals	害虫种内竞争强度评估；最适采样单元确定 Evaluation of intraspecific competition intensity in pests; Determination of optimal sampling units	反映个体平均遇到的同种个体数，结合密度指导防治时机和强度 Reflecting the average number of individuals of the same species encountered by individuals, combined with density guidance on timing and intensity of prevention
距离分析类 Distance analysis	最近邻距离法Nearest neighbor distance^[71-72]	$R=\frac{\bar{r}_{o}}{\bar{r}_{e}} \quad \bar{r}_{e}=\frac{1}{2 \sqrt{\rho}}$ $\bar{r}_{o}$：观测的平均最近邻距离Observed mean nearest neighbor distance；$\bar{r}_{e}$：期望最近邻距离Expected mean nearest neighbor distance；ρ：密度（个体数/面积）Density (number of individuals/area)	点格局分析；害虫发生中心识别；陷阱布设优化；种群分布模式判别 Point pattern analysis; Population distribution pattern identification; Trap deployment optimization; Identification of pest outbreak centers	通过计算每个点到其最近邻点的平均距离，与理论随机分布下的期望距离进行比较，以R值判断种群为均匀（R>1）、随机（R≈1）或聚集（R<1）分布；基于点位置数据，适用于诱捕器/陷阱监测数据分析 By calculating the average distance from each point to its nearest neighbor and comparing it with the expected distance under the theoretical random distribution, the R value determines that the population is uniform (R>1), random (R≈1), or clustered (R<1) distribution; Based on point location data, applicable for trap/trap monitoring data analysis
空间结构分析 Spatial structure analysis	半方差函数 Semivariogram^[10]	$\gamma (h)=\frac{1}{2N(h)}{\displaystyle \sum _{i=1}^{N(h)}{[Z({s}_{i})-Z({s}_{i}+h)]}^{2}}$ h：滞后距离Lag distance；N(h)：距离为h的点对数Number of sample pairs separated by lag distance h；γ(h)：半方差Semi- variance value	确定害虫空间依赖范围；优化监测网点间距；选择合适的克里金模型 Determining the spatial dependence range of pests; Optimizing monitoring network spacing; Selecting appropriate Kriging theoretical models	通过拟合理论模型（球状、指数、高斯）获得基台值、变程和块金值，揭示空间结构特征 Base values, variables, and block gold values are obtained through fitting theoretical models (sphere, exponential, gaussian), revealing spatial structural characteristics
多变量空间分析Multivariate spatial analysis	交叉半方差函数 Cross- variogram^[61]	${\gamma }_{12}(h)=\frac{1}{2N(h)}{\displaystyle \sum _{i=1}^{N(h)}[{Z}_{1}({s}_{i})-{Z}_{1}({s}_{i}+h)]}$ [Z₂(s_i)-Z₂(s_i+h)] Z₁、Z₂：两个变量（如害虫与天敌）Two different variables, e.g., pests and natural enemies；γ₁₂(h)：交叉半方差Cross semi- variance value	害虫-天敌空间关系；病害-环境因子关联；协同克里金前期分析 Pest-natural enemy spatial relationship analysis; Disease-environmental factor association studies; Pre- requisite analysis for Cokriging	量化两个变量间的空间协变关系，为协同克里金插值提供理论基础 Quantifying the spatial covariant relationship between two variables to provide the theoretical basis for the synergistic Kriging interpolation
空间回归类 Spatial regression	空间滞后模型Spatial lag model^[73]	Y=ρWY+Xβ+∈，Y：因变量（害虫密度）Dependent variable, e.g., pest density；WY：空间滞后项Spatial lag term；ρ：空间自回归系数Spatial auto regressive coefficient；Xβ：协变量项Covariate term	环境因子对害虫分布的影响建模；考虑邻域效应的预测模型 Modeling environmental impacts on pest distribution; Predictive models incorporating neighborhood spillover effects	处理因变量的空间溢出效应，适用于害虫扩散受邻近区域影响的场景 Handling spatial spillover effects of dependent variables is suitable for scenarios where pest propagation is affected by nearby areas
空间回归类 Spatial regression	空间误差模型Spatial error model^[73]	Y=Xβ+u；u=λWu+∈。u：误差项Error term；λ：空间误差系数Spatial error coefficient；Wu：空间滞后误差Spatial lag error	控制空间自相关偏误；提高回归模型精度Controlling spatial auto correlation bias; Improving the estimation accuracy of regression models	处理误差项的空间自相关，适用于残差存在空间聚集的回归分析 The spatial self-correlation of the error-handled terms is applicable for regression analysis of spatial aggregations with residual presence

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