Geostatistical Analysis of the Spatial Variation of Chrysolina aeruginosa Larvae at Different Stages in Desert Ecosystems

Simple Summary The spatial distribution of pests is a prominent topic of research in population ecology. Knowledge of pest distribution patterns (including the specific plant segments that are most heavily infested) is of utmost significance in devising appropriate monitoring programs that will effectively reduce the utilization of pesticides. Geostatistical analysis, which reveals spatial correlations and dependencies, is vital in achieving an accurate comprehension of the disparities in pest spatial distribution. In this study, we utilized geostatistical methods to identify the spatial distribution of Chrysolina aeruginosa, a commonly occurring pest that attacks Artemisia ordosica in desert ecosystems of Ningxia, at various developmental stages. Our results indicated differences in the vertical distribution of larvae at distinct stages of growth. The number of larvae varies in relation to the height of the plants, and various morphological characteristics such as crown width and ground diameter. Furthermore, the larvae exhibit an inclination to aggregate. Abstract Chrysolina aeruginosa is a major pest of Artemisia ordosica, and knowledge of the spatial distribution pattern of its larvae in their natural habitat is crucial for the implementation of effective control measures. This study employed geostatistical methods to investigate the damage caused by larvae of different age groups and their spatial distribution pattern. The distribution of C. aeruginosa larvae, which cause damage to A. ordosica, differed significantly according to their age. Younger larvae were predominantly found in the middle and upper parts of the plant, whereas older larvae were mainly distributed in the middle and lower parts, with significant differences in distribution location. A generalized linear model analysis revealed that the height of the plant, and plant morphological characteristics such as height, crown width, and ground diameter were significantly correlated with the number of larvae present. Furthermore, the interaction of age with other variables had an impact on the number of larvae. Kriging interpolation showed that C. aeruginosa larvae were distributed in aggregated patches with strong spatial heterogeneity. The younger larvae were more abundant in the center of the sample site, while the older larvae tended to be distributed toward the edges. These findings provide valuable information for designing effective control programs.


Introduction
The distribution of insect populations is determined by a combination of biological and environmental factors [1][2][3][4][5], which include the horizontal distribution (i.e., spatial distribution) and vertical distribution of individuals. The study of the distribution of individuals is crucial for sampling, investigating pest dynamics, determining control thresholds, and formulating effective control measures [6].
Spatial distribution patterns are typically described using traditional statistical methods such as binomial distribution, Taylor expansion analysis, and Iwao mean crowding regression. However, geostatistical methods can more accurately describe spatial correlations and dependencies. Ordinary kriging interpolation, in particular, can be used to Sophora alopecuroides L., Suaeda salsa (L.) Pall., Salsola passerina Bunge, Oxytropis aciphylla Ledeb., and Cynanchum chinense R.Br.
C. aeruginosa is a significant leaf-feeding pest of A. ordosica and undergoes four larval instars in one generation. The fourth instar larvae of C. aeruginosa overwinter in soil. The first and second instar larvae can consume up to half of the leaf, resulting in notched leaves, while the third and fourth instar larvae can completely defoliate the plant, and the adults feed on growing points and new leaves, ultimately causing the death of the entire plant [27]. Previous field studies indicated that C. aeruginosa larvae begin emerging in late September and start overwintering in late October. Therefore, three field surveys were conducted between 20 September and 18 October to investigate the population dynamics of C. aeruginosa.

Experimental Procedures
In the study area, a checkerboard sampling method was employed using 5 m × 5 m sample squares with a 10 m spacing between each sample point. A total of 63 sample points were set up for the study. To mitigate edge effects, sample points were located over 100 m away from the edge of the sample plots (as shown in Figure 1). For the study, one A. ordosica was chosen for each sample point, resulting in a total of 63 A. ordosica being surveyed three times (20 September,4 October, and 18 October). During each survey, their geographical coordinates, plant height, crown width, and ground diameter were recorded.
C. aeruginosa is a significant leaf-feeding pest of A. ordosica and undergoes four larval instars in one generation. The fourth instar larvae of C. aeruginosa overwinter in soil. The first and second instar larvae can consume up to half of the leaf, resulting in notched leaves, while the third and fourth instar larvae can completely defoliate the plant, and the adults feed on growing points and new leaves, ultimately causing the death of the entire plant [27]. Previous field studies indicated that C. aeruginosa larvae begin emerging in late September and start overwintering in late October. Therefore, three field surveys were conducted between 20 September and 18 October to investigate the population dynamics of C. aeruginosa.

Experimental Procedures
In the study area, a checkerboard sampling method was employed using 5 m × 5 m sample squares with a 10 m spacing between each sample point. A total of 63 sample points were set up for the study. To mitigate edge effects, sample points were located over 100 m away from the edge of the sample plots (as shown in Figure 1). For the study, one A. ordosica was chosen for each sample point, resulting in a total of 63 A. ordosica being surveyed three times (20 September,4 October, and 18 October). During each survey, their geographical coordinates, plant height, crown width, and ground diameter were recorded.

Population Survey of Different Instar Larvae
The number and age of all larvae present on each A. ordosica were recorded, alongside the geographic coordinates of C. aeruginosa larvae found on 63 A. ordosica trees. The larval stage was evaluated based on the criteria of morphology and size as outlined in Wei's description of C. aeruginosa larvae [20]. Due to the similarity in morphology between the first and second instars, they are indistinguishable and were therefore aggregated for the purposes of statistical analysis [20,27].

Vertical Distribution Survey of Different Instar Larvae
The larval count at various locations on each A. ordosica was recorded and subsequently categorized into five distinct height classes as follows: 0-20 cm, 21-40 cm, 41-60 cm, 61-80 cm, and 81-100 cm.

Geostatistical Analysis
Spatially dependent patterns of C. aeruginosa larvae populations were analyzed using variance and ordinary kriging based on the larval count at each sample point [18]. Field observations were treated as a stochastic process denoted as Z(x), where x represents the spatial location. The semi-covariance, which is indicative of the spatial correlation between adjacent samples, was used to measure this correlation as follows: where: N(h) is the number of measured pairs in the lag distance h; Z(x i ) is the sample point measured at x i ; Z(x i + h) is the sample point measured at x i + h. Figure 2 depicts the pattern diagram of the variance function, which consists of three ecologically significant parameters that influence the shape, structure, and ultimately, the spatial distribution of a population's semi-covariance function. These parameters include the nugget (C 0 ), the sill (C 0 + C), and the range (A). The nugget represents the non-zero intercept point on the y-axis, indicating spatial variation due to sampling error and distance. The sill is the value at which the curve stabilizes on the y-axis, while the range denotes the average distance between points where spatial correlation exists [29,30].
The number and age of all larvae present on each A. ordosica were recorded, alongside the geographic coordinates of C. aeruginosa larvae found on 63 A. ordosica trees. The larval stage was evaluated based on the criteria of morphology and size as outlined in Wei's description of C. aeruginosa larvae [20]. Due to the similarity in morphology between the first and second instars, they are indistinguishable and were therefore aggregated for the purposes of statistical analysis [20,27].

Vertical Distribution Survey of Different Instar Larvae
The larval count at various locations on each A. ordosica was recorded and subsequently categorized into five distinct height classes as follows: 0-20 cm, 21-40 cm, 41-60 cm, 61-80 cm, and 81-100 cm.

Geostatistical Analysis
Spatially dependent patterns of C. aeruginosa larvae populations were analyzed using variance and ordinary kriging based on the larval count at each sample point [18]. Field observations were treated as a stochastic process denoted as Z (x), where x represents the spatial location. The semi-covariance, which is indicative of the spatial correlation between adjacent samples, was used to measure this correlation as follows: where: N(h) is the number of measured pairs in the lag distance h; Z(xi) is the sample point measured at xi; Z(xi + h) is the sample point measured at xi + h. Figure 2 depicts the pattern diagram of the variance function, which consists of three ecologically significant parameters that influence the shape, structure, and ultimately, the spatial distribution of a population's semi-covariance function. These parameters include the nugget (C0), the sill (C0 + C), and the range (A). The nugget represents the non-zero intercept point on the y-axis, indicating spatial variation due to sampling error and distance. The sill is the value at which the curve stabilizes on the y-axis, while the range denotes the average distance between points where spatial correlation exists [29,30].  As these estimates may fluctuate substantially from point to point due to sampling errors, models describing spatial variation must be fitted. We tested multiple models, including exponential, spherical, linear, and Gaussian models, using the following criteria to select the optimal one: an intercept (β 1 ) near zero, a slope (β 0 ) near 1, a large regression coefficient, a mean error close to zero, and a low root mean square error. Nugget effects, ranges, sill, and coefficients of determination were calculated for each model [4,31]. For the selected model, we calculated the level of spatial dependence (LSD) and determined the range values using the following equation: The nugget, denoted by C 0 , and the sill, represented by C 0 + C, are used to describe the spatial autocorrelation of C. aeruginosa larvae. Additionally, strong, moderate, and weak spatial dependence are indicated by LSD values lower than 0.25, between 0.25 and 0.75, and higher than 0.75, respectively. The Geostatistical Analyst extension module in ArcGIS 10.4 (ESRI 2015) software was utilized to employ the kriging method for estimating values at unmeasured locations and creating predicted spatial distributions of C. aeruginosa larvae, as well as generating spatial distribution maps [32].

Statistical Analyses
To analyze the effect of plant morphological characteristics on the number of C. aeruginosa, a generalized linear model (GLM) with a Poisson distribution was used. We modelled the number of larvae according to their location at different sections of the plants (distribution height), plant height, crown width, and ground diameter. Additionally, the interaction terms of distribution height and plant height, crown width, and ground diameter of A. ordosica were included in the model. In order to prevent collinearity among the independent variables, according to the value of the variance inflation factor (VIF), the highly collinearity independent variables with VIF > 5 were eliminated. The data analysis was performed using SPSS ® 21. Plotting was performed using Origin ® 2023.

Basic Information of C. aeruginosa Larvae
A total of four larval instars were surveyed. The boxplots of the number of different ages are shown in Figure 3. Among the larvae of different instars, the third instar larvae had the largest number.
As these estimates may fluctuate substantially from point to point due to sampling errors, models describing spatial variation must be fitted. We tested multiple models, including exponential, spherical, linear, and Gaussian models, using the following criteria to select the optimal one: an intercept (β1) near zero, a slope (β0) near 1, a large regression coefficient, a mean error close to zero, and a low root mean square error. Nugget effects, ranges, sill, and coefficients of determination were calculated for each model [4,31].
For the selected model, we calculated the level of spatial dependence (LSD) and determined the range values using the following equation: The nugget, denoted by C0, and the sill, represented by C0 + C, are used to describe the spatial autocorrelation of C. aeruginosa larvae. Additionally, strong, moderate, and weak spatial dependence are indicated by LSD values lower than 0.25, between 0.25 and 0.75, and higher than 0.75, respectively. The Geostatistical Analyst extension module in ArcGIS 10.4 (ESRI 2015) software was utilized to employ the kriging method for estimating values at unmeasured locations and creating predicted spatial distributions of C. aeruginosa larvae, as well as generating spatial distribution maps [32].

Statistical Analyses
To analyze the effect of plant morphological characteristics on the number of C. aeruginosa, a generalized linear model (GLM) with a Poisson distribution was used. We modelled the number of larvae according to their location at different sections of the plants (distribution height), plant height, crown width, and ground diameter. Additionally, the interaction terms of distribution height and plant height, crown width, and ground diameter of A. ordosica were included in the model. In order to prevent collinearity among the independent variables, according to the value of the variance inflation factor (VIF), the highly collinearity independent variables with VIF > 5 were eliminated. The data analysis was performed using SPSS ® 21. Plotting was performed using Origin ® 2023.

Basic Information of C. aeruginosa Larvae
A total of four larval instars were surveyed. The boxplots of the number of different ages are shown in Figure 3. Among the larvae of different instars, the third instar larvae had the largest number.   (Figure 4a). The first and second instars were mainly distributed in the middle-upper parts (>60 cm) of the plant, the third instars were mainly found in the middle of A. ordosica (41-60 cm), while the older mature larvae were biased toward the middle-lower parts of A. ordosica (21-50 cm) (Figure 4b-d).

Correlation Analysis of the Number of C. aeruginosa Larvae and A. ordosica Characteristics
The variables contain classification variables; thus, the use of generalized linear models was deemed appropriate to analyze the relationship between variables. To reduce collinearity, independent variables with high variance inflation factor (VIF) were removed.
The GLM results revealed significant effects between the number of larvae on A. ordosica and distribution height, plant height, crown width, and ground diameter. Moreover, the number of larvae found on A. ordosica demonstrated a significant effect with the interaction between the position of the plant (distribution height) and ground diameter, as indicated in Table 1.

Correlation Analysis of the Number of C. aeruginosa Larvae and A. ordosica Characteristics
The variables contain classification variables; thus, the use of generalized linear models was deemed appropriate to analyze the relationship between variables. To reduce collinearity, independent variables with high variance inflation factor (VIF) were removed.
The GLM results revealed significant effects between the number of larvae on A. ordosica and distribution height, plant height, crown width, and ground diameter. Moreover, the number of larvae found on A. ordosica demonstrated a significant effect with the interaction between the position of the plant (distribution height) and ground diameter, as indicated in Table 1.

Geostatistical Analysis of C. aeruginosa Larvae
From the 12 semi-variogram models developed, four models were selected as optimal models (Table 2). Gaussian and spherical models were selected for different ages of larvae (Tables 2 and 3). β 0 and β 1 are the slope and intercept of the kriging cross-validation curve, respectively. RMSE = root mean square error, ME = mean error, and R 2 = coefficient of determination from the cross-validation curve. Model selection was based on the following criteria: lowest root mean square error (RMSE), highest coefficient of determination (R 2 ), slopes (β 0 ) and intercepts (β 1 ) of the cross-validation close to one and to zero, respectively, and ME close to zero. Selected models are in bold.  Fitting parameters demonstrated that the larvae of C. aeruginosa exhibited patchy distribution patterns within the sampled plots (Table 3 and Figure 5). The edges of the plots had a higher frequency of occurrence compared to the center, and the spatial distribution displayed significant heterogeneity and aggregation. The nugget value was found to be 0.100, and the LSD value was 0.615, indicating a moderate level of spatial dependence and a small degree of randomness of the variables. Furthermore, the nugget value showed a gradual decrease, while the range increased with the larvae age, and the degree of spatial dependence shifted from strong to moderate over time. gradual decrease, while the range increased with the larvae age, and the degree of spatial dependence shifted from strong to moderate over time. The application of kriging for interpolating the abundance of C. aeruginosa larvae indicated that the spatial dependence varied across different larval age groups. Specifically, Figure 5. Semi-variogram curves (left panels) and kriging maps (right panels) of spatial patterns for C. aeruginosa larvae for the mean number of larvae (a), 1st and 2nd instar larvae (b), 3rd instar larvae (c), and 4th instar larvae (d).
The application of kriging for interpolating the abundance of C. aeruginosa larvae indicated that the spatial dependence varied across different larval age groups. Specifically, a higher concentration of young larvae was observed at the center of the sample plot compared to the edge, whereas as the larvae aged, the concentration at the edge surpassed that at the center.

Discussion
The examination of distribution patterns constitutes a significant component of research in population ecology, and it is vital in forecasting the dynamics of pest populations, enhancing sampling techniques, and formulating policies for pest management [30,33,34]. In this regard, this investigation employed geostatistical methods to investigate, for the first time, the spatial distribution of different larval instars of C. aeruginosa on A. ordosica.
Regarding vertical distribution, our study revealed that the first and second instars were predominantly concentrated in the upper-middle parts of A. ordosica, whereas the third instar larvae were mainly found in the middle section. These findings are consistent with the outcomes of prior studies by Tian et al., on the life history of C. aeruginosa [27]. Specifically, C. aeruginosa lays its eggs at the top of branches, enabling larvae to emerge effortlessly from their shells due to ample sunlight [20,27]. The hatchlings possess small mouthparts, rendering them incapable of feeding strongly, hence, making the upper shoots of branches easy targets. Conversely, as larvae mature into the fourth instar, they gradually descend downwards, gnawing on leaves for nourishment before eventually crawling into sand, where they overwinter as fully mature larvae [19,20,27].
By analyzing the variograms, it is possible to assess the degree of independence of infestations in nearby plants. A variogram that increases in value indicates a correlation between neighboring plants in the tested scales and directions [6]. In this study, the semivariograms of the developmental stages of C. aeruginosa demonstrate that various larval instars possess small nuggets and large ranges. These results demonstrate that the spatial distribution of C. aeruginosa larvae is aggregated, indicating a spatial dependence of pest specimens over a spatial range.
The degree to which insects exhibit aggregation is influenced by various factors, such as vegetation cover, species interactions, plant characteristics, pest abundance, anthropogenic disturbance, landscape composition, and geographic area [5,[33][34][35][36][37][38][39][40][41]. Changes in vegetation cover in desert regions, which provides rich food resources and suitable habitats for desert insects, inevitably affect insect population patterns [42,43]. The spatial distribution of C. aeruginosa larvae is associated with the cover of A. ordosica, and its aggregation intensity increases with an increase in planting density. A high planting density of A. ordosica in a sample plot increases the aggregation distribution of larvae [28]. During field surveys, it was observed that the presence of boring pests in A. ordosica, such as Holcocerus artemisiae, Adosomus sp., and Sphenoptera sp., caused poor growth of A. ordosica, resulting in low egg production and uneven spatial distribution of C. aeruginosa larvae [21]. Different growth factors in A. ordosica can affect C. aeruginosa larvae differently. Tall plants with a high number of new shoots can provide a suitable environment for larvae to survive, allowing for a large accumulation of pests [44]. In this study, the GLM analysis revealed that the distribution height of pests and plant morphological characteristics (plant height, ground diameter, and crown width) had a significant impact on the number of larvae of C. aeruginosa. Additionally, the interaction term between larval distribution height and ground diameter also showed an impact on the number of larvae of C. aeruginosa. There were observed differences in the distribution of pests at different heights. Due to the height-oriented nature of C. aeruginosa larvae, the first and second instar larvae were found predominantly on the top of A. ordosica, moving gradually downward with development [20]. The taller the plant was, the more space there was available for insect distribution, and larger crown widths caused the larger feeding range of the larvae, ultimately influencing their spatial distribution. Conversely, the larger ground diameter of the plant led to a more scattered growth pattern [16], which was less conducive to the oviposition and larvae aggregation of C. aeruginosa. Interestingly, the interaction term between larval distribution height and ground diameter showed a positive effect, indicating that plants with larger ground diameters would attract more larvae at various distribution heights.
The spatial distribution of adults can impact the spatial distribution of larvae. Zhang et al.'s research on the spatial distribution of adults of C. aeruginosa indicates that adults are distributed in a non-random manner [28]. The findings of Zhang et al.'s study on the population dynamics of adults were consistent with the aforementioned research, with a higher number of adults observed in the upper region compared to the middle and lower regions [45]. After the adults lay eggs on the upper layer of the plant, the first and second instar larvae are primarily distributed in the middle and upper parts of the plant. As the larvae develop, they move downward, and the third and fourth instar larvae become mainly distributed in the middle and lower parts.
Anthropogenic disturbances can have a significant impact on the spatial distribution of species [46]. Blanchet et al. evaluated the reasons for the distribution of carabid beetles and found that human interference substantially affected the distribution of these insects [47]. In several different habitats, Zhang et al. found that human factors might be responsible for the differences in the distributions of adult C. aeruginosa [45]. Our survey revealed that grazing likely reduced the number of larvae around the sample plots, resulting in a heterogeneous spatial distribution. Investigating the influence of landscape structure on the spatial distribution patterns of pests in patches is important, as changes in landscape structure can affect the foraging behavior of phytophagous pests [48]. Further research is needed to determine how landscape changes can be regulated to reduce pest damage [23,49,50].
The edge effect is a common phenomenon in ecology, as pest abundance is generally greater at the edge of a sample than at its center [51,52]. Our results showed that the spatial distribution of C. aeruginosa larvae was consistent with that of most pests, with more individuals at the edge of the sample plot than in the center [4,9,53,54]. The main reason for the difference in the spatial distribution of the pests is the distribution of plants. Better plant growth leads to greater aggregation of pest individuals [2]. The quality and quantity of resources vary along the gradient from the patch edge to the interior, which affects the habitat quality for C. aeruginosa and subsequently leads to changes in the distribution of its larvae in response to A. ordosica growth conditions [2]. The center of the sample site is less populated than the edge, resulting in a higher rate of egg laying by adults in the center than at the edge. Since larvae do not migrate, the number of first and second instar larvae is greater in the center of the sample plot than at its edges. As the larvae mature, intra-specific competition increases, leading to a decrease in the population density of fourth instar larvae and a higher number of fourth instar larvae at the edge of the sample plot than at its center [19,[55][56][57][58].
Integrated pest management includes chemical control, but the misuse of pesticides can lead to environmental pollution, pest resistance, and a significant decline in biodiversity [4]. Previous studies have shown that 50% caprylic acid or 2.5% deltamethrin insecticide preparations can effectively control C. aeruginosa [27]. By analyzing the spatial distribution of beetle larvae, pesticide applications can be planned according to their distribution, which optimizes the use of pesticides, reduces costs, and minimizes environmental pollution.

Conclusions
The infestation of C. aeruginosa has significant negative impacts on the growth of A. ordosica in China. In this study, we used geostatistical methods to determine the spatial distribution of different C. aeruginosa larval instars and also developed kriging interpolation models to map the distribution of C. aeruginosa larvae of different ages within the sample plots. At the same time, we investigated the vertical distribution of C. aeruginosa larvae on A. ordosica. Our findings provide a scientific basis for controlling C. aeruginosa infestations. For instance, starting treatment at the edges of A. ordosica sample plots may be more effective in reducing the pest's population density. Additionally, information on the distribution of larvae at various ages can help concentrate control actions on the plant parts where larvae are more abundant. At a later stage, both ecological and chemical control methods should be used to minimize the damage caused by C. aeruginosa infestations.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.