In the study of spatial variability of soil attributes, it is essential to define a sampling plan with adequate sample size. This study aimed to evaluate, through simulated data, the influence of parameters of the geostatistical model and sampling configuration on the optimization process, and resize and reduce the sample size of a sampling configuration of a commercial area composed of 102 points. For this, an optimization process called genetic algorithm (GA) was used to optimize the efficiency of the geostatistical model estimation based on the Fisher information matrix. The simulated data evidenced that the variation of the nugget effect or practical range did not significantly alter the sample size. GA was efficient in reducing the sample size, determining for soil chemical attributes a sample size between 30 and 40 points (29.41 to 39.22% of the initial sampling grid). The presence of spatial dependence was observed for all soil chemical attributes in the two sampling configurations (initial and optimized). The optimized sampling configuration evidenced an increase in trend intensity in the north direction and a more efficient estimation of parameters of the linear spatial regression model.

Aim of study: To evaluate the influence of the parameters of the geostatistical model and the initial sample configuration used in the optimization process; and to propose and evaluate the resizing of a sample configuration, reducing its sample size, for simulated data and for the study of the spatial variability of soil chemical attributes under a non-stationary with drift process from a commercial soybean cultivation area. Area of study: Cascavel, Brazil Material and methods: For both, the simulated data and the soil chemical attributes, the Genetic Algorithm was used for sample resizing, maximizing the overall accuracy measure. Main results: The results obtained from the simulated data showed that the practical range did not influence in a relevant way the optimization process. Moreover, the local variations, such as variance or sampling errors (nugget effect), had a direct relationship with the reduction of the sample size, mainly for the smaller nugget effect. For the soil chemical attributes, the Genetic Algorithm was efficient in resizing the sampling configuration, since it generated sampling configurations with 30 to 35 points, corresponding to 29.41% to 34.31% of the initial configuration, respectively. In addition, comparing the optimized and initial configurations, similarities were obtained regarding spatial dependence structure and characterization of spatial variability of soil chemical attributes in the study area. Research highlights: The optimization process showed that it is possible to reduce the sample size, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in future experiments.

Aim of study: To reduce the sample size in an agricultural area of 167.35 hectares, cultivated with soybean, to analyze the spatial dependence of soil penetration resistance (SPR) with outliers. Area of study: Cascavel, Brazil Material and methods: The reduction of sample size was made by the univariate effective sample size ( ) methodology, assuming that the t-Student model represents the probability distribution of SPR. Main results: The radius and the intensity of spatial dependence have an inverse relationship with the estimated value of the . For the depths of SPR with spatial dependence, the highest estimated value of the  reduced the sample size by 40%. From the new sample size, the sampling redesign was performed. The accuracy indexes showed differences between the thematic maps with the original and reduced sampling designs. However, the lowest values of the standard error in the parameters of the spatial dependence structure evidenced that the new sampling design was appropriate. Besides, models of semivariance function were efficiently estimated, which allowed identifying the existence of spatial dependence in all depth of SPR.Research highlights: The sample size was reduced by 40%, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in the next mappings in the agricultural area. The spatial t-Student model was able to reduce the influence of outliers in the spatial dependence structure.

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In agricultural soils with low cation exchange capacity, it is essential to analyze the bivariate spatial correlation of soybean productivity and organic matter with the soil chemical attributes. Using bivariate spatial correlation makes it possible to identify patterns and behaviors that suggest a spatial association between two soil attributes, thus enabling better soil management and more efficient use of resources. The main objective of this study was to analyze bivariate spatial correlation considering variables with different spatial dependence structures. The bivariate Lee index was also calculated for this purpose. To model and describe the spatial pattern of two spatially correlated variables, the Bivariate Gaussian Common Component Model was used. In addition to calculating the bivariate spatial correlation of soil chemical attributes with soybean productivity and organic matter, the Lee index was also calculated for pairs of simulated variables with different weight matrices and geographic distance functions. It was observed that the greater the common practical range, the higher the Lee index value, indicating a higher bivariate spatial correlation. Furthermore, shorter distances between neighboring point pairs caused higher Lee index values. The distance function to calculate the distance between the point pairs was more relevant than the weight matrix in estimating the spatial dependence radius and the Lee index value. Soybean productivity showed a direct spatial correlation with the sum of bases, as well as with the calcium and magnesium contents. Organic matter had a direct spatial correlation with the sum of bases and an inverse one with the phosphorus content