# Using Geospatial Information to Map Yield Gain from the Use of _Azospirillum brasilense_ in Furrow
## 4 Discussion  
Regarding the behavior of regionalized variables (yield) when analyzing the samples separately (i.e., points derived from the TS and STD treatments), stationarity is evident. This is because in places under different management conditions, the expected yield values vary regularly in the surrounding area. In the analysis of the yield points considering the areas as a whole, the function presents characteristics of little stationarity (anisotropy). This condition is caused by the variability resulting from the different management techniques, in which _A. brasilense_ is applied in alternate strips [20]. Spatial behaviors were evaluated by semivariograms adjusted to the Gaussian model in the cases of STD, and spherical for TS. The findings indicated the spatial dependence of all factors. Even with yield samples as a lower coefficient of variation, the Gaussian semivariogram infers that the yield of the STD area is an event with an apparent continuity greater than the yield defined by TS. In other words, the modeling of corn yield for these conditions cannot be modeled by parametric mathematical functions (linear regression). The difficulty of modeling STD plots is due to the variability and trend of yield conditioned to environmental factors, given that without treatment conditions, the crop is subject to biotic and abiotic factors [21]. For the plots treated with ST, the adjustment of spherical semivariograms with little dispersion in the plateau's position reflects a normality condition in the probability distribution function (probability frequency diagrams, Figure 3) of the treated areas. This condition occurs given the application of _A. brasilense_, which was applied in the same amount along the TS plots, which reduced the variability caused by biotic and abiotic factors in the planting area [22]. Regarding biotic factors (exposure to pests, fungi, and insects) and abiotic factors (including climate, soil parameters, and topography), it is important to note that they were practically identical for both control and treatment locations. In this context, the only difference between the two sites was defined by management practices (an abiotic factor). This factor was decisive in the variability of yield and, consequently, in the modeling and performance of yield gain surfaces. We observed that applying _A. brasilense_ to the crop resulted in lower variability in yield and reduced susceptibility to typical biotic factors affecting maize cultivation in tropical regions. Regarding yield prediction, the models generated by Kriging were more accurate and less biased than those generated by images because they were modeled with a larger number of training samples. The precision and accuracy of Kriging are related to the distance and continuity between pairs of samples [23]. For the present study, the high density of yield data favored the generation of accurate and precise models. The models generated by images had lower RMSE%, MAPE%, and R\({}^{2}\) because they were trained on a considerably smaller contingent of yield samples. Furthermore, it should be considered that, unlike Kriging, the accuracy and precision of the models depend on the correlation between the bands and derived indices with yield and the spatial, spectral, and radiometric resolutions of the sensor [24]. The highest RMSE% and MAPE% errors observed in Br1 were associated with the fact that the area presented a higher coefficient of variation in yield (Figure 3). Another factor to consider is the spectral mixture, given the larger spacing between rows for this area, which is evidence of a greater response from the exposed soil. This condition occurs because the images used in the generation of the models were taken at the phenological stage of R1 in the corn crop, the phase in which the crop stabilized the vegetative development, and closing of the inter-row is defined. The discrepancies between the yield gain maps generated by the different techniques are due to the nature of the modeling used in each technique.