# Using Geospatial Information to Map Yield Gain from the Use of _Azospirillum brasilense_ in Furrow
## 1 Introduction  
Synthetic fertilizers are used in maize cultivation to meet the nitrogen (N) demand. The most widely used synthetic fertilizer is urea, which has the advantage of easy availability of N for plant uptake. However, the utilization of urea by plants is low, ranging from 42% to 49%, due to losses of N to the environment. These losses can occur in two ways. One way is via microbial immobilization, in which soil microorganisms absorb the nutrient to meet their needs and, after the end of their life cycle, mineralize and release the N back to the soil, mainly in the form of NO\({}_{2}\) and NO\({}_{3}\). The other way is by the volatilization of ammonia, which returns N to the atmosphere. These losses mainly occur when urea is used as a source of N under inadequate humidity and temperature conditions [1]. Among the alternatives for reducing the consumption of synthetic fertilizers by maize crops is the use of diazotrophic bacteria, which can fix atmospheric N and make it available to plants in labile forms. The fixed N becomes available to plants by direct excretion of the bacteria or by mineralization of dead bacteria; thus, the rhizosphere is colonized by the bacteria [2]. _Azospirillum_ is one of the genera that can associate with grassroots; its efficiency in biological N fixation is up to 78% higher than other genera found near rice roots [3]. _Azospirillum_ includes more than 14 species. _Azospirillum brasilense_ is the most important in agriculture and there are several biological growth-promoting products that have this bacterium as an active ingredient. The effects of _A. brasilense_ on the development of grasses have been studied in recent years in terms of crop yield and the physiological causes that possibly increase yield. Physiological causes include antagonism to pathogens, production of phytohormones, increased photosynthetic rate, assistance in the absorption of water and nutrients, and biological nitrogen fixation [3]. However, research results have been inconsistent concerning the real yield gain from the use of biologicals, such as _A. brasilense_, given the negligible statistical significance evident in the comparison of yield between treated and untreated areas [4]. Owing to a symbiotic relationship between the plant and bacteria, the increase in crop yield after the application of biological products is sometimes so subtle that classical models, such as analysis of variance (ANOVA), are unable to demonstrate differences in productivity between treatment and control groups in various situations. This occurs because such models do not account for factors that can affect crop yield, such as physiological variables and the spatial dependence of yield among the population of plants in a given plot [5]. In addition, it is important to note that ANOVA is a test of statistical significance and not practical relevance. Therefore, a statistically insignificant difference does not necessarily imply practical relevance. Given the importance of the use of products based on _A. brasilense_, it is believed that studies related to the manipulation of geospatial information in agriculture present a range of solutions through geostatistical techniques and spectral models, which can offer more accurate and robust information about the yield of crops, such as corn. Geostatistical tools have been used to estimate spatial relationships between crop production and soil parameters under organic farming field conditions [6]. From the yield gain surfaces generated by Kriging, the authors showed significant relationships between the amount of organic material in the soil and the most and least productive regions. In recent studies, spectral models based on machine learning and Moderate Resolution Imaging Spectroradiometer (MODIS) [7], Landsat 8 [8], and aerially surveyed [9] images were used to estimate yield.