ARTIFICIAL INTELLIGENCE IN THE SIMULATION OF FUNGICIDE MANAGEMENT SCENARIOS FOR SATISFACTORY YIELD AND FOOD SAFETY IN OAT CROPS

Purpose: The objective of the study is to analyze the management of the fungicide that seeks a longer interval between the last application and the harvest of oat grains, with an indication of the cultivars with the highest satisfactory productivity without application in the grain filling. Validate artificial neural network models in the expectation of satisfactory productivity with food security, through the interaction between management, pathogen, genotype, and environment. Method/design/approach: The study was conducted in 2015, 2016, 2017, in a randomized block design, in a 22 x 4 factorial scheme, for 22 white oat cultivars (recommended and no longer present in the current Brazilian recommendation) and 4 fungicide application conditions (no application; one application at 60 days after emergence (DAE); two applications, 60 and 75 DAE; and three applications, at 60, 75, 90 DAE), with three repetitions.


INTRODUCTION
White oat (Avena sativa L.) is one of the main cereal and forage crops grown in the world and an important alternative winter crop in southern Brazil . This cereal is important as a human food due to its high nutritional value and contents of amino acids, fatty acids, vitamins, mineral salts, and especially dietary fibers. β-glucan stands out among these fibers, which is a soluble fiber recognized for reducing cholesterol levels and blood glucose and preventing heart disease (Basso et al.,2022).
Oat yield is connected to the cultivar genetic characteristics, weather conditions, soil fertilization and fertility management, and weed, pest, and disease control during the crop cycle (Silva et al., 2015;Reginatto et al., 2021). Leaf rust (Puccinia coronata Cda. f.sp. avenae) and helminthosporiose [Dreschslera avenae (Eidam) El Sharif] are among the most important diseases; they cause leaf necrosis and grain yield and quality losses in oat crops (Chen et al., 2022). The emergence and progression of these diseases are strongly related to meteorological conditions; their incidence and progression is favored by increases in air temperature and humidity, which are frequent conditions in southern Brazil during the crop flowering and grain filling stages (Danielowski, 2021;Screminn et al., 2023).
Oat foliar diseases are not satisfactorily controlled by genetic resistance; fungicide applications are the most used form of control, which positively affect grain yield and quality (Basso et al., 2022), therefore, more sustainable processes to reduce the use of pesticides are needed (Naraghi & Nataj, 2022). However, oats are usually consumed as a fresh product; after threshing, it is used for production of bran, flour, or flakes, which highlights the need for care in fungicide management to avoid agrochemical residue in the grains (Silva et al., 2015;Jiang et al., 2021). In addition, most fungicides are systemic, i.e., absorbed by leaves and translocated through the plant system to reach the target fungus (Carmona et al., 2020). Thus, accumulation of residues can be greater when the applications are carried out at the grain filling stage, where a large part of photoassimilates are mobilized to the grains, carrying traces of pesticides (Basso et al., 2022;López-González et al., 2022).
Chronic intoxications caused by a prolonged contact with small amounts of pesticides are directly related to emergence of diseases, such as cancer, diabetes, respiratory and neurological disorders, and reproductive syndromes (Hassaan and El Nemr, 2020;Rani et al., 2021). Apart from public health problems, inadequate use of fungicides can be harmful to fauna and flora, causing soil, water, and air pollution and death of different animal species, including those that have pollinating function (Rani et al., 2021). In this sense, more efficient and sustainable managements of fungicides are decisive in preventing or reducing food contamination and environmental pollution (Oliveira et al., 2014;Zanatta, Rizzi & Schorr, 2022).
Mathematical and computational models describing agricultural processes can assist in developing and validating technologies and managements that are more adequate from a technical, economic, and environmental point of view . In this sense, artificial intelligence techniques have emerged as an alternative for simulating and optimizing agricultural systems . Artificial neural networks (ANN) are among artificial intelligence techniques focused on implementing models that resemble biological neural structures . Therefore, they can learn and generalize information from external data and provide consistent results for unknown data De Mamann et al., 2019). Artificial neural network models can efficiently simulate and estimate results based on common characteristics of the selected input variables .
Researches on fungicide managements that allow for reductions in number of applications and longer intervals between the harvest and the last application are decisive for a satisfactory control of foliar diseases and guarantee of food safety. In this context, the development of simulation models involving non-linearity of environmental conditions and analysis of disease progression provides information for the analysis of different scenarios and facilitates the validation of management practices that promote food safety. The objective of this work was to evaluate fungicide managements focused on a longer interval between the last application and the oat grain harvest, indicate the cultivars with the highest satisfactory yield without fungicide application at the grain filling stage, and validate artificial neural network models for satisfactory yield and food safety, through the interaction between management, pathogen, genotype, and environment.

MATERIALS AND METHODS
A field experiment was carried out in , 2016. The soil in the experimental area is classified as Typical Distroferric Red Latosol (Santos et al., 2018). The climate of the region is humid subtropical, according to the Köppen classification. The soil was analyzed before sowing and showed the following chemical characteristics: pH = 6.2; P = 33.9 mg dm -3 ; K = 200 mg dm -3 ; organic matter = 3.0 %; Al = 0 cmolc dm -3 ; Ca = 6.5cmolc dm -3 ; and Mg = 2.5cmolc dm -3 .
Oat sowing was carried out preferably in the first half of June, using a seeder-fertilizer. Each plot consisted of five 5-meter rows spaced 0.2 m apart, composing experimental units of 5 m². The population density used was determined according to technical recommendations (400 seeds m -2 ) for oat crops to reach an expected grain yield of 4 Mg ha -1 . Soil fertilization consisted of applying 10 kg ha -1 of nitrogen at planting and as topdressing at the fourth expanded leaf stage. Considering the soil P and K contents, 45 and 30 kg ha -1 of P2O5 and K2O, respectively, were applied at sowing.
The experimental was conducted in a randomized block design with three replications, in a 22×4 factorial arrangement consisted of 22 white oat cultivars and 4 fungicide application conditions, in a soybean-oat cropping system. Oat cultivars recommended and no longer recommended for cultivation in Brazil were evaluated, namely: URS Altiva, URS Brava, URS Guará, URS Estampa, URS Corona, URS Torena, URS Charrua, URS Guria, URS Tarimba, URS Taura, URS 21, FAEM 007, FAEM 006, FAEM 5 Chiarasul, FAEM 4 Carlasul, Brisasul, Barbarasul, URS Fapa Slava, IPR Afrodite, UPFPS Farroupilha, UPFA Ouro, and UPFA Gauderia. The fungicide use conditions were: no fungicide application; one application at 60 days after emergence (DAE); two applications, at 60 and 75 DAE; and three applications, at 60, 75, and 90 DAE. The last application (90 DAE) was chosen to ensure a considerable interval between the fungicide application and the grain harvest, without application of pesticide at the grain filling stage to avoid or reduce the risk of translocation of residues to grains, considering that the fungicides used are systemic products.
Foliar diseases in 2015 and 2016 were controlled using the fungicide FOLICUR ® CE at 0.75 L ha -1 (active ingredient: tebuconazole; class: systemic of the triazole group; and formulation: emulsifiable concentrate); in 2017, the fungicide PRIMO ® was used at 0.3 L ha -1 (active ingredients: azoxystrobin and cyproconazole; class: systemic from the strobilurin and triazole group; and formulation: concentrated suspension). The products were sprayed using a BD 04 fan nozzle with a pressure of 45 PSI and a spray volume equivalent to 120 L ha -1 . A pH reducer at 30 mL ha -1 and Nimbus ® mineral oil at 0.5 L ha -1 were used in all treatments. Weed control consisted of application of a metsulfuron-methyl herbicide (ALY ® ) at 4 g ha -1 of the commercial product and manual weeding whenever necessary.
Necrotic leaf area (NLA, %) was determined using three randomly collected plants from each plot. The plants were collected at 60, 75, 90, and 105 DAE in all plots (cultivars and fungicide use conditions). The three upper leaves were removed from each collected plant to evaluate the leaf area; the leaves were scanned using a leaf area reader and the WinDIAS software (Copyright 2012, Delta-T Devices Limited).
Grain yield (GY, kg ha -1 ) was estimated using the 3 central rows of each plot, which were harvested manually when the grains had approximately 15% moisture. The plants were then threshed on a stationary threshing machine and taken to a laboratory for correction of grain moisture to 13%, cleaning, and estimation of yield (kg ha -1 ).
Data of rainfall depth (mm) and minimum (Tmin, °C), maximum (Tmax, °C), and mean (Tmean, °C) temperatures were obtained by an automated meteorological station installed 500 meters from the experiment.
Thermal sum (TS, degrees day -1 ) was obtained using Equation 1: where: is the number of days from emergence to harvest, and is the base temperature for oat development. The base temperature used was 4°C, as recommended by Pedro Júnior et al. (2004).
The neural network toolbox available in the software Matlab was used for the development of simulation models through artificial neural networks to estimate oat grain yield. A feedforward artificial neural network was implemented using the multilayer Perceptron, whose structure consisted of three layers: the input, and the hidden and output layers. The input 5 layer had eight neurons, and the input variables were: number of fungicide applications; number of days after emergence; necrotic leaf area; rainfall depth; minimum, maximum, and mean temperatures; and thermal sum. The output layer had 1 neuron, considering grain yield as the output data. The number of neurons in the hidden layer was determined following the methodology recommended by Hecht-Nielsen (1989), in which the number of neurons in the hidden layer will be equal to twice the number of neurons in the input layer plus one. In this way, seventeen neurons were considered in the hidden layer. The hyperbolic tangent function was defined and the network training was performed by the backpropagation algorithm, using the Levemberg-Marquardt method, for the neuron activation function. The backpropagation training algorithm is conceptually a generalization of the Widrow and Hoff's learning algorithm "Least Mean Square" (LMS), known as the Delta Rule (Faraco, Costa and Cruz 1998), and fits into the supervised learning category.
The network performance was measured by an error function, which considers the square of the difference between the expected value and the respective calculated output for each different input pattern, i.e., the error is the sum of squared errors, defined by the equation: where: is the error on the i-th neural element for the p-th input pattern; is the expected output on the i-th neural element for the p-th input pattern; and is the output produced, defined as the equation: where: is the j-th component of the input pattern . The backpropagation algorithm acts on the synaptic weights, minimizing the error function, through the gradient descent technique. In this method, the weight values are modified proportionally to the opposite of the derivative of the error, according to the equation: where: is the learning rate and controls how big the "step" to take should be. Defining , as the expected output in the i-th unit of the k-th layer, when the p-th pattern is presented to the network, and as the actual output in the unit, where , = ∑ , −1 − e ,0 = , the error function in layer k can be written as: 6 The correction in the weights in the output layer K is given by applying the chain rule: where: Similarly, in the intermediate layers, the correction is given by: where: The Levenberg-Marquardt training is a function that updates the weights and values of the biases according to the optimization. It is often considered to be the fastest of the error backpropagation training algorithms, but it requires more computational memory than the others. In the Levenberg-Marquardt algorithm, the changes (∆) in the weights (⃗⃗ ) are obtained by: where: E is the root mean square error of the network, represented by: where: N is the number of examples; ( ) is the network output corresponding to the example ; and is the desired output for that example. The elements of the matrix are given by: where: p is the number of network outputs. Starting with the initial random weights, both and ∇ are calculated by solving Equation 10. The correction for the weight values is obtained by ( ′ ⃗⃗⃗⃗ = ⃗⃗ + Δ), known as the Levenberg-Marquardt learning epoch. Each iteration with these epochs reduces the error until a minimum is found. The variable λ in Equation 12 is the parameter that is adjusted for each epoch, according to the evolution of the error. Sample data were normalized for training and simulation using the equation: where: is the normalized, dimensionless value; is the observed value; is the smallest sample value; and is the largest sample value. This data normalization was necessary because the defined activation function provides values in the range -1 to 1. The sample data (input and output) were randomly divided into 70% for training, 15% for testing, and 15% for validation. Twenty-three simulation models were generated at the end of this process: one simulation model for each cultivar, regardless of the agricultural year, and a general model involving all cultivars and agricultural years.
The simulations were carried out considering the data of mean rainfall depth, minimum, maximum, and mean temperatures, thermal sum, and necrotic leaf area of the agricultural years for each fungicide application condition. After training, the artificial neural network models obtained were validated based on the calculation of the absolute error, given by the difference between the simulated and observed grain yield data obtained through bioexperimentation.

RESULTS AND DISCUSSIONS
Air temperatures were higher in 2017 when compared to those in 2015 and 2016, with a strong instability at the vegetative stage (Table 1). The most expressive rainfall depths during the grain filling stage of the crop were also observed in 2017. Therefore, these conditions of high temperatures and excess humidity are conducive to the development of foliar diseases. Soil moisture conditions were low at the time of nitrogen application ( Figure 1A), generating losses due to volatilization; this is the nutrient that affects the most the crop development and yield. These conditions resulted in a low grain yield, 1861 kg ha-1 (Table 1), classifying 2017 as an unfavorable agricultural year for oat cultivation (UY). Lower air temperatures and greater stability throughout the crop cycle were found in 2016 (Table 1) when compared to 2017. The rainfall depths in 2016 were lower than the historical mean, but showed an adequate distribution ( Figure 1B), which were conditions that hindered the development of foliar diseases. In addition, nitrogen was applied under adequate soil moisture conditions due to rains that occurred in the days prior to the management, favoring the use of the nutrient by the plant. The obtained mean grain yield of 3854 kg ha-1 (Table 1) was within the expected, considering the fertilizer applications, classifying 2016 as a favorable year (FY) for oat cultivation. Air temperatures in 2015 (Table 1) were intermediate when compared to the other years, with a greater stability in relation to 2017. The rainfall that occurred was similar to the historical mean of the last 25 years, however, with a high volume during the crop vegetative stage. Thus, the the conditions of medium to high temperatures and high rainfall depths until the first half of the crop cycle ( Figure 1C) indicated favorable conditions for earlier development of foliar diseases. Although nitrogen management was carried out under favorable conditions, the grain yield obtained was lower than the expected. These results classified 2015 as an intermediate year (IY) for oat cultivation.
Agriculture is the economic activity most dependent on meteorological conditions; crop yield is strongly affected by air temperature and rainfall distribution and volume (Mantai et al., 2015). According to Marolli et al. (2018), rainfall is the meteorological variable that affects the most the crop yields due to its interaction with temperature, insolation, and radiation. Thus, water stress has negative effects on plant survival and growth (Machado et al. , 2017). Moreover, the rainwater stored in the soil affects the dynamics of humidity in the environment, which is directly linked to the efficiency of nitrogen absorption by the plant Trautmann et al., 2020). Air temperature and photoperiod also interfere with the development of grasses (Castro, Costa and Ferrari Neto, 2012;Mantai et al., 2017). Air temperature is decisive for plant development and productivity, acting as a catalyst for biological processes, which is why plants require a minimum and maximum temperature for normal physiological activities . Air temperature, together with relative humidity, directly affects the infection and development of the main foliar diseases that affect oat cultivation (Bhardwaj, Banyal and Roy, 2021). Table 2 shows the minimum, maximum, and mean necrotic leaf areas for each fungicide use condition, and meteorological and grain yield indicators, regardless of the agricultural year and oat cultivar. The most expressive necrotic leaf areas were found at 90 and 105 DAE, when the most favorable conditions for the development of leaf diseases in oats were evidenced. Furthermore, the means of leaf necrosis decreased as the number of fungicide applications was increased. These results explain the more expressive grain yield found for the conditions with two and three fungicide applications. Therefore, there was a greater control of pathogens that cause leaf necrosis, which is consistent with studies showing the importance of fungicide management for ensuring yield. The conditions with two and three fungicide applications resulted in similar grain yields, although with higher absolute values for the condition with three applications. These results indicate that the conditions with two (60 and 75 DAE) and three fungicide applications (60, 75, and 90 DAE) control leaf diseases while maintaining a long interval between the last application and the grain harvest, with a satisfactory yield. Table 3 shows the ranges of grain yield and percentage of necrotic leaf area, regardless of the agricultural year. These results provide a dimensioning of the variability of the values used for developing the computational simulation model by artificial neural networks. The highest grain yields were found for the two and three fungicide application conditions, carried out at 60 and 75 DAE and at 60, 75, and 90 DAE, respectively. The lowest necrotic leaf areas were found under these conditions, denoting the possibility of fungicide managements with early applications, prior to the grain filling stage. In this context, although some cultivars responded with increasing grain yield to the three applications prior to grain filling, the result with two fungicide applications already showed satisfactory economic results. In addition, the understanding of product cost, operation time, and soil and human contaminations adds elements that should be considered for a new application in the field. Therefore, choosing cultivars and proper managements for oat production is important for ensuring yield and food safety, considering their good response when using early fungicide applications.
Tables 2 and 3 presents real data obtained under experimental conditions, providing qualified information for development, comparison, and validation of simulation models via artificial neural networks and for recommendation of potential cultivars focused on managements with greater food safety. Therefore, the mean squared error values are presented in relation to the training, validation, and testing of the artificial neural networks developed for grain yield simulation for each cultivar and for the general model, from the database (Table 4). The artificial neural networks developed to simulate oat grain yield presented low mean squared errors for training, validation, and testing, considering necrotic leaf area, number of fungicide applications, number of days after emergence, and meteorological indicators as input variables of the model, regardless of the cultivation year conditions (unfavorable, favorable, or intermediate). The low errors found indicate the excellent ability to learn and extract information from the experimental data and the good generalization ability of the developed models. The low mean squared error found for the general model, which encompasses data referring to all cultivars and cultivation years, is emphasized as an excellent response, considering the great diversity of values and results. Table 5 presents the grain yields observed and those simulated by artificial neural network, with the absolute errors for each cultivar and for the general model. The grain yield simulations showed values close to those observed in the field (Table  5). This is shown by the low absolute errors found for the artificial neural network models developed for each cultivar and, especially, for the general model which includes all cultivars and agricultural years under study. Considering the Barbarasul cultivar as a reference, which is known for its susceptibility to leaf diseases, the differences obtained between actual and simulated yields indicated low absolute errors: 4, 15, 20, and 0 kg ha-1 for absence, one, two, and three fungicide applications, respectively. This similar scenario between observed and simulated values confirms the qualified structure of the input variables, supporting an efficient prediction involving the interaction between genotype, pathogen, and environment.
Based on these results, the efficiency and capacity for simulation and generalization of artificial neural networks was confirmed regarding the expression of grain yield in oat crops as a function of the number of fungicide applications, meteorological conditions, necrotic leaf area, and number of days after emergence. These conditions make it possible to generate elements for the formulation of more adequate managements for use of fungicides, based on this database structure. A greater number of years of study may bring elements to increase the working range of the models, allowing the proposition of a greater number of simulation scenarios.
The observed and simulated values found for the conditions with two and three fungicide applications, seeking an early control action and no application at the grain filling stage, showed satisfactory yields and lower risk of pesticide residues in oat grains. The cultivars URS Altiva, URS Brava, URS Guará, URS Charrua, URS Corona, FAEM 007, FAEM 006, FAEM 4 Carlasul, Brisasul, Barbarasul, IPR Aphrodite, and UPFPS Farroupilha stood out, reaching yields higher than 3000 kg ha-1 in the treatment with two fungicide applications.
In the condition with three fungicide applications, the cultivars that obtained the highest yield were URS Altiva, URS Corona, FAEM 006, FAEM 4 Carlasul, Brisasul, Barbarasul, and IPR Afrodite, presenting yields higher than 3500 kg ha-1. Considering the performance of the cultivars under these two management conditions, URS Altiva, URS Corona, FAEM 006, FAEM 4 Carlasul, Brisasul, Barbarasul, and IPR Aphrodite stood out with the highest yields, indicating that they are alternatives to achieve management objectives intended for food security. In the absence of fungicide application, the yield of the cultivars URS Altiva, URS Guará, URS Charrua, FAEM 4 Carlasul, IPR Afrodite, and UPFPS Farroupilha were higher than 2000 kg ha-1, indicating that they are possible alternatives for commercial use in organic production of the cereal.
Artificial neural networks can learn and generalize information from successive presentation of examples (Rocha, Matos and Frei 2011). This process is called training and allows the network to extract information regarding the existing relationships between the variables that affect a given event (Sheikhtaheri et al., 2014). Thus, the use of artificial neural networks allows to improve the understanding of agricultural production systems, optimize cultivation technologies, and accurately simulate the complex variables that involve plant production (Soares et al., 2015). Adisa et al. (2019) developed an artificial neural network structure to predict corn yield, using rainfall, maximum temperature, minimum temperature, potential evapotranspiration, soil moisture, and cultivated area as input variables. Conceicao et al. (2021) developed models using artificial neural networks that predict papaya yield as a function of vegetative and reproductive variables and fruit quality characteristics.  developed artificial neural network models for simulating and predicting oat grain yield, using meteorological variables, nitrogen management, and biomass obtained throughout the development cycle, enabling a more efficient and sustainable management of the nutrient..

FINAL CONSIDERATIONS
Regardless of the oat cultivar, obtaining satisfactory grain yields in the absence of fungicide applications and in the longest interval between the last application and the grain harvest depends on the favorable and unfavorable agricultural year conditions for the plant and the disease.
Regardless of the agricultural year conditions, the oat cultivars URS Altiva, URS, Guará, URS Charrua, FAEM 4 Carlasul, IPR Afrodite, and UPFPS Farroupilha showed satisfactory grain yields in the absence of fungicide applications. Therefore, they are more suitable for an agroecologically based management. Among these, URS Altiva, FAEM 4 Carlasul, and IPR Aphrodite showed significant yield increases with fungicide application before grain filling.
Artificial neural networks are efficient to predict oat yield involving fungicide management, necrotic leaf area, development cycle, and meteorological indicators, and is an alternative for simulating scenarios for the validation of more sustainable managements.
The results obtained show the possibility of advances in oat production with a reduction in use of fungicides, bringing environmental and food security benefits. Also, the use of artificial intelligence modeling makes it possible to analyze and validate scenarios for advances in agricultural sustainability.
The validation of the results requires a sequencing of the determinations, allowing for a greater variability of scenarios. However, society has been demanding fast advances in food production to achieve zero hunger with a sustainable agriculture, therefore, in line with objective 2 of the UN 2030 agenda.