Productive Potential and Economic Viability of Soybeans in Response to Potassium Application

The objective of this study was to find the best potassium dose to increase soybean yield, taking into account the economic viability of the crop in the studied region. Sixteen treatments of the interaction between potassium doses (0, 50, 100 and 150 kg ha) and application times (sowing, vegetative stage (V3), vegetative stage V3 + reproductive stage Journal of Agricultural Studies ISSN 2166-0379 2020, Vol. 8, No. 3 http://jas.macrothink.org 222 (R1) and reproductive stage). The experiment was set up in a randomized complete block design with four replications. Plant growth and production characteristics were analyzed and a preliminary analysis of variance was applied to check the significance of the interactions for each characteristic by Tukey’s test (α = 0.05). Subsequently, the regression analysis was performed using SAS software (2013). The economic analysis was made using the Monte Carlo methodology (Lima, 2008), and processed with the software @Risk 7 (PALISADE, 2016). Potassium fertilization was positive with increase in yield, but there was no direct relation with the application period. The 109 KCl ha dose provided greater economic viability in soybean cultivation.


Introduction
Soybean (Glycine max L. Merrill) is one of the most cultivated crops in the world and is highly important for the Brazilian agribusiness with prospects for increased production. Such perspective is due to the large extension of arable land in the Cerrado, especially in the North and Northeast regions of the country (GAVIOLI, 2012).
In the Northeast region is the Cerrado of the State of Piauí that constitutes the MATOPIBA (States of Maranhã o, Tocantins, Piauí and Bahia) and has stood out in the Brazilian scenario due to its flat topography, deep soils and favorable climate for the cultivation of major crops of grains and fibers (BORGHI et al., 2014), which allowed agricultural expansion in this region.
Increased production is also directly related to proper plant nutrition and fertilizer management (OOSTERHUIS et al., 2014). Essential nutrients for soybean include potassium (K), which plays a particularly key role in plant production and vital physiological processes (HAO et al., 2015), such as growth and development, water relations, photosynthesis and enzymatic activity (MEENAA et al., 2014;PETTIGREW, 2008).
K availability depends on soil type and its physicochemical properties (ZÖRBA et al., 2014). Inadequate management of K can directly affect plant performance (SRINIVASARAO et al., 2016), as stomatal opening and closing becomes slower, which implies a more pronounced result of water deficit (SERAFIM et al., 2012). Thus, it causes inhibition of soybean plant photosynthesis, slower plant growth, poorly developed roots, lighter seeds and reduced yield (WANG, 2015).
There are recommendations of economically and environmentally appropriate doses for crops and soil classes, however, soybean response to K application is still divergent in the Cerrado region (PETTER et al., 2014), because nutrients have different responses in soil and according to plant mobility, influenced by the dose and time of application of the supplied nutrients (MARTINS et al., 2014).
To make the best decision, the producer needs to know the cost of production, especially related to fertilization, observing the optimal dose and timing of nutrient application. This is because the dose that gives the best result will not always be the dose that will result in the greatest economic return. Therefore, we have to be sure that the decision to be made is the one that requires less effort, fewer resources and guarantees the best result (RICHETTI, 2015).
There is still little research involving the productive potential and economic viability of soybean in the Cerrado of the State of Piauí . In this context, the goal of this study was to analyze the management of doses and times of application of potassium and the economic viability of soybean crop in the study region.

Material and Methods
The experiment was conducted in the 2016/2017 growing season, in the experimental area of Sã o Joã o do Pirajá Farm, State of Piauí , Brazil (9°3'25.69"S and 44°33'12.89"W, and 570 m altitude).
The soybean cultivar used was characterized as genotype 1, transgenic, determinate growth habit, maturity group 9.3, glyphosate-tolerant, with high yield and production stability.
Seeds were inoculated and treated with the following products: 4 doses of inoculant 5x10 9 colloid forming units (CFU) mL ha -1 + 140 mL ha -1 Fipronil, Thiophanate Methyl and Pyraclostrobin; 1 dose of Bradyrhizobium elkanii strain 5019, 1 dose of Bradyrhizobium japonicum strain 5079; 1 dose of Bradyrhizobium japonicum 1x10 8 cell; and 1 dose of Bradyrhizobium japonicum semia 1 x 10 9 to obtain good root nodulation and to protect the seed during germination.
The experiment was set up in a 4x4 randomized complete block design with four replications. The first factor consisted of 0, 50, 100 and 150 kg ha -1 potassium doses and the second, of four application times: at sowing, vegetative stage (V3), vegetative stage V3 + reproductive stage (R1) and reproductive stage. (R1) ( Table 1) using potassium chloride (KCl) as a source. Each experimental plot consisted of ten rows, five meters long and 0.5 meters apart.    ISSN 2166-0379 2020 Growth data were evaluated at the end of the experiment, in which five soybean plants were randomly selected and marked in the useful area of the plot by repetition, where the following analyses were performed: Plant height: measured with a measuring tape, from the base of the plantś to the end of the main stem in cm (BOHN et al., 2016); Number of nodes, number of branches and number of trifoliate leaves: done manually (SOUZA et al., 2013).

Journal of Agricultural Studies
After reaching physiological maturity and drying naturally, when the plants reached the R9 phenological stage, the grains were harvested. The collected pods were stored in plastic bags and taken to the Phytotechnics laboratory of the Federal University of Piauí (UFPI/CPCE), and threshed. Yield components comprise the following evaluated parameters: Number of pods per plant (NVP) -obtained by the ratio of the total number of pods to the total number of plants collected (Dalchiavon and Carvalho, 2012) In order to meet the assumptions of the analysis of variance, the number of pods in the middle third was transformed into logarithm base 10 ( ). Statistical analyses were performed using the GLM (General Linear Model) and CORR (Correlation) procedures contained in the SAS -Statistical Analysis Systems (University Edition). Significances were declared at 5% and 1% (P = 0.05 and P = 0.01) by the F-test.
The economic analysis was performed using Monte Carlo methodology (PAZZINI et al., 2014), with data simulation, considering a normal distribution of residues with adoption of 10,000 samples or iterations per treatment.
Subsequently, the statistical differences for K doses were tested and regression analysis was performed to obtain the production function, whose adjustment model was a third order polynomial. The calculations defined for this analysis follow the models prescribed by Theory of the Firm (CAMARGOS, 2008).
After obtaining the regression function, considering the standard error, normality was adjusted. From the polynomial function, to set the limits of rational use of KCl doses. Taking ISSN 2166-0379 2020 into consideration the purchase values of the products equivalent to January 2017, the bag with 60 Kg ha -1 soybeans U$$ 17.57 and KCl U$$ 0.47 kg. The economic analysis was processed with the aid of @Risk 7 software (PALISADE, 2016).

Results and Discussion
For the growth traits of soybean, there was no statistical significance for the dose x application time interaction. Considering the factors separately, dose and application time, only the plant height was significantly different between different doses and application times. The other variables had no statistical difference (Table 2). Both dose and time of application influence the plant height. This was observed in the regression (Figure 2), where the highest plant height was found at 59.75 kg ha -1 KCl. The use of potassium at the optimal dose is essential for soybean cultivation, as it is related to several positive factors of the plant such as increased osmotic function, enzymatic activator, with participation in protein metabolism, photosynthesis, assimilate transport and cellular water potential (TAIZ and ZEIGER, 2013). In addition, weeds, grain yield and harvest losses can be controlled by taking into account mechanized operations. ISSN 2166-0379 2020  After the optimal dose, the height of the plant begins to decrease, this is because the excess of one nutrient reduces the effectiveness of others (law of the maximum), which in this case provides a nutritional imbalance with the gradual increase of K decreasing and affecting the effectiveness of Ca and Mg. This is because they act directly on the cell wall structure and chlorophyll, respectively, because absorption of high amounts of K may reduce the uptake or physiological availability of Ca and Mg (PETTER et al., 2012).

Journal of Agricultural Studies
The results show that for plant height, the most appropriate time of K application was at sowing. However, for soybean cultivation, potassium fertilization can be applied both at sowing and topdressing (SILVA and LAZARINI, 2014).
Topdressing application of potassium at different times in the Cerrado of the State of Piauí did not affect the weight of one thousand grains, despite being one of the main yield components. Thus, no significant effect was detected for time, nor for K doses, as well as the length of pods and the number of pods in the upper and lower thirds (  ISSN 2166-0379 2020  There was interaction between dose and time of application for the number of pods in the middle third ( Figure 3) and yield; in which NVTM is a direct indicator related to increased crop yield. The dose of 109 kg ha -1 KCl resulted in a higher number of grains in the middle third and the best time for application was at sowing. For yield, in general, the ideal dose was 105.67 kg ha -1 (Figure 4).

Journal of Agricultural Studies
In the V3 + R1 stage, the number of pods in the middle third was reduced, however it was not enough to decrease the yield. This is due to the potassium exploitation capacity in the soil, which even with the occurrence of water deficit during the experiment (Figure 1), was able to reduce its effects, presenting positive response to potassium fertilization with significant increase in yield.  ISSN 2166-0379 2020 Yield was influenced by KCl doses, but it was not related to the time of application of this nutrient. Potassium fertilization induced the response in soybean plants increasing yield (Figure 4). These results corroborate Foloni and Rosolem (2008), who verified higher soybean yields with applications of 90 kg ha -1 K2O. For Duarte et al. (2016), the number of seeds per plant and grain yield increase linearly with increasing fertilizer doses.

Journal of Agricultural Studies
The increasing yield response can be attributed to the increase in production components and is related to the ways in which plants use Km as it can provide plants with the most efficient use of water and nutrients, so that plants become more tolerant to environmental stress (PETTIGREW, 2008). In addition, potassium fertilization directly interferes with crop yield, since K is related to protein synthesis, and its deficiency can lead to accumulation of free amino acid concentration in soybean plant tissue, and increase the susceptibility to pests and diseases (MYERS et al., 2005).
For better use of K by plants in Cerrado soils, it is still necessary to define the best time of application of this nutrient, due to the specific soil and climatic conditions of the region. Therefore, the choice of applying total K at sowing or according to the stages of crop development should be a function of the costs or optimization of application operations, as well as the greater economic efficiency in using K, with reduced production costs according to fertilization management.
Given this, economic analysis was performed to evaluate the economic viability of the potassium doses tested. Considering the maximum economic efficiency (MEE), the dose that provides the maximum economic return for the applied fertilizer, taking into account the price of KCl and the soybean price, this means that applications above the dose to reach the MEE may provide higher yield, but with lower profit.
The regression results and the coefficient of determination are listed in Table 4. With the available equation, it was possible to calculate the production stages 2 and 3, to set the limits of rational use of potassium, as well as the optimal dose to reach the highest yield. Taking into account the soybean price of US $ 21.66 per 60 kg bag and the KCl of US $ 476.19 per ton for January 2017, the application of 109.9 kg ha -1 KCl generates a profit of US $ 309.39. While applying 112.56 kg KCl per hectare, the profit is US $ 308.77, thus it is observed that with increasing doses of K the net revenue tends to grow to a maximum, then begins to decrease. These results reinforce and corroborate Mitscherlich's law of diminishing returns, which states that as the dose of a given fertilizer increases, the yield response is reduced exponentially.
Yield reduction from 112.56 KCl ha -1 dose may be due to salt concentrations in KCl, which hinders water absorption by seeds, and compromises root and vegetative development of plants due to external osmotic pressure (TAVARES, 2012). In studies with different doses of KCl, Petter et al. (2012) verified the absence of the increasing effect on yield with applications above 90 kg ha -1 K2O, attributing the nutritional imbalance of K to Ca and Mg.
The maximum dose of technical viability was 112.56 KCl ha -1 , which generates a profit of US $ 307.65 and the optimal dose of economic viability is 109.9 KCl ha -1 with a profit of US $ 308.27, when compared to the zero dose of KCl. The economic analysis of soybean cultivation showed a grain yield of 2295 kg ha -1 , obtained by applying 109.9 kg KCl ha -1 , while the control presented a yield of 1231.4 kg ha -1 , which accounted for around 86.5% more grain yield than the control. These results are related to the adequate supply of K, since it increases the efficiency in the uptake and use of nutrients such as nitrogen, due to the development of a strong and healthy root system, thus providing higher yield with lower production costs (IPI, 2013).

Conclusions
Potassium fertilization had a positive effect on soybean yield and there was no direct relationship with the time of application.
The dose of 105.7 KCl ha-1, under the conditions of this experiment, obtained the highest soybean yield.
The dose 109 KCl ha-1 provided greater economic viability in soybean crop.