Evaluating the Contribution of Soybean Rust- Resistant Cultivars to Soybean Production and the Soybean Market in Brazil: A Supply and Demand Model Analysis

Soybean rust (SBR), caused by Phakopsora pachyrhizi (Sydow & Sydow), has become a serious issue in Brazil. As Brazil is one of the largest soybean-producing and exporting countries in the world, a considerable decrease in soybean production due to SBR would have a significant impact on the global soybean market. SBR-resistant cultivars have been developed to prevent a decrease in soybean production. This study was conducted to evaluate the effect of SBR-resistant cultivars on soybean production and the soybean market in Brazil using a supply and demand model. This model consists of functions of yield, cultivated area, exports, and stock changes of soybean and soybean products, demand for soybean products, and price linkages. Five scenarios were simulated to evaluate the economic impact of adopting SBR-resistant cultivars as follows: One without SBR infection, two with serious production losses due to SBR in the south and southeast regions and all the states of Brazil, and two with the adoption of SBR-resistant cultivars in the south and south-east regions and all the states of Brazil. Our simulations suggest that adopting SBR-resistant cultivars reduces the cost of controlling SBR by approximately half and is essential for sustainable soybean production and a stable global soybean market.


Introduction
Soybean rust (SBR) caused by the harmful fungus, Phakopsora pachyrhizi (Sydow & Sydow), is one of the most serious threats to stable soybean production in Brazil [1,2]. Yield losses of over 80% have been reported during times when environmental conditions are optimal for the growth of this pathogen [3,4]. Infected leaves undergo chlorosis, defoliation, and early maturation of the pod, which leads to decrease in yield [2,5]. In Brazil, SBR first occurred in the 2001/2002 crop year, spreading to almost all the soybean-producing states by the 2003/2004 crop year, following which fungicide was applied. However, SBR has proven to be difficult to control and the economic loss in the 2003/2004 crop year was 1.22 billion USD for grain loss and 2.08 billion USD for the cost of applying fungicide [5]. One common strategy of mitigating SBR is by using fungicide, but it increases production costs for farmers [4]. The cost of fungicide accounted for 7.09% of total production cost of soybeans in the 2016/2017 crop year [6], while the average production cost of Brazil in 2013/2014 was approximately twice as high as that in the USA and Argentina [7]. Some studies have suggested that adopting fungicide becomes ineffective and soybean production gradually decreases due to SBR in south and southeast Brazil; Scenario 3, which assumes the same case as in Scenario 2, but for entire Brazil; Scenario 4, which assumes the adoption of SBR-resistant cultivars in south and southeast Brazil; and Scenario 5, which assumes the same case as in Scenario 4, but for entire Brazil. We evaluated the economic impacts of SBR on soybean production and the adoption of SBR-resistant cultivars by comparing Scenarios 3 and 5.

Supply and Demand Model of Soybeans and Soybean Products
To investigate the effects of damage due to SBR on the supply and demand of soybeans and soybean products, we used a supply and demand model based on the models of Koizumi and Ohga [24] and Hung et al. [28]. We modified the original model and used state-level data. Because the data, in some states in the north and northeast region, were not available, we summed the data of the north (Rondônia, Roraima, and Tocantins) and northeast (Bahia, Maranhão, and Piauí) regions as north and northeast.
The supply and demand model for soybeans in Brazil consists of 29 structural equations and five identities, specified as follows: Yield (Y) function of soybeans in each state or region (10 functions): where α and β are the parameters and the subscripts i and t are state and year, respectively, T is the time trend, and ε is an error term. Planted area of soybeans in each state or region (10 functions): where sbRFP and maRFP are the real farm prices of soybean and maize, defined as sbFP/(CPI/100) and maFP/(CPI/100). sbFP and maFP are the farm prices of soybean and maize. CPI is the consumer price index (2010 = 100). Country level production (sbQ): where bal is the adjustment factor. The export (sbEX) function: where sbRWP is the real-world price of soybeans (USD/metric ton) defined as sbWP/(CPI/100). Here, sbWP is the world price of soybeans in US dollars, represented by US No. 2, yellow meal, CIF Rotterdam. The stock change (sbSTC) function: where sbSTC is the annual change of stock, i.e., ending stock minus beginning stock. Soybean supply identity: where sbPR, sbIM, sbFO, sbSE, and sbFE are the quantities of soybean processed, imported, used as food, seed, and feed for livestock. Soybean processing identity: where oilQ is the quantity of soybean oil production, cakQ is the quantity of soybean cake production, and LO is the adjustment factor. Export function of soybean oil (oilEX): where oilEX is the quantity of soybean oil exports and oilWP is the world price of soybean oil in US dollars, represented by the Dutch crude degummed, FOB NW Europe. Export function of soybean cake (cakEX): where cakEX is the quantity of soybean cake exports, cakRWP is the real-world price of soybean cake (USD/metric ton) defined as cakWP/(CPI/100). Here, cakWP is the world price of soybean cake in US dollars, represented by the Brazilian pellets 48% protein, CIF Rotterdam. Demand function of soybean edible oil: where oilED is the per-capita consumption of soybean oil, cotRFP is the real farm price of cottonseed oil defined as cotFP/(CPI/100), and GP is defined as per capita real gross domestic product (GDP) divided by POP. Here, the real GDP is GDP converted to 2010 constant international dollars using purchasing power parity rates. Demand function of soybean oil for biodiesel: where oilBD is the quantity of soybean biodiesel oil and croRWP is the real-world price of crude oil defined as croWP/(CPI/100). Here, croWP is the world price of crude oil, represented by the average spot price of Brent, Dubai, and West Texas Intermediate, equally weighed. Demand function of soybean cake feed: where cakFE is the quantity of soybean cake for feed and chQ is chicken production (metric ton). Chickens, swine, and cattle have been reared mainly in Brazil, and their productions are strongly correlated (p < 0.001). When multiple regression is applied to their production, it will be affected by multicollinearity. To avoid the effect of this problem, we used chicken production as a representative of livestock in Brazil. Soybean oil identity: where oilIM is the imports of soybean oil and oilSTC is the stock change in soybean oil.
Soybean cake identity: where cakSTC is the stock change in soybean oil and cakIM is the imports of soybean oil. The farm price is linked to the world prices of soybeans and soybean oil and cake. Price linkage functions are as follows: Farm price is the equilibrium price when the quantity demanded is equal to the quantity supplied. Figure 1 shows the flowchart of supply and demand for soybean in Brazil in the econometric model. Total production is the sum of production in all the states. Domestic utilization of soybeans is defined as the sum of feed, seed, food, and other forms of utilization. Supply for soybeans is influenced by total production, stock changes, domestic utilization, and the volumes of exports and imports of soybeans. Processing of soybeans is divided into soybean oil and cake production. Supply for soybean oil is influenced by the volumes of exports, imports, and stock changes of soybean oil. Demand for soybean oil is classified into edible soybean oil and biodiesel. The demand for edible soybean oil is affected by population, GDP, and domestic farm price of soybeans and cotton seed. The demand for soybean oil for biodiesel is affected by domestic farm price of soybeans and domestic farm price and world price of crude oil. The production of soybean cakes is influenced by the volume of exports and imports and stock changes of soybean cake. The demand for soybean cakes is affected by domestic farm price of soybeans and maize and chicken production. Farm prices are determined when supply and demand are in equilibrium. The movements of soybean oil and cake prices are reflected by farm price through the price linkage functions. The farm price affects the next year's supply. In this sector, import of soybeans and soybean oil and cakes, stock changes of soybean oil and cakes, domestic farm price of cottonseed and maize, world price of crude oil, population, and GDP are exogenous variables. An augmented Dickey-Fuller (ADF) test was applied to examine the stationarity of all variables, except the yield functions. Johansen cointegration tests were applied in the next step if the variables had unit roots. If the variables did not have cointegrating relations, then difference functions were applied, as described in Hung et al. [28].

Scenario Setting
We set up five scenarios to simulate the effect of SBR-resistant cultivars on soybean production ( Table 1). The base scenario was maintaining the current status. In Scenario 1, soybean production is not affected by SBR. In Scenarios 2 and 3, fungicide becomes ineffective and soybean production gradually decreases due to SBR in south and southeast Brazil and entire Brazil, respectively. In Scenarios 4 and 5, SBR-resistant cultivars are adopted in south and southeast Brazil and entire Brazil, respectively. The equilibrium domestic farm prices were estimated in each scenario. Table 1. Scenario setting, assumptions in each scenario.

Setting Assumptions
Baseline Continuing current situation Forecasting began in 2019.

Scenario 1
No damage due to SBR Recover the historical yield due to SBR and measure yield function.

Scenario 2
Loss of soybean production in south and southeast regions of Brazil Fungicide becomes ineffective (Equation (18)) and there is a production loss of 8.49% in south and southeast region.

Scenario 3 Loss of soybean production in all the states of Brazil
Fungicide becomes ineffective (Equation (18)) and there is a production loss of 8.49% in all the states of Brazil.
Scenario 4 SBR-resistant cultivars will be adopted under Scenario 2 SBR-resistant cultivar will be diffused (Equation (19)) up to 60.9% of planted area in south and southeast region under Scenario 2.
Scenario 5 SBR-resistant cultivars will be adopted under Scenario 3 SBR-resistant cultivar will be diffused (Equation (19)) up to 60.9% of planted area in all the states of Brazil under Scenario 3.
In Scenario 1, according to the information on soybean production loss, we divided the loss of production based on the proportion of planted area of states where damage was reported from 2001/2002 to 2013/2014 crop years [5]. We measured the yield functions by considering the proportion of damaged yield in each state or region. Subsequently, from the estimated yield and projected area of baseline analysis, we calculated the soybean production in Scenario 1. For Scenarios 2 and 3, we referred to the case of demethylation inhibitor (DMI), which is the most utilized fungicide in Brazil, but has a decreasing efficacy [30]. We applied the logarithmic function to describe the efficacy of DMI (E DMI ) as follows because the decrease in efficacy followed a curvilinear path and not a linear one: where a e and b e are the minimum and maximum levels of efficacy, respectively, c e is the efficacy reduction rate, d e is the inflection year, and e e is the slope of the time trend. The largest loss was incurred in the 2003 to 2004 crop season in Brazil, with a loss of 8.49% of total soybean production [5].
The minimum level of efficacy in Equation (18) reflects the largest rate of loss in this year. For Scenarios 4 and 5, we referred to the case of genetically modified (GM) Intacta soybean cultivars in Brazil. In 2016, 94% of cultivars were GM soybean [31]. Out of these, 89% registered in 2017 were Intacta soybeans [32].
In 2013, the planted area of Intacta soybeans in Brazil was only 7.9%, but this increased to 60.9% in 2016. On the basis of the diffusion rate of Intacta soybeans, we estimated the diffusion area by the following logistic function [33]: where, i is the identification number of the state, A c is the planted area of SBR-resistant cultivars, t is time (year), a c is area in Scenario 2, b c is the maximum planted area of SBR-resistant cultivars (60.9% of baseline area), c c is the diffusion rate, d c is the inflection year, and e c is the slope of the baseline area. We applied e c : in only the case where baseline area increased. With respect to the case of Intacta soybeans, we assumed that the SBR-resistant cultivars are GM cultivars, spreading since 2017 and covering 3.89% of total planted area in each state or region [2]. The inflection point will be 2021 and it should have the same diffusion rate as Intacta. The planted area of SBR-resistant cultivars will be diffused up to 60.9% by 2023. The planted area of conventional cultivars was determined by subtracting the planted area of SBR-resistant cultivars from the planted area of soybeans in each state or region. The yield of SBR-resistant cultivars was assumed to be 3.11 metric ton/ha, which is equal to the SBR-resistant cultivar, TMG7067IPRO, that has already been released [34]. The same trend was considered for each state or region. The yield of conventional cultivars in Scenarios 4 and 5 was initially assumed to be the same as that in Scenarios 2 and 3, which then decreases with the decrease in the efficacy of fungicides in Scenarios 4 and 5. Production of SBR-resistant cultivars was examined by multiplying the yield by area of SBR-resistant cultivars.

Baseline Analysis
The estimation period was 1981 to 2013, for which all data were available. The assumptions of the simulation were as follows ( Figure A1): (1) The forecasted growth of CPI is the average annual growth between 2011 and 2013, (2) the forecasted value of real GDP is the annual average between 2011 and 2013, (3) the forecasted growth of population is the average annual growth between 2011 and 2013, and (4) the linear trend of the yield functions continues during the simulation period. The base year of the simulation of Y, A, sbEX, STC, oilEXP, cakFE, cakEX, and sbFP was 2019. The latest data for the calibration of sbEX, sbSTC, cakFE, cakEX, and sbFP was taken from the USDA [35]. The base year of the simulation of oilED, oilBD, oilWP, and cakWP was 2013. The forecasted period was from the base year untill 2030. Hence, the intercepts of the functions were calibrated to the latest data. Tables 2 and 3 show the parameters of yield and planted area functions of soybeans in each state or region. The yield of soybeans depends on the time trend, denoted by a wide range of technological developments, such as improved irrigation systems. Some reports have indicated that the yield of soybeans in Brazil would increase if the water deficit and crop management systems were improved [36,37]. Our model included this potential increase in the yield of soybeans. The planted area was expanded when the farm price rose in the previous year in each state or region and it was affected by the previous crop year in a positive direction (Table 3). This indicates that rising farm prices encourage farmers to cultivate and expand the planted area. The production of soybeans, which depends on yield and planted area, will increase with an increase in yield (Figure 2). Figure 2 shows the simulation results of the production of soybean in the top three producing states and throughout Brazil. The production of soybeans in Mato Grosso, Paraná, and Rio Grande do Sul is expected to increase to 44.1 million, 23.8 million, and 20.4 million metric tons between 2019 and 2030, respectively. The production of soybeans in Brazil will increase to 143.4 million metric tons during the forecasted period.   Soybeans produced in Brazil are either exported or processed into soybean oil and cake. Soybean oil corresponds to approximately 20% of crushed soybeans. During the estimation period, 34% of soybean oil was exported (54% edible on average) [11]. Figure 3 shows edible soybean oil consumption per capita and soybean oil consumption for biodiesel. Figure 4 shows soybean cake consumption for feed. Soybean cake, corresponding to approximately 80% of crushed soybeans, was exported (67%) and used as feed for livestock (34%) during the estimated period [11]. Consumption of soybean cake for feed will increase due to a global shift towards more meat consumption, but the consumption of soybean oil will not increase as much [12]. Figure 5 shows the simulation result of the equilibrium farm price. The farm price is estimated to be 334.2 USD/metric ton in 2030.    Figure 6 shows the outlook of the production of soybeans in Mato Grosso, Paraná, Rio Grande do Sul, and throughout Brazil in the five scenarios. The production of soybeans in Mato Grosso, Paraná, Rio Grande do Sul, and throughout Brazil is expected to be 44.5 million, 24.0 million, 21.4 million, and 146.8 million metric tons in 2030, respectively (Scenario 1). Although the estimated recovery of soybean production from SBR seems small, this small damage will affect the domestic farm price in Scenario 1. The domestic farm price is estimated to decrease due to an increase in soybean production in this scenario (Figure 7a). In Scenario 2, production loss in these areas will increase the domestic farm price (Figure 7b) as the soybean production decreases in south and southeast Brazil. In Scenario 3, the domestic farm price increases due to the reduction in the production of soybeans throughout Brazil (Figure 7a).

Discussion
Does adopting SBR-resistant cultivars help maintain a stable supply of soybeans? The yield in each state or region determines the total soybean production, which is also the total supply of soybeans. The yield of conventional cultivars in Mato Grosso was high, at 3.39 (metric ton/ha) in 2018, while that in Rio Grande do Sul was 3.01 (metric ton/ha) [20]. In this study, the yield of SBR-resistant cultivars is assumed to be 3.11 (metric ton/ha), based on Dorneles et al. [34]. Moreover, we considered technological advancement based on trends in each state or region. When the SBR-resistant cultivar is disseminated in Mato Grosso, the yield of this state is projected to increase to 3.54 (metric ton/ha) by 2030, which is lower than that of the conventional cultivar at 3.74 (metric ton/ha) ( Figure A2). In the case of Rio Grande do Sul, the yield of conventional cultivar was 3.01 (metric ton/ha) in 2018 [20] and disseminating SBR-resistant cultivars will increase the soybean production there. Disseminating SBR-resistant cultivars in the south and southeast regions will increase soybean production, thus, the domestic farm price will almost be the same as that at the baseline (Figure 7b). However, the regions where the yield of conventional cultivars is higher than that of SBR-resistant cultivars cannot alleviate the rise of domestic farm price of soybean to a large extent (Figure 7a). Thus, the extent of alleviation of rising domestic farm price due to the decrease in soybean production caused by SBR depends on the yield of conventional cultivars in each state or region. Researchers who breed SBR-resistant cultivars aim for similar yields without compromising the taste and appearance of conventional cultivars in each area [38]. Thus, there is a possibility that the results of our simulation analysis could be somewhat different. Moreover, we assumed that the dissemination of SBR-resistant cultivars was the same as the dissemination of Intacta cultivars as mentioned earlier. These assumptions are possible limitations of our estimation.
We estimated the cost-saving due to the adoption of SBR-resistant cultivars based on the equilibrium quantities in each scenario (Table 4). In Scenario 3, we assumed that fungicide is applied twice for SBR-resistant cultivars and four times for conventional cultivars in Scenario 5 according to Dorneles et al. [34]. The cost of fungicide was assumed as 25 USD/ha [5]. The cost-saving due to the adoption of SBR-resistant cultivars in Mato Grosso, Paraná, and Rio Grande do Sul are estimated to be 338 million, 185 million and 170 million USD, respectively. The cost-saving due to the adoption of SBR-resistant cultivars in Brazil is projected to reach 1.28 billion USD by 2030 ( Table 4). The cost of applying fungicide in the 2013/2014 crop year was 2.2 billion USD countrywide [5]. Thus, adopting SBR-resistant cultivars could save almost half of the amount spent on SBR control.  Fungicide was applied twice on the resistant cultivars and four times on the conventional cultivars [34]. The cost of fungicide is assumed to be USD25/ha/spray [5].

MT
We proposed the worst case in Scenario 3, although it seems improbable. However, there are some factors other than SBR that reduce soybean production, such as climate change. There is an increase in droughts, especially in the northeast region, where rainfall has been below normal in the last two decades [39]. It is forecasted that drought will increase in this region, while rainfall will increase in the south and southeast regions [40]. As the growth of SBR is influenced by precipitation and moisture [41], there is a possibility of an epidemic in the south and southeast regions [13]. Caetano et al. [42] showed that cultivation of soybeans in the central region, which is the most productive area, will not remain environmentally suitable due to climate change. As our models do not consider climate change, further studies must be conducted to take into account the effect of climate change on both soybean production and SBR in the future. Furthermore, our scenarios assume damage due to SBR, and not by climate change. However, production loss will actually occur because of climate change. If production throughout Brazil falls, domestic farm price will rise ( Figure 7). As Brazil is one of the top soybean-producing and exporting countries in the global market, increase in domestic farm price will affect the world price of soybeans and the global market.
Scenarios 4 and 5 assume that the effect of SBR-resistant cultivars will last up to 2030. However, there is a possibility that SBR-resistant cultivars could be ineffective. In Brazil, herbicide-tolerant GM soybean cultivar, Roundup Ready, has been registered since 1999 [32], and herbicide-tolerant and soybean cultivars that are herbicide-tolerant and pesticide-resistant are being used in Brazil. Many pesticide-resistant GM soybean cultivar, Intacta, has been registered since 2012 [32]. As of 2019, GM Brazilian cultivars have been developed and registered each year [43]. The SBR-resistant cultivars in Scenarios 4 and 5 are assumed to correspond to several types of rust populations. Hence, Scenarios 4 and 5 would be realistic. As Brazil is a major soybean producing and exporting country [11], early and quick diffusion of SBR-resistant cultivars in Brazil is desirable to maintain stable and sustainable soybean production.

Conclusions
SBR is one of the most severe threats to soybean production in Brazil. If soybean production reduces, soybean oil and cake production will also fall. This would have a significant impact on the global soybean and soybean products market, as Brazil is a major player in this sector. To avoid significant loss due to SBR, several SBR-resistant cultivars have been developed. We analyzed the impact of SBR-resistant cultivars on soybean production in Brazil with a supply and demand model. The baseline analysis, which is used in subsequent scenarios, showed that soybean production will steadily increase due to the technological progress over the simulation period. This simulation was used as the starting point of the five scenarios. Scenario 1 assumed that soybean production was not affected by SBR. Scenarios 2 and 3 assumed that fungicide becomes ineffective and soybean will be damaged gradually by SBR in the south and southeast regions and all the states of Brazil. Scenarios 4 and 5 assumed SBR-resistant cultivar adoption in the south and southeast regions and all the states of Brazil. We compared the cost-saving on fungicide use by adopting SBR-resistant cultivars. Cost-saving by adopting SBR-resistant cultivars in Mato Gross, Paraná, and Rio Grande do Sul, and throughout Brazil will be 338 million, 185 million, 170 million, and 1.28 billion USD in 2030, respectively. If the environment becomes increasingly favorable for SBR due to global warming, there is a possibility that the worst-case scenario could happen. The adoption and early and quick diffusion of SBR-resistant cultivars will be needed for sustainable soybean production not only as a source of food, but also as biodiesel and feed for livestock.