Predicting Asian Soybean Rust Epidemics Based on Off-Season Occurrence and El Niño Southern Oscillation Phenomenon in Paraná and Mato Grosso States , Brazil

The study aimed to propose models to predict Asian soybean rust epidemics based on both the occurrence of the disease in the period between seasons and the climate variability index, which is influenced by the El Niño Southern Oscillation (ENSO) phenomenon. The data used to develop these models were obtained from 11 crop seasons, distributed among six regions of Paraná and twelve regions of Mato Grosso which was determined by the National Institute for Space Research (INPE). The three-dimensional model was obtained from linear and quadratic polynomial regression analyses, considering the following climatic variables as independent (Y axis): Rainfall (PP), Standardized Precipitation Index (SPI), Southern Oscillation Index (SOI) and Temperature on the sea surface (SST Niño 3.4). The independent variable (X axis) was the number of occurrences of rust in the off-season, and the dependent variable (Z axis) was defined as rust occurrences during the season, which were reported by the Anti-rust Consortium. The best model that explains the epidemic of the disease during the season in Paraná state was composed by Rainfall or SST Niño 3.4 variable as the Y axis. The best model for Mato Grosso state used SST Niño 3.4 or SOI variable. The variable number of occurrences in the off-season significantly influenced the model, indicating the potential use of this variable and meteorological variables on a macro scale to predict epidemics even before the start of the season.


Introduction
Brazilian soybean production in the 2017/18 season has been estimated in 114.96 million tons, sowned in an area of approximately 35 million hectares.Paraná and Mato Grosso states were responsible for approximately 45% of total production of Brazil, which correspond to 50.7 million tons, averaging 3,407 kg ha -1 (CONAB, 2018).High productivity is linked to disease control.Asian soybean rust (ASR), caused by Phakopsora pachyrhizi Syd.& P. Syd, is the main soybean disease in Brazil (Godoy et al., 2016).
The pathogen is considered an obligate parasite requiring the presence of a living host.Brazil established a period in which the cultivation of soybean is prohibited as an alternative attempt to reduce the inoculum and minimize the risks of the disease.Despite of management strategies, soybean rust epidemics has been occuring constantly in Brazil. Godoy, Bueno, and Gazzieiro (2015) reported that the presence of voluntary plants from fallen grains during harvesting could contribute to the maintenance of inoculum in production areas in the "off-season" period.The emergence of epidemics from this inoculum is mainly related to climatic factors such as rain, which provides favourable conditions for infection and disease progression (Del Ponte, Godoy, Canteri, Reis, & Yang, 2006).
winter in the second year.The cold phase (La Niña) presents precipitation below normal in the spring and early summer (Berlato, Farenzena, & Fontana, 2005).
Forecasts of epidemics can be performed based on meteorological variables (Del Ponte & Esker, 2008;Tao et al., 2009).One example is the monitoring of changes in climatic conditions and use of computing platforms that generate risk maps of epidemics.Usually, these forecasting models are based on meteorological variables such as relative humidity above 90% and air temperature to estimate the duration of the wet period (Canteri, Del Ponte, Godoy, & Tsukahara, 2007;Reis, 2004).However, according to Reis (2009), these types of models do not consider the amount of initial inoculum, which can significantly alter forecasts.One way to estimate the amount of initial inoculum for biotrophic fungi would be to monitor the reported cases of the disease the "off-season".In Brazil, the Asian Soybean Rust Consortium-CAF (http://www.consorcioantiferrugem.net) is the main project that provides information on the occurrence of soybean rust throughout the national territory as a way to reduce yield losses causes by ASR.The consortium information is provided by network laboratories and researchers in the main growing regions (Asian Soybean Rust Consortium, 2015).
This study aimed to propose mathematical models to predict the occurrence of soybean rust epidemics in soybean crop based on both the number of occurrences in the off-season in the states of Mato Grosso and Paraná and the following climate indices: the inter-annual variability of rainfall, accumulated precipitation, standardized precipitation index (SPI), southern oscillation index (SOI) and temperature index at the sea surface (SST).

Meteorological Data
Mathematical models to explain ASR epidemics for Paraná State were developed using meteorological data on the ENSO phenomenon, the main source of inter-annual climate variability that is responsible for changes in the global atmospheric flow (Kousky, Kayano, & Cavalcanti, 1984;Kousky & Cavalcanti, 1984).The effects of ENSO in Brazil can be observed in the northern part of the Northeast and in the South.In the South, the warm phase (El Niño) generally provides excess rainfall during the spring of the first year and then at the end of fall and beginning winter in the second year.In the cold phase (La Niña), precipitation is below normal in the spring and early summer (Berlato, Farenzena, & Fontana, 2005) The average accumulated precipitation (mm) was calculated with the standardized index of precipitation (SPI) value to the timescale of three months (quarter), from January 1981 to 2015, covering 124 quadrants (2.5° × 2.5° latitude and longitude).The quadrants were contained within regions 68, 69, 70, 71, 80, 81, 82, 89, 90, 91 and 98 for Mato Grosso State (Figure 1A) and regions 111, 112, 113, 115, 116 and 117 for Paraná State (Figure 1B) and (Inpe, 2015).This same division into six regions for the State of Paraná and 12 regions for the State of Mato Grosso guided all other data collection and calculations in preparation for this study.

Asian S
The inform obtained f the season is containe quarters, (January-F MJJ (May October), "off-seaso and JAS w

Statistics and Data Analysis
The coefficients used in the models are independent variable "X" (occurrence of soybean rust in the "off season" period) with independent variable "Y" (climatic variables in the "Season" period) and their effects on the occurrence of soybean rust in the "Season" period for math constant different and equals zero.
The best models for Paraná state describes were represented by the average quarterly values of the climate variability index SST Niño 3.4 Season (R 2 = 0.87).The 3D models are useful to explore the relationship between variables and to define predictive variables of major importance (Canteri & Godoy 2005;Igarashi, França, Aguiar e Silva, Igarashi, & Abi Saab, 2016).
The outcomes of Paraná state developed models (Table 1) presented a high correlation of climate variables for linear and quadratic polynomial regression for both mathematical constants.The SPI-3 climate variable had the highest coefficient of determination (R 2 ), which was equal to 0.78, and was significant (p < 0.01) when used in a linear polynomial regression with a constant of zero.For non-zero values, the season precipitation variable had a higher R 2 (0.87).The other climate variables presented an R 2 between 0.72-0.77and were significant (p < 0.01).The linear regression model was the preferred model to present the highest and lowest p-value of R 2 , which in this case happened to be the climate variable of rainfall in the "season" period.
The models for Mato Grosso state also presented a high correlation of climate variables for linear and quadratic polynomial regression for both mathematical constants, however, the higher correlation was observed for SOI-3 Season and SST Niño 3.4.The variables of the season rainfall and SST Niño 3.4 Season presented the highest R 2 index for a quadratic polynomial regression, which 0.87 and 0.96 for Paraná and Mato Grosso, respectively (Table 2).

Discussion
The results confirmed the influence of rainfall on the epidemic (Tsukahara, Hikishima, & Canteri, 2008;Del Ponte & Esker, 2008;Megeto, Oliveira, Del Ponte, & Meira, 2014).However, considering the off-season period, the amount of initial inoculum also explains the positive effects on the season period.The results also showed that the regressions using several cases in the off-season (initial inoculum) other than zero showed higher coefficients of determination, which better explains the number of cases that occurred during the season.The Figure 2 suggesting which the increase of occurrence in the season was directly influenced by the off-season occurrence.The increased focus on the number of ASR occurrences in the off-season is justified because it will enable development of possible models for predicting the disease.
Problems in the estimation of the initial inoculum may underestimate or overestimate the epidemic.Campbell and Madden (1990) noted that the amount of the initial inoculum is a limiting factor for the evolution of the epidemic.Berger (1981) worked with disease simulation models and mentioned that the accuracy and precision of the models at the end of the epidemic was influenced by the amount of the initial inoculum estimated at the beginning of the calculations.Upper and Pfender (2015) developed a disease simulation model and estimated the initial inoculum from subsequent observations when the first symptoms were detected.
Most forecasting models use only environmental factors; these usually include hours of wetness and temperature, considering that the pathogen and host (the other vertices of the triangular disease), are always present (M.C. Alves, Pozza, Costa, Carvalho, & L. S. Alves, 2011).In addition, the models usually not consider factors such as leaf age and susceptibility (Xavier, Martins, Fantin, & Canteri, 2017) and plant nutrition (Gaspar et al., 2015).The present study demonstrated that the presence of inoculum (the pathogen vertex) exerts a great influence on epidemics during the season.
According to Aylor (1986), setting the arrival date of the inoculum is the main problem in the air transport of fungal spores because often, the disease cannot be observed until the pathogen has suffered one or more spore production cycles.If the initial inoculum pressure is light and the pathogen latency period is over, the disease may not be displayed until one or two weeks after the arrival of the inoculum.
Esker et al. ( 2007) noted that the forecast models have a limited ability to correctly estimate the presence and concentration of inoculum that will start epidemics.The authors concluded that although forecasting models are available, they still cannot function without monitoring of the spread of the disease or disclosure of outbreaks; these models also show the inoculum presence on site for real-time assessment of the disease.
In the case of P. pachyrhizi, a biotrophic pathogen, there are two possibilities for completing the pathogen vertex at the beginning of the season; the fungus either remains in host plants in the same region or comes from other regions by air.Pivonia, Yang, and Pan (2005), citing Hamilton and Stakman (1967), studied the second hypothesis for the wheat rust pathosystem.The authors observed that the time of the first disease occurrence over a number of years presented a gradual south to north occurrence.The calculated daily disease front movement from Texas to North Dakota was approximately 30 km/day.Isard et al. (2011), working with the dispersal of P. pachyrhizi spores to the interior of the North American continent using collectors, cited the low potential for transport over long distances.According to Pivonia, Yang and Pan (2005), P. pachyrhizi urediniospores are coarse particles that obey the laws of gravity or rapid sedimentation or settling to the surface once released into the atmosphere.Thus, they cannot travel long distances close to the surface within the mixed boundary layer (MBL, which is when the atmosphere is influenced by surface heat exchange and turbulent mixing) (Krupa et al., 2006).For regions where host is not present during throughout year the main source of inoculum depends on spore dispersion over long distances (Pivonia, Yang, & Pan, 2005).Already in regions where it is possible Minchio, Canteri, Fantin and Aguiar e Silva (2016) suggest that the presence of host plants in the area or in nearby areas during the off-season is one of the main responsible sources of epidemic of ASR.
Thus, evidence indicates that the variable number of occurrences in the off-season significantly influenced the model, indicating the potential use of this variable and meteorological variables on a macro scale to predict epidemics even before the start of the season jas.ccsenet.

Table 1 .
Coefficients of determination (R 2 ) and p-values for linear and quadratic polynomial regressions released by soybean rust occurrence in the season, off-season and climatic variables collected between 2004 and 2015 in state of Paraná, Brazil

Table 2 .
Coefficients of determination (R 2 ) and p-values for linear and quadratic polynomial regressions released by soybean rust occurrence in the season, off-season and climatic variables collected between 2004 and 2015 in state of Mato Grosso, Brazil