A Bayesian Probability Model Can Simulate the Knowledge of Soybean Rust Researchers to Optimize the Application of Fungicides

Asian﻿rust﻿is﻿the﻿main﻿soybean﻿disease﻿in﻿Brazil,﻿causing﻿up﻿to﻿80%﻿of﻿yield﻿reduction.﻿ The﻿use﻿of﻿fungicides﻿is﻿the﻿main﻿form﻿of﻿control;﻿however,﻿due﻿to﻿farmer’s﻿concern﻿ with﻿ outbreaks﻿ many﻿ unnecessary﻿ applications﻿ are﻿ performed.﻿ The﻿ present﻿ study﻿ aims﻿to﻿verify﻿the﻿usefulness﻿of﻿a﻿probability﻿model﻿to﻿estimate﻿the﻿timing﻿and﻿the﻿ number﻿of﻿fungicides﻿sprays﻿required﻿to﻿control﻿Asian﻿soybean﻿rust,﻿using﻿Bayesian﻿ networks﻿and﻿knowledge﻿engineering.﻿The﻿model﻿was﻿developed﻿through﻿interviews﻿ with﻿rust﻿researchers﻿and﻿a﻿literature﻿review.﻿The﻿Bayesian﻿network﻿was﻿constructed﻿ with﻿the﻿GeNIe﻿2.0﻿software.﻿The﻿validation﻿process﻿was﻿performed﻿by﻿42﻿farmers﻿and﻿ 10﻿rust﻿researchers,﻿using﻿28﻿test﻿cases.﻿Among﻿the﻿28﻿tested﻿cases,﻿generated﻿by﻿the﻿ system,﻿the﻿agreement﻿with﻿the﻿model﻿was﻿47.5%﻿for﻿the﻿farmers﻿and﻿89.3%﻿for﻿the﻿ rust﻿researchers.﻿In﻿general,﻿the﻿farmers﻿overestimate﻿the﻿number.﻿The﻿results﻿showed﻿ that﻿the﻿Bayesian﻿network﻿has﻿accurately﻿represented﻿the﻿knowledge﻿of﻿the﻿expert,﻿and﻿ also﻿could﻿help﻿the﻿farmers﻿to﻿avoid﻿the﻿unnecessary﻿applications.

The present study aims to verify the potential for using a probability model constructedwithexpertknowledgetoestimatetheneedforfungicidesandthenumber of applications required to control ASR using the formalism of Bayesian networks andknowledgeengineering.
Subnetwork 2 (Figure 1 and Table 2) is intended to simulate the decision of the expert "A" in relation to the additional fungicide applications, that is, the applicationsperformedbecausetheprotectionperiodofthefirstapplicationends.Thetablesofconditionalprobability(TCPs)fortheothervariablesindicatethe values determined by experts A, B, C, and D during the interviews in which they described expectations based on their experiences.Tables 4a, 4b, and 4c show the TCPsforthevariablesA1,A2,andA3.Theothernodesdevelopedforthenetwork-withtheexceptionofMS,D12,andD23-werealsoprobabilistic.
AssumingtheBayesiandecisionruleofmaximumposteriorprobability,the decisionreportedbythesystemindicatedtheperformanceofthefirstfungicide application, in accordance with the choice of the expert.The results can be explained by the combination of the evidence of rain (Del Ponte et al., 2006;Tsukahara, et al., 2008), leaf moisture (Igarashi et al., 2014), andinoculum (Minchioetal.,2016).

CONCLUSION
Based on what has been stated, it can be concluded that the Bayesian network systemsimulatesexpertknowledgetoassistindecisionmakingregardingtheneed forfungicideapplications.Consideringthatthenumberoffungicideapplicationsis generally overestimated, the system has potential to reduce environmental damage causedbytheexcessiveuseoffungicidesandtogeneratesavingsforproducersdue reducedunnecessaryapplications.

CONFLICT OF INTEREST
Theauthorshavenoconflictsofinteresttodeclare.

Figure 1 .
Figure 1.Graph of a Bayesian network (subnetwork 1 and 2) model obtained from an expert to estimate fungicide applications to soybean crops to control Asian rust

Figure 2 .
Figure 2. Algorithm with the logic for the representation of the values used in the Bayesian network model for estimating fungicide application to soybean crops to control Asian rust

Figure 3 .
Figure 3. Probabilities for A1 variable (first application of fungicide), given the evidence for R (rain) and IP (inoculum coming from Paraguay), for the Bayesian network model for estimating the fungicide application to soybean crops to control Asian rust

Table 1 . Variables of the Bayesian model for estimating fungicide application to soybean crops to control Asian rust, subnetwork 1
subject to quantification of their values.The variables WF, R, ONP, VM, SCT, PS, PF, SP, FA, SS, WR, FR, OP,andACwerenotinfluencedbyanyothervariablein themodel.Thea prioridistributionsforthesevariableswereassumedtobeuniform becausetheprototypewasnotdevelopedforuseataspecificlocationoronaspecific

Table 4 . Conditional probability for the (a) first application, (b) second application, and (c) third application variables for the Bayesian network model for estimating fungicide application to soybeans to control Asian rust
ValidationTheBayesiannetworkfordefiningfungicideapplicationtocontrolAsianrustwas testedandvalidatedforthestateofParanáinthesouthernregionofBrazilusingthe 2013 knowledge of fungicide application.The Bayesian model test was performed with42farmersand10ASRresearchers.Thetestwascomposedoftestcases,which represent the conditions or situations (i.e., rain, detection of Asian rust) used for decisionmakingregardingfungicideapplication.

Table 5 . Table of conditional probability (TCP) for the "maturation stage" (MS) variable for the Bayesian network model for estimating fungicide application to soybeans to control Asian rust
value that represents the probability of reaching the R6 stage, even without the presence of all of the evidence.untilR6:theplants in the phenological stage by R6 (EMBRAPA, 2013).fromR6Onward: the plants in the phenological stage in or after R6(EMBRAPA, 2013).