An Influence Diagram for Management of Mildew in Winter Wheat Allan Leck Jensen Danish Informatics Network in the Agricultural Sciences Research Center Finn Verner Jensen Department of Computer Science Aalborg University -presented by Bingyu Zhu and Sen Xu

Abstract A prototype of a decision support system for management of the fungal disease powdery mildew in winter wheat A prototype of a decision support system for management of the fungal disease powdery mildew in winter wheat An influence diagram which is used to determine the optimal time and dose of mildew treatments An influence diagram which is used to determine the optimal time and dose of mildew treatments Practical and theoretical problems during the construction of the influence diagram, and also the experience with the prototype Practical and theoretical problems during the construction of the influence diagram, and also the experience with the prototype

Background In Denmark, environmental impacts of agricultural production must be reduced. In Denmark, environmental impacts of agricultural production must be reduced. Findings of pesticides and nitrogen residues in drinking water have induced the government to take actions for a significant reduction of the consumption of fertilizers and pesticides. Findings of pesticides and nitrogen residues in drinking water have induced the government to take actions for a significant reduction of the consumption of fertilizers and pesticides.

Dilemma of farmers Agricultural input factors: fertilizers and pesticides—very expensive Agricultural input factors: fertilizers and pesticides—very expensive Reductions in these input factors can cause inadequate effects and hence economical losses Reductions in these input factors can cause inadequate effects and hence economical losses Farmers: apply excessive amounts of input factors to avoid inadequate effects of input factors. Farmers: apply excessive amounts of input factors to avoid inadequate effects of input factors.

How to solve … Reduce the consumption of input factors and save money if they can get the recommendations that when it is safe to reduce the doses. Reduce the consumption of input factors and save money if they can get the recommendations that when it is safe to reduce the doses. These recommendations could come from decision support systems These recommendations could come from decision support systems Insurance farming  Precision farming Insurance farming  Precision farming

Decision Support System MIDAS – Mildew Influence Diagram for Advice of Sprayings. MIDAS – Mildew Influence Diagram for Advice of Sprayings. Influence diagram: Case-specific recommendations of timing and dosage of mildew treatments. Influence diagram: Case-specific recommendations of timing and dosage of mildew treatments. The Ph.D. thesis can be downloaded from

The Disease-Powdery Mildew Weather condition—temperature, humidity and wind Weather condition—temperature, humidity and wind Under favorable conditions Under favorable conditions –Spread rapidly Under unfavorable conditions Under unfavorable conditions –Not spread, the present disease may disappear with time due to the emergence of new, uninfected leaves and the death of old, infected leaves

MIDAS Based on the field observations and the expectations to the future Based on the field observations and the expectations to the future Determine the optimal treatment decision for the current disease problem Determine the optimal treatment decision for the current disease problem Assumption: all future decisions will be made optimally according to the available information at the time Assumption: all future decisions will be made optimally according to the available information at the time

Decision Optimization Affected by uncertainty of Affected by uncertainty of –Stochasticity Weather and disease infections with elements of unpredictability Weather and disease infections with elements of unpredictability –Inaccurate observations Field recordings of disease level are difficult and error prone Field recordings of disease level are difficult and error prone –Incomplete knowledge Interpretations of relations in domain involves uncertainty Interpretations of relations in domain involves uncertainty

Dynamic Influence Diagram A sequence of time steps. A sequence of time steps. Each time step Each time step –Information variables –A single treatment decision variable –Chance variables Time is an important parameter Time is an important parameter

Variable types Static information Winter wheat variety, Soil type, Nitrogen fertilization strategy, Plant density Dynamic information Weather, Disease incidence, Remaining time to harvest, Cost of fungicide and spraying, Label dose of fungicide, Expected price of grain and yield Decision Dose of treatment (0 possible) Utilities Value of yield, Cost of treatment, Value of disease induced yield loss

Thermal Time Scale Three influentials Three influentials –Chronological time –Temperature –Crop development stage Thermal time scale Thermal time scale –Definition: The expected temperature sum remaining to crop maturity –Divided into thermal time periods, each corresponding to a time step of the decision model. –Length of a time step is called a thermal week. –Farmers give their estimates of the number of weeks to crop maturity

The Initial Influence Diagram GDM module GDM module Case-specific time step modules Case-specific time step modules Decision model Decision model TnTn Ti Time Fiel d T2T2 T1T1 T2T2 T1T1 TnTn

The GDM module

Dynamic Programming First, the final decision is considered First, the final decision is considered For each information scenario at that time, the decision alternative with optimal expected utility is determined. For each information scenario at that time, the decision alternative with optimal expected utility is determined. The preceding decisions are considered in reverse order, and each of them is optimized under assumption of optimal decision making in the future. The preceding decisions are considered in reverse order, and each of them is optimized under assumption of optimal decision making in the future.

Computation Complexity Problem The set of information scenarios at the time of a decision consists of all configurations of observed variables which are d-connected to a utility node influenced by the decision. The set of information scenarios at the time of a decision consists of all configurations of observed variables which are d-connected to a utility node influenced by the decision. DiseaseLevel in initial GDM DiseaseLevel in initial GDM the current state of the disease depends on not only the current value of DiseaseObser, but also all the previous, together with all previous treatment decisions.

Information Blocking Condition The local information of the system overwrites all previous information. The local information of the system overwrites all previous information. P(Y | I k, D k, X) =P(Y | I k, D k ) P(Y | I k, D k, X) =P(Y | I k, D k ) for X є U T i (i=1,…,k-1), for X є U T i (i=1,…,k-1), Y є U T i (i=k+1,…,n). P(Y | T k, X) =P(Y | T k ) P(Y | T k, X) =P(Y | T k )

Change the structure DiseaseObserv_1 DiseaseLevelB_1DiseaseLevelA_1 DiseaseObserv_1 DiseaseLevelB_1DiseaseLevelA_1 Figure3: Left: The initial causal structure of the relationships between the DiseaseObserv and the DiseaseLevel nodes. Right: The modified structure to achieve a blocking of the past by the observed nodes(DiseaseObserv).

A Decision Model with 3 Time Step

Experience--Quantitative Single model clique size probabilities, for each additional time step. Single model clique size probabilities, for each additional time step. 1.6 Million for a model with 20 time steps, 14.8M to store. 1.6 Million for a model with 20 time steps, 14.8M to store. Performance on SUN Performance on SUN Assemblage 1 sec Compilation 100 secs Loading 25 secs Propagation 25 secs

Experience--Qualitative Evaluation of the predictions of DiseaseLevel Evaluation of the predictions of DiseaseLevel True and Approximate Structures True and Approximate Structures –True structure are good. –Approximate Structure less satisfactory underestimate high disease levels and overestimate low disease levels. –Predicted probability distributions are too narrow. –DiseaseObserv was intended to be a simple measure for DiseaseLevel.

Future Work--Improvement Several Different Prior Distribution for P(DLB) in order to fit actual situation. Several Different Prior Distribution for P(DLB) in order to fit actual situation. Additional information node introduced, in order to improve the calibration of DeseaseLevel. Additional information node introduced, in order to improve the calibration of DeseaseLevel. Relaxation of the information blocking condition. Relaxation of the information blocking condition. Approximative for decision, true for reasoning. Approximative for decision, true for reasoning. Other problems. Other problems.