# Comparison of Three Modelling Approaches for Predicting Deoxynivalenol Contamination in Winter Wheat

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^{st}International MYCOKEY Conference: Advances on Mycotoxin Reduction in the Food and Feed Chain)

## Abstract

**:**

**Key Contribution:**Cross-validation of the three modelling techniques was done to further understand the advantages and disadvantages of each technique, and contribute to future research and progress in the prediction of mycotoxin contamination in food and feed. Adapting a mycotoxin forecasting model that was developed for certain agronomic and weather conditions to other conditions should always be done with the utmost care and proper model testing and validation.

## 1. Introduction

## 2. Results

#### 2.1. Mixed Effect Logistic Regression Model

#### 2.1.1. Model C (for Farmers W0–W4)

#### 2.1.2. Model D (for Collectors W0–W6)

#### 2.2. Bayesian Network Model

#### 2.3. Mechanistic Model

#### 2.4. Validation of Three Models

## 3. Discussion and Conclusions

## 4. Materials and Methods

#### 4.1. Data

- W0: FD − 24 1 pm to FD − 17 12 am,
- W1: FD − 17 1 pm to FD − 10 12 am,
- W2: FD − 10 1 pm to FD − 3 12 am,
- W3: FD − 3 1 pm to FD + 4 12 am,
- W4: FD + 4 1 pm to FD + 11 12 am,
- W5: FD + 11 1 pm to HD − 3 12 am,
- W6: HD − 3 1 pm to HD + 4 12 am

- Tavg: Average hourly temperature in the time window (°C)
- Tmin: Minimum hourly temperature in the time window (°C)
- Tmax: Maximum hourly temperature in the time window (°C)
- P: Sum of the precipitation in the time window (mm)
- RHh80: Number of hours that relative humidity was higher than 80% (hour)
- Th25: Number of hours that temperature was higher than 25 °C (hour)

#### 4.2. Mixed Effect Logistic Regression Model

^{th}subset was used to test the model’s performance. This process was repeated 10 times, every time with a different test subset. So, all of the records were used for both training and testing, and each record was used for validation once. The mean area under the curve (AUC) was calculated.

#### 4.3. Bayesian Network Model

#### 4.4. Mechanistic Model

#### 4.5. Validation of Three Models

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Mean receiver operating characteristic (ROC) curves for 10-fold cross-validation of Model C class low/medium (

**a**), and Model C class medium/high (

**b**).

**Figure 2.**Mean receiver operating characteristic (ROC) curves for 10-fold cross validation on the Model D medium/high class.

**Figure 3.**The Bayesian network model structure resulting from learning the model with field data collected during 2001–2013 in the Netherlands. Circles represent nodes of the Bayesian network model, and arrows indicate the relationship/conditional dependencies among the nodes. Tavg_W0–W4: average temperature in the time windows W0 to W4; Tmax_W0–W4; maximum temperature in the time windows W0 to W4; Tmin_W2–W3: minimum temperature in the time window W2 to W3 ; RHh80_W1: number of hours that relative humidity is higher than 80% in the time window W1; Th25_W0–W5: number of hours that average temperature is higher than 25°C in the time windows W0 to W5; Spray_freq: frequency of fungicides application around wheat flowering for controlling Fusarium head blight; FD: flowering date; HD: harvesting date.

**Figure 4.**Observed deoxynivalenol (DON) concentrations in mature winter wheat in the Netherlands, 2001–2011, 2013, and 2015–2016. The midline (bold) of the box represents the median of the data, with the upper and lower limits of the box being the third and first quartile (75

^{th}and 25

^{th}percentile), respectively. The whiskers extend 1.5 times the interquartile range, from the top/bottom of the box to the furthest value within that distance. Data beyond that distance are represented individually as outliers (black circles). The box width is proportional to the square roots of the number of observations in that year. In all of the samples from 2006, the DON concentration was below the (highest) limit of quantification (100 µg/kg).

**Figure 5.**Simplified relational diagram of the Fusarium head blight (FHB) model predicting the probability of DON contamination in wheat. T = temperature; WD = leaf wetness duration; RH = relative humidity; GS = wheat growth stage; a

_{w}= water activity; R = rainfall. Triangles: equations; Black circles: data inputs.

**Table 1.**Model C performance comparing predicted deoxynivalenol (DON) contamination classes versus observed DON classes (N = 625). 81.8% are correctly classified, 3.5% are overestimated, and 14.7% are underestimated by Model C.

Confusion Matrix | DONclass | Predicted | ||
---|---|---|---|---|

Low | Medium | High | ||

Observed | Low | 471 | 10 | 6 |

Medium | 70 | 5 | 6 | |

High | 17 | 5 | 35 |

**Table 2.**Model D performance comparing predicted DON contamination classes versus observed DON classes (N = 625). 81.4% are correctly classified, 3.4% are overestimated, and 15.2% are underestimated by Model D.

Confusion Matrix | DONclass | Predicted | ||
---|---|---|---|---|

Low | Medium | High | ||

Observed | Low | 469 | 11 | 7 |

Medium | 70 | 8 | 3 | |

High | 18 | 7 | 32 |

DONclass | ||||
---|---|---|---|---|

Low | Mid | High | ||

GArea | Green | 0.835 | 0.117 | 0.048 |

Yellow | 0.677 | 0.175 | 0.148 | |

Red | 0.363 | 0.050 | 0.587 |

**Table 4.**Bayesian network model performance comparing predicted DON contamination classes versus observed DON c classes (N = 625). 82.8% are correctly classified, 7.7% are overestimated, and 9.4% are underestimated.

Confusion Matrix | DONclass | Predicted | ||
---|---|---|---|---|

Low | Medium | High | ||

Observed | Low | 444 | 29 | 14 |

Medium | 45 | 31 | 5 | |

High | 8 | 6 | 43 |

**Table 5.**Coefficients for discriminant variables in each canonical function (F1) used to classify the DON contamination (N = 625 samples) based on the mechanistic model output using Fusarium head blight (FHB)-tox, ResisL, and GArea as discriminant variables.

Discriminant Variables | Canonical Coefficient ^{1} | Standardised Canonical Coefficient ^{2} | Correlation Coefficient ^{3} |
---|---|---|---|

GArea | 1.837 | 0.905 | 0.837 * |

ResisL | 0.724 | 0.555 | 0.442 |

FHB-tox | 0.075 | 0.073 | −0.043 |

Constant | −4.429 | - | - |

^{1}Coefficients of the discriminant function. The discriminant function takes the form: F = a + b1 × GArea + b2 × ResisL + b3 × FHB-tox, where a is the constant, and bn are the canonical coefficients.

^{2}The standardized canonical coefficient is an indicator of the weight of each variable in the discriminant function.

^{3}The correlation coefficient indicates the discriminant power of each variable in each function. * indicates the largest absolute correlation between each variable and any discriminant function. Variables with correlation coefficient ≥0.3 are interpreted as important.

**Table 6.**Parameters and statistics of the equations describing the relationship between F1 and the probability of belonging to the DON contamination low or high classes.

a ^{1} | Standard Error | b | Standard Error | R^{2} | |
---|---|---|---|---|---|

Low | −1.455 | 0.009 | −0.853 | 0.007 | 0.973 |

high | 3.063 | 0.012 | 1.382 | 0.007 | 0.994 |

^{1}The regression equation was Equation (1) (see Section 4.4). a: constant; b: canonical coefficient.

**Table 7.**Mechanistic model performance comparing predicted DON contamination classes versus observed DON classes (N = 625). 76.5% are correctly classified, 2.2% are overestimated, and 18.4% are underestimated by the mechanistic model.

Confusion Matrix | DONclass | Predicted | ||
---|---|---|---|---|

Low | Medium | High | ||

Observed | Low | 478 | 0 | 9 |

Medium | 76 | 0 | 5 | |

High | 39 | 0 | 18 |

**Table 8.**Comparison of predicted versus observed DON contamination class using the 87 samples collected in the years 2015 and 2016. One sample had no information on spray frequency, and was excluded from validation of the regression models.

Predicted | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Regression Model (for Farmers) | Regression Model (for Collectors) | BN Model | Mechanistic Model | ||||||||||

Low | Mid | High | Low | Mid | High | Low | Mid | High | Low | Mid | High | ||

Observed | Low | 76 | 5 | 0 | 76 | 3 | 2 | 74 | 0 | 8 | 69 | 0 | 13 |

Mid | 3 | 0 | 0 | 3 | 0 | 0 | 3 | 0 | 0 | 3 | 0 | 0 | |

High | 2 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 1 |

**Table 9.**Pros and cons of the regression model, Bayesian network model, and mechanistic model. DFA: discriminant function analysis.

Regression Model | Bayesian Network Model | Mechanistic Model | |
---|---|---|---|

Prediction accuracy low DON | 93.8% | 90.2% | 84.1% |

Prediction accuracy medium DON | 0% | 0% | 0% |

Prediction accuracy high DON | 0% | 0% | 50% |

Possibility to apply in other conditions (e.g., countries)? | High data dependency. Only in those countries/regions with similar agricultural and weather conditions. Validation needed before its use in new agricultural contexts | High data dependency. Only in those countries/regions with very similar agricultural and weather conditions. Validation needed before its use in new agricultural contexts | Low data dependency. The model can be implemented in other countries/regions given that the fungal species are similar. The combination of model output with influencing agronomic practices in a new country/region needs calibration through a specific DFA. |

Prediction time | One week before flowering, using 10 days’ weather forecast data | From beginning of the growing season | From heading date |

Capability to predict unknown situations | No | No | Yes |

Requirement for specific data | Low | Low. Possible to combine expert knowledge with statistical relationships. | High, e.g., heading date, and leaf wetness duration. |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, C.; Manstretta, V.; Rossi, V.; Van der Fels-Klerx, H.J. Comparison of Three Modelling Approaches for Predicting Deoxynivalenol Contamination in Winter Wheat. *Toxins* **2018**, *10*, 267.
https://doi.org/10.3390/toxins10070267

**AMA Style**

Liu C, Manstretta V, Rossi V, Van der Fels-Klerx HJ. Comparison of Three Modelling Approaches for Predicting Deoxynivalenol Contamination in Winter Wheat. *Toxins*. 2018; 10(7):267.
https://doi.org/10.3390/toxins10070267

**Chicago/Turabian Style**

Liu, Cheng, Valentina Manstretta, Vittorio Rossi, and H. J. Van der Fels-Klerx. 2018. "Comparison of Three Modelling Approaches for Predicting Deoxynivalenol Contamination in Winter Wheat" *Toxins* 10, no. 7: 267.
https://doi.org/10.3390/toxins10070267