Field history data were taken from two previous studies. The data include the field histories and resistance status of black-grass of 98 fields from the Hohenlohe area in Germany (Herrmann, 2016; Lepke et al., 2020) and of 131 fields from the Champagne area in France (Lepke et al., 2024). Predictor variables comprise crop rotation, number of crops, seeding date, soil cultivation, and herbicide applications. There are 20 predictors ( Table 1 ). The Hohenlohe data include soil properties, which were not recorded in the French study. An additional predictor management diversity was devised, which is an index for the diversity of A. myosuroides management (Herrmann, 2016). This variable considers the number of different measures specific for weed control within a year. These comprise delayed seeding, ploughing, summer crops, and the use of multiple modes of action. If a measure is applied, the respective score takes the value of 1; otherwise, the value of 0. If all measures are applied, the maximum value of management diversity is 4; if none is applied, the score is 0. The index ranges therefore between 0 and 4. For example, in winter wheat, using two modes of action (score 1) and ploughing (score 1) results in a management diversity value of 2, while shallow tillage (score 0) and only one mode of action (score 0) give a management diversity value of 0. Management diversity values are averaged for the time frame of the 6 years (6 yrs) being considered.

A descriptive data analysis was performed to ensure that the datasets of both countries have a similar structure (Lepke et al., 2020, 2024). There are only slightly different management practices concerning late seedings and summer crops. In France, herbicides that are specific for A. myosuroides are applied more frequently than in Germany. In both regions, non-inversion tillage is common. The correlation structures of the predictor variables are similar for both datasets of A. myosuroides (Lepke et al., 2020). Climatic conditions are slightly different in the two regions; mean temperature and precipitation are slightly higher in the Champagne than in the Hohenlohe region.

The field data used in this paper were obtained from previous studies (Herrmann et al., 2016; Lepke et al., 2024). A. myosuroides samples were harvested by walking every second tractor track and monitoring two borders of the field. It was ensured that only one ear per plant was sampled. Resistance status was established by greenhouse biotests with collected seeds and subsequent genetic analysis of the seedlings to determine target site resistance and analytics to determine metabolic resistance when appropriate for the samples from Champagne and Hohenlohe (Lepke et al., 2020, 2024; Beffa et al., 2012). Fields were classified as resistant if target-site resistance or metabolic resistance or both were detected in the samples and/or survivals were observed in the greenhouse. More than 95% of the samples showed the presence of target site resistance. Therefore, the model was focused on target site resistance risk evolution. The stochastic process of the assessment of the resistance status is part of the model.

For a classification problem with 20 predictor variables, partly correlated samples, and small sample sizes, the RF method (Breiman, 2001) is the most convenient. All calculations were carried out by the R Project for Statistical Computing (R Core Team, 2018; R-package‚ ‘random forest’, 2018). In all analyses, the data were split into training data (75%) and test data (25%). To test which predictor variables have a significant impact on the response, importance measures were analyzed. Usual importance measures are the Gini index, the mean decrease accuracy index, and the area under the receiver operating characteristic curve (AUC) (Hastie et al., 2017). RF outcomes are random due to random sampling of training data points when building trees and the random selection of subsets of features considered when splitting nodes. Therefore, the evaluation of feature importance based on a single run is not reliable especially if predictor variables are correlated. To assess the importance of prediction variables, RF analyses were performed for each dataset separately with the usual random splitting of training and test data with a ratio of 75% and 25%, respectively. Statistics of performance measures were generated by 50 simulation runs respectively.

Figure 2 shows the graphical user interface of the model. The user may select among seven herbicides or group of herbicides, application rates, and application period among 14 crops and soil cultivation for each year. In addition, parameters for the random feature of such random seeds and variation coefficients can be chosen. The model output comprises time series of the portion of resistant seeds, weed density, and others (see Figure 3 ). Figure 3B presents the results of a sampling for resistance (0: no resistance detected, 1: resistance confirmed). The figure shows what can happen in the worst case, when always the same herbicide (here ALS inhibitor) and the same crop are chosen. Until year 6 to 7, the seedbank is decreasing. From year 7 onward, a sharp rise in resistant weeds occurs. Resistance is confirmed only in year 9. Under a management scheme with a high degree of diversity, i.e., frequent change of mode of action and crop rotation ( Figure 4 ), resistance development is delayed during the simulation period.

The field data are taken from previous studies (Lepke et al., 2024). The MM data were obtained from the model described above. These were generated in accordance with the field history data over a period of 6 years. In addition, simulations were performed with time horizons greater than 6 years, showing that under some management schemes, resistance in development was too low to be detected after 6 years but only later. Therefore, some datasets were generated with a simulation time of 8 years. Because of the random features in the model, identical management scenarios were repeated several times. Resistance status was determined by taking a random sample of five weed plants at the end of the simulation period and the field was classified as resistant if at least one of the plants was found to be resistant. Further datasets were generated with the pure deterministic model and on the model with all stochastic features described above. As usual, model data were split into a training sample (75%) and into a prediction sample (25%). It turned out that the model dataset obtained for an 8-year simulation period with stochastic features gave the best results. Further analyses were therefore performed with this dataset.

The final question remains: which predictions are better, those based on real datasets only or those based on model data. This question is answered in Figure 5 where performance criteria are compared for five combinations of training and test data: test data model generated (1); training data model generated (2); training data model generated and test data GER and FRA combined (3); training data model, test data FRA, training data model, and test data GER (4); and finally test and training data combined GER and FRA data (5).

With the exception of combination (1), mean accuracies range between 75% and 80%. It is interesting to note that all predictions based on model data have lower variations than predictions based on real data. AUC values exhibit large variation for all combinations. In those combinations with real data as test sets, type II errors are lower than type I errors, i.e., false-positive classifications are more frequent. There are two possible explanations:

The misclassified sensitive field has features similar to the features of resistant fields, but resistance has not developed as yet or has not been found in the plant samples.

There are other factors not considered, e.g., soil properties and weather patterns.

Statistics of performance measures were generated by 50 simulation runs respectively (cf. methods). Table 3 shows the frequencies of prediction variables falling into the group of the nine highest-ranked importance measures in 50 RF runs with randomly split training and test datasets for the two cases considered. It turns out that the prediction variables Alomy group 2 (B), the index management diversity, ploughing, and the proportion of late seeding are among the most frequent common ranks for combinations of training and datasets.