## 3 Results and Discussion
### Evaluation of Model Performance  
Predicting tools dedicated to supporting systems of postharvest grain preservation and storage are highly promising and essential to maintain the quality of this raw material and nutritional safety of cereal-based products. Previous research has shown that hybrid models using genetic algorithms have been successful in optimizing and modeling complex non-linear natural growth and developmental processes [46; 55; 56; 57]. This study is a new modeling approach and focuses on predicting the population level of fungi that contaminate cereal ecosystems using a mathematical model, which is a hybrid of the B-spline technique and genetic algorithms. The use of both of these techniques in research facilitates the elaboration of a model in which the coordinates of the control point shaping the B-spline were related to the storage conditions of the considered malting barley ecosystems. The computerized values of learning and validation errors obtained in the simulations indicated good prediction quality of the elaborated model. Nevertheless, for a more detailed assessment of the model efficiency, the statistical indicators recommended for predictive model evaluation have also been calculated. The comparison of the model responses with the observations presented in Figure 5 proves a high correspondence of the analyzed data. The RMSE and MAE values also indicate a high agreement between model predictions and experimental fungal CFU levels in barley ecosystems (Table 6). The high efficiency of the developed model was also confirmed by the values of bias indexes (B\({}_{\text{f}}\) and MRPE), designating that the negative and positive distinctions of the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Statistical Indices**} & \multicolumn{3}{c}{**DATASET**} \\ \cline{2-4}  & **Learning** & **Validation** & **Full** \\ \hline Number of experimental points (N) & 201 & 63 & 264 \\ Coefficient determination (R\({}^{2}\)) & 0.944 & 0.916 & 0.938 \\ Mean absolute error (MAE) & 0.208 & 0.210 & 0.209 \\ Root mean square error (RMSE) & 0.278 & 0.247 & 0.276 \\ Bias factor (B\({}_{\text{f}}\)) & 0.996 & 1.009 & 0.999 \\ Mean relative percentage error (MRPE), (\%) & \(-0.162\) & \(-1.058\) & \(-0.048\) \\ Accuracy factor (A\({}_{\text{f}}\)) & 1.041 & 1.040 & 1.041 \\ Mean absolute percentage error (MAPE), (\%) & 4.000 & 4.000 & 4.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical indicators used to evaluate the performance of the developed model to assess the mycological state of malting barley grain with a\({}_{\text{w}}\) = 0.78–0.96 stored at T = 12–30 \({}^{\circ}\)C.  
Figure 5: The comparison of fungi population levels in malting barley ecosystems with a\({}_{\text{w}}\) = 0.78–0.96 stored at temperature 12–30 \({}^{\circ}\)C estimated by the model Log(CFU\({}_{\text{M}}\)) and experimental data Log(CFU\({}_{\text{E}}\)) taken from [PERSON] et al. [47]. model are almost equal. A negative MRPE value suggests that the model slightly tended to overestimate the level of mold in the examined grain. However, in the case of the growth of microorganisms, this can be considered as an increase in the safety of the model in its practical application. A slight overestimation of the model (which is a model of quality degradation) is not limitative [58] and means that its outputs are slightly higher than the actual levels of grain contamination with fungi, which can allow to react in time and avoid risky situations. The accuracy factor and mean absolute percentage error values presented in Table 6 are convergent and indicate that the model prediction error is about 4%. The results are comparable with those obtained in the case of models based on artificial neural networks (ANN) and the kinetic equation in the form of the modified Gompertz equation that were developed for the same data describing the level of fungal infection in barley ecosystems [24; 39].