# Quantitative Characterization of _Geotrichum candidum_ Growth in Milk
## 3 Results
### Statistical Evaluation and Validation of Models  
The reliability of the predictive models used was assessed with the mathematical indices that are summarised in Table 3. Although the most common statistical index, \(R^{2}\), was higher than 0.8 in all cases of the predictions in our study, this index is primarily adequate for linear models [53]. Therefore, the suitability of the primary predictive model used was also assessed with the _RMSE_ index, which was higher in the case of \(G\). _candidum_ growth in milk with 1% NaCl in comparison with the _RMSE_ index of the model used in the predictions of the growth of the isolate in milk without salt. However, the values were still close to zero. The model is considered to be more suitable, as the _RMSE_ value is closer to zero [54].  
A similar pattern of higher _RMSE_ index values in the case of \(G\). _candidum_ growth in milk with 1% NaCl was also demonstrated in the secondary modelling. The CM showed better performance for modelling of the lag phase than for the growth rate based on the _RMSE_ indices, and the values were in the range of or lower than the values of the _RMSE_ reported by [PERSON] et al. [55], who applied extended Davey and general polynomial models to study fungal radial growth. Satisfactory predictions of fungal growth in relation to temperature with the use of the CM were also reported by other authors [56; 57].  
Figure 4: Plots of the maximum specific growth rate of \(G\). _candidum_ J versus temperature (6–37 \({}^{\circ}\)C) in milk (blue line) and milk with 1% NaCl (yellow line) according to the CM (solid line). The symbols indicate the experimental \(\mu_{\max}\) estimated from the primary growth curves at each incubation temperature. Solid lines represent the fitted model estimates. Dashed lines represent the 95% confidence intervals.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Model** & **\% NaCl** & \(\mathbf{R^{2}}\) & _RMSE_ & _Af_ & _Bf_ \\ \hline \multirow{2}{*}{Primary models} & \multirow{2}{*}{**BR**} & 0 & 0.985–0.997 & 0.092–0.027 & - & - \\  & & 1 & 0.966–0.999 & 0.166–0.062 & - & - \\ \hline \multirow{3}{*}{Secondary models} & \multirow{2}{*}{**CM\({}_{\text{H/A}}\)**} & 0 & 0.983 & 0.127 & 1.116 & 1.007 \\  & & 1 & 0.926 & 0.238 & 1.237 & 0.998 \\ \cline{1-1} \cline{2-6}  & \multirow{2}{*}{**CM\({}_{\text{H}}\)**} & 0 & 0.981 & 0.015 & 1.259 & 0.902 \\ \cline{1-1}  & & 1 & 0.888 & 0.035 & 1.296 & 0.909 \\ \hline \hline \end{tabular} _RMSE_—root mean square error; \(R^{2}\)—coefficient of determination; _Af_—accuracy factor; _Bf_—bias factor; BR— [PERSON] and [PERSON] model; CM\({}_{\text{H/A}}\)—cardinal model applied to its lag phase data set; CM\({}_{\text{H}}\)—cardinal model applied to its growth rate.  
\end{table}
Table 3: Mathematical indices and validation factors of the models used, which describe the effects of temperature and NaCl presence on \(G\). _candidum_ J growth in milk.  
Ideally, predictive models would have \(A_{f}=B_{f}=1\). However, \(A_{f}\) can increase by 10-15% for every variable in the model [58]. Therefore, if the model predicts the effect of the temperature (as the only factor) on the microbial growth, the best expected \(A_{f}\) would be 1.1-1.2 [58, 59]. In our study, the \(A_{f}\) factors were slightly higher than 1.2. The satisfactory \(B_{f}\) factor limits were related to the specific application of the model. If \(B_{f}<1\), then the model overpredicts the observed growth rate and, thus, the model is considered to be \"fail-safe\" in terms of the growth rate predictions for spoilage or pathogenic microorganisms [58]. However, an acceptable interval of the \(B_{f}\) factor for predictive models is 0.75-1.25 [34]. All \(B_{f}\) factors calculated in our study were in the acceptable interval.