## 3 Results and Discussion
### Differentiation Models of Berries According to Botanical Origin and Growing System  
In order to differentiate the berry samples according to the botanical origin (raspberry, seaberry, blackberry, cranberry, and blueberry) and growing system (wild and cultivated), the PLS-DA supervised method was performed on the data associated with the isotopic content (\(\delta^{13}\)C, \(\delta^{2}\)H, \(\delta^{18}\)O) and multi-element concentration (Li, Na, Mg, P, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, As, Rb, Sr, Ag, Cd, Ba, Pb, La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb). First, the measured isotope and elemental concentrations were preprocessed through the auto scale method. After that, to identify the variables with the highest influence on  
Figure 5: The mean concentration of macro-, micro-, and trace elements in mg/kg dry weight (d.w) in cultivated (C) and wild berries (W) (raspberry, seaberry, blackberry, cranberry, and blueberry). the botanical/growing system differentiation of berries, a model-based feature selection method built on PLS was applied. The determined parameters which potentially have the highest influence on berries' differentiation according to botanical origin were: \(\delta^{13}\)C, \(\delta^{2}\)H, \(\delta^{18}\)O, Li, Na, Mg, P, Ca, V, Mn, Co, Ni, Zn, As, Rb, Sr, Ba, and Eu. The PLS-DA differentiation model constructed based on these features was characterized by four LVs, as it illustrated the lowest cross-validation classification error average. The performance of the model corresponded to an 85% accuracy in the cross-validation procedure, which was obtained after correctly predicting 66%, 70%, 88%, 100%, and 100% of the blackberry, blueberry, cranberry, raspberry, and seaberry samples, respectively. The score and loading plots (LV1 vs. LV2 vs. LV3) associated with the PLS-DA model are displayed in Figure 6a,b, respectively, illustrating and supporting the influence of the identified parameters for differentiating berries according to botanical origin. The PLS-based feature selection method indicated that the variables that are the most significant for classifying berry samples according to the growing system are: \(\delta^{13}\)C, \(\delta^{18}\)O, Li, Na, Ca, Cr, Mn, Ni, Rb, and Ba. The PLS-DA model constructed based on these 10 variables was characterized by a single LV and conducted the correct assessment (in the cross-validation procedure) of 94.4% and 77.2% of the cultivated and wild berries, respectively. Therefore, a model accuracy of 85% was obtained. One cultivated berry sample was assigned as a wild sample, while five samples from the wild class were predicted as cultivated berries. The score plot of the PLS-DA model is presented in Figure S1, in the Supplementary Materials. Nonetheless, PLS-DA was applied for a particular case, namely for the differentiation of wild blueberries from cultivated ones. Firstly, the PLS-DA model was developed, based on the entire set of data (33 variables, corresponding to all of the isotopic and elemental contents measured). In this case, an accuracy of 80% was obtained in the cross-validation procedure. One blueberry sample from the wild group was assigned to the cultivated group and one cultivated blueberry sample was predicted as a sample from the wild group. When the model-based feature selection method was applied, the variables that significantly contributed to the discrimination model were: \(\delta^{13}\)C, \(\delta^{18}\)O, Mg, P, Ca, Mn, Zn, Ga, Rb, and Ba. To refine the classification model of blueberry samples according to the growing system, the most significant parameters identified by the feature selection method were used to build a final PLS-DA model. The developed PLS-DA model illustrated the use of 5 LVs and showed excellent levels of sensitivity (100%) and specificity (100%), both in the calibration  
Figure 6: PLS-DA score (**a**) and loading plot (**b**) associated with the differentiation of berries according to botanical origin. and cross-validation methods.