## 2 Results and Discussion
In order to explain relationships between the different groups of volatile compounds in the oils of the Core-36 cultivar collection, a PCA was performed (Figure 2). The first two PCs explain 34.21% of the total variance, 20.42% for PC1 and 13.79% for PC2, reasonably similar to what found for the content of the volatile compounds in the oils of the progeny of the Picul \(\times\) Arbequina cross (25.73% and 11.47% for PC1 and 2, respectively) [30]. The C6 aldehydes and C5 compounds derived from LnA clustered together between the first and fourth quadrants, and their variances are mostly explained by PC2 (Figure 2). Isomers (\(Z\))-pent-2-en-1-ol (5C-5) and (\(E\))-pent-2-en-1-ol (5C-6) are markedly separated in the plot, indicating that probably they have different origins. According to the grouping, (\(E\))-pent-2-en-1-ol would have a biochemical origin, synthesized through the LOX pathway (homolytic branch), however the origin of (\(Z\))-pent-2-en-1-ol is unknown. The C6 compounds (6C-8, 6C-9) and the C5 alcohol (pentan-1-ol, 5C-16) derived from LA clustered also separated from the LnA-derived C6 aldehydes and C5 compounds. This was also observed when examining the oil volatile profile from the progeny of the Picaul \(\times\) Arbequina cross [30]. The synthesis of these compounds could be ascribed to a mixture of chemical and biochemical oxidation processes, the latter through the LOX pathway. Actually, [PERSON] et al. [26] proposed that hexanal formation during VOO extraction maybe due to both enzymatic and non-enzymatic synthetic methods. C6 alcohols derived from both LA and LnA clustered along the PC2 negative axis clearly distanced from the rest of compounds synthesized by the LOX pathway (Figure 2). The distance in the plot from their precursors in the LOX pathway could be explained by the weak correlation displayed by these groups of compounds mentioned above, probable consequence of ADH inactivation during the oil extraction process [33]. The esters clustered along the PC2 negative axis, overlapping the space of their metabolic precursors synthesized through the LOX pathway, which suggests that, on average, cultivars from the Core-36 collection seem not to have limited AAT activity and that only the limitation of ADH activity during the oil extraction process would be responsible for the moderate correlation between esters and the C6 alcohols (Table S1 in Supplementary Materials). The BC compounds clustered away from the rest of compounds were synthetized by the LOX pathway, indicative of a different metabolic origin. Among the main volatile compounds in the oils from the Core-36 collection, only some of them have OAVs greater than one, thus, theoretically contributing to the oil aroma (Table 2). In this regard, PCA was carried out taking as variables only those volatile compounds having OAV \(>\) 1 in at least 5% of the cultivars (Figure 3). Apart from hexan-1-ol (6C-9) and pent-1-en-3-one (5C-1), responsible for unpleasant odor notes [5; 14; 32], most compounds contribute with pleasant odor notes to the oils. As shown in Figure 3, the first two PCs explain 44% of the total variance. The vector distribution of volatile compounds may distinguish pleasant and unpleasant areas in the Core-36 distribution plot. Figure 2: Vector distribution of the main volatile compounds in the oils of the Core-36. Thus, those cultivars producing oils with a high content of the desired fruity esters are located in the first quadrant of the plot. Meanwhile, cultivars featuring high contents of (_E_)-hex-2-renal (6C-4) are positioned in the third quadrant as well as those having high contents of the branched-chain aldehydes (BC-1 and BC-2), delivering green-fruity odor notes in the oils according to [PERSON] et al. [31]. On the contrary, cultivars whose oils have high contents of the unpleasant hexan-1-ol (6C-9) and pent-1-en-3-one (5C-1) are located along the bisector of the fourth quadrant. Figure 3: Bi-plot of selected volatile compounds contributing to the aroma (OAV > 1) of the Core-36 oils.