## 2 Results and Discussion
Pearson's correlation coefficients were calculated in order to study the relationship between the main groups of volatile compounds found in the oils from the Core-36 cultivar collection (Table S1 in Supplementary Materials). As expected, the total content of volatile compounds in the oils correlated significantly with the major group of volatile compounds in the oils (C6). Particularly remarkable is the strong and very significant correlation with the C6/LnA aldehydes (\(r\) = 0.91). On the contrary, the rest of the C6 groups showed a significant, but moderate, correlation (\(r\) = 0.35, 0.46, and 0.32). By contrast, most of the C5 compounds displayed a low correlation coefficient except for the pentene dimers that carried a moderate level of correlation (\(r\) = 0.38) with total volatiles. Esters and BC compounds displayed no correlation with the total oil volatile compound contents. These data are in good agreement to those found for the oils of the segregating population of the Picul \(\times\) Arbequina cross [30], except for the fact that the relationship of the C5 compounds with total volatiles was moderate to high in the latter. A conceivable explanation might be that the parents of the cross, Picul and Arbequina, are cultivars whose oils contain average to high contents of C5 compounds compared to the rest of the Core-36 cultivars. Despite the significant impact of LOX esters and BC aldehydes on VOO aroma, it is remarkable their low correlation coefficients in relation to the total contents of volatiles. Actually, no high correlations were found with any other groups of compounds. BC compounds do not share any synthetic pathways with the rest of the volatile compounds, so these findings are logical from a metabolic point of view, however they are not for the LOX esters. Esters were moderately correlated with the C6/LA alcohol (\(r\) = 0.42) but to a much lower level with their main precursors, the C6/LnA alcohols (\(r\) = 0.23), suggesting either a limitation of AAT activity or that the synthesis of alcohol by ADH during VOO production is generally reduced in the Core-36 cultivars, as demonstrated to occur to two cultivars from this collection, Arbequina and Picul [33]. In this sense, although a high and significant correlation between C6/LnA and C6/LA alcohols (\(r\) = 0.73) was found, suggesting the same biochemical origin, however, a weak correlation was observed between the content of C6/LnA aldehydes and their metabolic products, the C6/LnA alcohols (\(r\) = 0.15). This low correlation was also noticed for the C6/LA aldehyde contents and those of the C6/LA alcohol (\(r\) = 0.39). On the other hand, a significant but weak correlation was observed between the contents of C5/LnA carbonyls and C5/LnA alcohols (\(r\) = 0.36), quite similar to that found for each of these groups of compounds with the contents of pentene dimers (\(r\) = 0.50 and 0.29, respectively). According to these results, these groups of compounds might be metabolically related, as described also for the oils from the progeny of the Picul \(\times\) Arbequina cross [30] and, consequently, supporting the hypothesis that the synthesis of C5 alcohols and pentene dimers occurs at the same time catalyzed by a LOX activity [34]. Moreover, it seems that the pentene dimers are only produced from LnA, since no significant correlations were found for pentene dimers and the carbonyl and alcohol derived from LA (C5/LA). The cultivars included in the Core-36 collection could not be grouped in terms of harvest year or geographical origin when analyzed by a principal component analysis (PCA) using all of the volatile compounds as the variables (Figure S1 in Supplementary Materials) despite the fact that [PERSON] et al. [14] did find some grouping between cultivars from the different geographical origins after PCA of the whole olive bank. Thus, most of the variability among the Core-36 volatile profiles seems to correspond exclusively to the cultivar.