## 3 Results and Discussion
### Association of Most Influential VOCs to Spoilage  
A procedure for identifying a set of influential log-ratios while simultaneously controlling the progressive variance explained by the selection was achieved using the function STEP of the easyCODA package. After six steps, the corresponding log-ratios accounted for 97.87% of the variance (Table 3). The VOCs involved in such a log-ratios were: methyl propanoate (V8), 2-pentanone (V11), 2-methyl-2-buttenal (V24), (Z)-3-hexenyl acetate (V40), (Z)-2-hexen-1-ol (V47), (E)-2-hexen-1-ol (V48), 5-hexen-1-ol (V49), butanoic acid (V62), \(\beta\)-damascenone (V72), ethyl hydrocinnamate (V79), and 4-ethyl phenol (V88). However, notice that the selection is not unique, and other sets of log-ratios could also have been chosen. As such log-ratios are data in the Euclidean space, they can be subjected to the usual PCA analysis (Figure 8A), which separated the samples affected of btwric spoilage, based on log-ratio ln((Z)-3-hexen-1-ol (V48)/butanoic acid (V62)), strongly and negatively related to PC1; a low value of this log-ratio characterises then the btwric samples. Besides, two samples from industry B (F508, with sulfidic spoilage, and F502, less strongly) were associated with ln(2-pentanone (V11)/\(\beta\)-damascenone (V72)), which was negatively linked to PC2, but the rest of samples were considered somewhat similar. The PCA based on these log-ratios did not distinguish between normal fermentation in industry A and the putrid (F562)/normal (F592) samples from B, as already shown by other analyses like clustering, but identified several log-ratios that accounted for most of the original dataset variance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Log-Ratios**} \\ \hline  & **V47/V62** & **V24/V49** & **V40/V88** & **V40/V48** & **V8/V79** & **V11/V72** \\ \hline
**Sample** & 1 st step & 2 nd Step & 3 rd step & 4 th step & 5 th step & 6 th step \\
*** F508** & 11.5366736 & \(-\)3.34584729 & \(-\)0.79449967 & \(-\)11.5366736 & \(-\)5.24925185 & \(-\)3.60413823 \\
*** F562** & 4.31194432 & \(-\)5.26685746 & 9.25254389 & \(-\)0.39287304 & \(<\)10\({}^{-8}\) & 2.36124225 \\
*** F282** & \(<\)10\({}^{-8}\) & \(<\)10\({}^{-8}\) & \(<\)10\({}^{-8}\) & 10.1927924 & 4.28393332 & 11.0951384 \\
*** F283** & \(<\)10\({}^{-8}\) & \(<\)10\({}^{-8}\) & \(-\)4.18599046 & 10.3222438 & \(-\)4.18599046 & 11.0754892 \\
**F284** & 8.35119765 & 8.61352368 & \(-\)3.35607594 & \(-\)8.35119765 & \(-\)10.3377366 & 11.0976654 \\
**F285** & 8.27834396 & 7.27272682 & \(-\)0.85347747 & \(-\)8.27834396 & \(-\)8.97662228 & 11.338771 \\
**F286** & 8.89742579 & 6.63844165 & \(-\)1.35585478 & \(-\)8.89742579 & \(-\)10.2055787 & 11.0516611 \\
**F309** & 6.64586886 & 7.28309525 & \(-\)1.656955554 & \(-\)6.64586886 & \(-\)9.85671251 & 11.3299799 \\
**F502** & 8.36178107 & 2.52536384 & \(-\)3.21526325 & \(-\)0.00764613 & \(-\)10.8405329 & 2.59544661 \\
**F592** & 5.45442103 & \(-\)7.2474397 & 9.22333371 & 0.09096199 & \(<\)10\({}^{-8}\) & 1.99738057 \\
**Cummulative** & 69.35 & 82.9 & 90.35 & 93.86 & 96.32 & 97.87 \\  variance (\%) & 69.35 & 82.9 & 90.35 & 93.86 & 96.32 & 97.87 \\ \hline \hline \end{tabular}  
* Notes: V8, methyl propanate; V11, 2-pentanone; V24, 2-methyl-2-buttenal; V40, (Z)-3-hexenyl acetate; V47, (Z)-3-hexen-1-ol; V48, (E)-2-hexen-1-ol; V49, 5-hexen-1-ol; V62, butanoic acid; V72, \(\beta\)-damascenone; V79, ethyl hydrocinnamate; V88, 4-ethyl phenol.
* Spoiled samples.  
\end{table} 
Table 3: Spoiled (*) and normal samples of Spanish-style Manzanilla table olives fermentations. Most influential VOCs’ logratios progressively selected by the function STEP of the easyCODA package, and their cumulative proportions of explained variance. The plot using this reduced number of VOC log-ratios is, theoretically, similar to that obtained by the function LRA from the easCODA package (Figure 8B). They were pretty similar after rotation, except for F502 (industry B), not segregated.