## 4 Materials and Methods
### Data Analysis  
Data acquisition was performed from the volatile profiles of five biological replicates for each treatment using MSD ChemStation D.02.00.275 (Agilent Technologies), and automatic integration was performed using a threshold of 14 units. The reported abundance values are relative abundances of compounds, obtained by integrating the signal in their chromatographic peaks. Putative annotation of the aligned compounds was conducted by searching spectra against NIST MS 2.0 with the NIST 14 database and comparing the experimental retention index (RI) with the RI of compounds reported in the literature. Only those peaks absent in any of the five replicates of each uninoculated control were considered to be volatiles released by the _Malassezia_ species. In addition, compounds found in only one replicate across all treatments were discarded. This exclusion criterion was selected as a compromise to guarantee some level of reproducibility while also allowing for some biological variability often found in experiments involving live biological systems [62]. Finally, compounds that did not provide an accurate match with the library were considered unknown. After automatic integration, the obtained results were rigorously reviewed, and peak areas were used to construct the original matrix in which tentatively annotated VOCs were reported as columns (variables) and estimated peak areas were reported as rows (observations). As grouping variables, we included the three tested _Malassezia_ species (_M. globosa_, _M. restricta_, _and M. sympodialis_), both growth phases (exponential and stationary), and the combination species/phase. Data were processed using a Hellinger transformation suitable for reducing the horseshoe effect in matrices with many zeros [63]. Then, Pareto scaling was applied, which allows for scaling of the data obtained from the chromatographic analysis, reducing the relative importance of large values but keeping the data structure partially intact [64; 65]. Statistical analyses were performed to establish relationships between tested variables and to correlate how important each one is to the outcome where dependencies exist for dimension reduction of variables [66]. Permutational multivariate analysis of variance (PERMANOVA) was applied to a dataset as a nonparametric method to conduct multivariate ANOVA and test for differences between variables [67]. Afterward, multivariate analysis was conducted using two different approaches (unsupervised and supervised). The unsupervised method is principal component analysis (PCA), which allows for the visualization of complex data while reducing its multidimensionality [66]. Supervised multivariate analyses, such as discriminatory analysis, where the measured variables (VOCs) are considered the predictor variables and those that define object classes are treated as the response variable (grouping variables), were performed [66]. Projection to latent structures-discriminant analysis (PLS-DA) is based on the principle of partial least-squares (PLS) regression, which aims to predict response variables (Y) from a broad set of predictor variables (X) [68]. The output of PLS provides measures of the model fit (R\({}^{2}\)), model predictive power (Q\({}^{2}\)), and model accuracy based on a cross-validation procedure [66]. Moreover, other statistical features could be evaluated, such as the variable importance in the projection (VIP) score of a variable, which is calculated as a weighted sum of the squared correlations between the PLS-DA components and the original variable. The weights correspond to the percentage variation explained by the PLS-DA component in the model. The number of variables in the sum depends on the number of PLS-DA components found to be significant in distinguishing the classes. Factors with VIP scores greater than one are regarded as significant [35]. These statistical analyses were performed to analyze the volatile profile differences comparing species, growth phases, and the combination of species/growth phases.