# Assessment of Milk Quality in Skopelos Goats Under Low- and High-Input Farming Systems
## 2 Materials and Methods
### Milk Chemical Composition, Milk Physical Properties, SCC, and TBC  
The milk samples were allowed to reach room temperature and then placed in a heated water bath. After that, they were thoroughly mixed by gently inverting the sample container multiple times, ensuring no frothing occurred.  
Chemical composition analysis was conducted using the Foss MilkoScan FT-plus fully automatic milk FTIR analyser (Foss Electric A/S, Hillerod, Denmark) following the ISO/IDF method [33]. Milk pH was measured with a portable pH/conductivity meter SG23-FIELD-KIT2 (51302602) (Mettler Toledo, Schwerzenbach, Switzerland) using an electrode equipped with a built-in temperature sensor (pH InLab(r) Expert-Go-ISM (IP67), 1.8 m cable, Schwerzenbach, Switzerland). The pH meter was calibrated using standard pH 4.0 and 7.0 buffer solutions, following the manufacturer's guidelines. The EC of the milk samples was also assessed with a pH/conductivity meter SG23-FIELD-KIT2 (51302602) (Mettler Toledo, Schwerzenbach, Switzerland) and an In-Lab(r)r)r)r)r)r)r)r)r)r)r\(10\10\100\10\1\10\1\1\1\1\1\1\1\1\1\1\1\1\1\1\1\1\\1\\1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\  
with correlation coefficients (r values) ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).  
Before PCA, the dataset was standardized (mean-centered and scaled to unit variance) to ensure comparability among variables with different units. The eigenvalues and screen plots were examined to determine the number of significant principal components, with components retaining eigenvalues greater than 1 considered for interpretation ([PERSON]'s criterion). Individual samples were color-coded in the PCA scatterplot to explore the potential differences between farming systems (extensive vs. intensive), with confidence ellipses representing group variability. Following the PCA, cluster analysis was conducted to further explore the patterns and groupings in the milk trait data, beyond the dimensions captured by PCA. This method allows the identification of natural groupings without predefined categories. Statistical analyses were performed in R, and results were considered significant at \(\alpha\) = 0.05.  
The effect of farming system, lactation stage, year on am_milk yield (am_MY), and milk quality traits, accounting for random variability among individual animals, was assessed with the following linear mixed-effects model (1); each trait was analyzed separately as follows:  
\[\mathrm{Y_{ijkl}}=\mu+\mathrm{FS_{i}}+\mathrm{LS_{j}}+\mathrm{Y_{k}}+\left( \mathrm{LS_{j}}\times\mathrm{Y_{k}}\right)\mathrm{FS_{i}}+\mathrm{A_{m}}+ \mathrm{e_{ijkm}} \tag{1}\]  
where \(\mathrm{Y_{ijkl}}\) denotes the dependent variable (am_MY, chemical composition, physical properties, SSC, and TBC); \(\mu\) the overall mean; \(\mathrm{FS_{i}}\) the fixed effect of farming system (i = 1-2); \(\mathrm{LS_{j}}\) the fixed effect of the LS (j = 1-4); \(\mathrm{Y_{k}}\) the fixed effect of the year (k = 1-2); (\(\mathrm{LS_{j}}\times\mathrm{Y_{k}}\)) the interaction effects of LS and year within each farming system (\(\mathrm{FS_{i}}\)); \(\mathrm{A_{m}}\) the random effects of the animal within farming system; and \(\mathrm{e_{ijkm}}\) the residual error associated with observation ijkm. The model was fitted using the linear mixed-effects (\(\mathrm{Imer()}\)) function from the lme4 package [38] in R. Fixed effects included farm, lactation stage (each sampling corresponded to a specific lactation stage), year of sampling, and the interaction effects of year and lactation stage within the farming system, while animals were included as a random effect to account for repeated measures and inter-individual variability. Model assumptions were assessed by inspecting residual plots, ensuring normality and homoscedasticity. Model significance was evaluated using likelihood ratio tests, and estimated marginal means were obtained using the emmeans package [39] for post hoc comparisons. SCC and TBC data were log-transformed to normalize their distributions prior to statistical analysis.