## Materials and Methods
### Dimensionality Reduction: Linear Appraisal System Optimization  
The optimization of the LAS used in Murciano-Granadina goats was performed using principal component analysis (PCA). PCA can be used to perform an efficient selection of the minimum number of zoometric traits which are able to capture the highest fraction possible of variability for a given set of traits. Birth data for all animals were provided by CAPRIGRAN. Zoometric data collection was performed using a zoometric stick, a zoometric compass and a tape measure. All measurements were recorded once by the same person to avoid inter-recorder effects. Descriptive statistics were calculated for each of the 17 zoometric variables studied, and Spearman's correlation coefficients were computed for all possible combinations of the variables. A significant Spearman's correlation between two variables in a pair may result when the two variables involved in the comparison are monotonically related, even if they share a nonlinear relationship [12]. The correlation matrix for the variables must contain at least two correlations of \(|0.30|\) or greater [13] in terms of the absolute value, which is the minimum magnitude for variables to be suitable for structure detection and thus for PCA to be valid. Data for the PCA were generated from the variance-covariance matrix. The Kaiser-Meyer-Olkin (KMO) test of sampling adequacy and [PERSON]'s test of sphericity were computed to establish the validity of the data set for structure detection (the KMO test determines whether the common factor model is appropriate as it measures the extent to which the original variables belong together). The KMO should be greater than 0.5 for a satisfactory factor analysis to proceed. [PERSON]'s test of sphericity tests the hypothesis that a correlation matrix is an identity matrix, which would indicate that variables are unrelated and therefore unsuitable for structure detection. Small p-values (less than 0.05) of the significance level indicate that factor analysis may be useful for the analysis of data [14]. Communalities were assessed to determine which variables should be maintained or discarded from PCA. Initial communalities are indicative of the total amount of variance that certain original variables share with all other variables included in the analysis. Extraction communalities are estimates of the variability of each variable that can be accounted for by the factors in the factor solution. Small values (close to zero) are indicative of variables that do not fit well within the factor solution and thus should possibly be dropped from the analysis. Communities after extraction should be above 0.3 [15]. The rotation of principal components was performed to transform components into a simple structure. The raw varimax criterion of the orthogonal rotation method was used for the rotation of the factor matrix. The varimax rotation aims to maximize the sum of variances of a quadratic weight. Furthermore, when varimax rotation is applied via Kaiser normalization, it corrects for the bias resulting from the fact that some factors may have high correlations with a small number of variables and zero correlations with the others. The cumulative proportion of variance criterion was finally used to determine the number of components to extract. [PERSON]'s alpha statistic was used to confirm the reliability and validity of the reduced variable set. The concept of procedure validity can be understood as the degree to which a certain scale measures the factor which it claims to measure. [PERSON]'s alpha measure of validity assumes a high correlation among the elements measuring the same construct. The closer the value of alpha is to 1, the greater the internal consistency of the analyzed elements. [PERSON] and [PERSON] [16] provided a rule of thumb for the interpretation of Cronbach alpha which establishes thresholds as follows: 0.9 is excellent, 0.8 is good, 0.7 is acceptable, 0.6 is questionable, 0.5 is poor, and less than 0.5 is unacceptable.