## 2 Materials and Methods
### Data Analysis  
Descriptive statistics were computed to summarize the main features of data distribution of response variables to be used in the regressive approach. In addition, variables were tested for normality, using Shapiro-Wilk and Kolmogorov-Smirnov tests, and for heteroscedasticity by soil management with Levene homogeneity of variance test. Data distribution and presence of heteroscedasticity were also examined for soil variables.  
The set of twenty soil variables was first analyzed through a nested analysis of variance (ANOVA) considering replicates within plots as pseudo-replicates. Then, data were analyzed using Principal Component Analysis (PCA), Stepwise Discriminant Analysis (SDA) and Partial Least Square Regression (PLSR) with Variable Importance for Projection (VIP) statistics.  
PCA was applied to the correlation matrix of the soil variables in order to obtain few new components explaining most of the variation of the original variables. The principal components (PCs) that explained cumulatively a high percentage of the total variance and had an eigenvalue greater than one ([PERSON] criterion) were retained. Together with eigenvalue, percentage of variation explained by the single component was taken into account, considering the threshold of 5% suggested by [PERSON] and [PERSON] [48]. Variable loadings were examined. Within each PC, only highly weighted loadings, defined as having absolute values within 10% of the highest loading [49], were considered and signs were examined to investigate relationships among selected variables.  
SDA was applied to identify the variables enabling maximum discrimination among the compared classes (soil management treatments). The Wilks' lambda statistic was used as multivariate measure of separability [50]. The use of SDA requires that a set of assumptions should be checked, among which normality of data distributions, homoscedasticity and not complete redundancy of considered variables. However, a moderate departure from such assumptions does not affect seriously analysis outcomes as shown by a large literature concerning SDA application [51; 52; 53]. SDA was carried out using the STEPWISE algorithm of STEPDISC procedure of SAS/STAT [54]; significance level to entry and to stay was set at 0.05.  
PCA and SDA were first performed separately on the set of chemical variables (plus carbon of the microbial biomass) and physical variables, and then were carried out on the whole dataset of indicators.  
PLSR was carried out on mean-centered and variance-scaled data of predictors and response variables. In this study, predictors were represented by soil chemical, physical and biological properties; response variables were grain yield and grain protein content, as integrated indicators of quantitative and qualitative crop response to different soil management conditions. The optimal number of factors to be retained in the model was based on the minimum predicted residual sum of squares statistics (PRESS) [54]. In this study, both approaches were used in running PLSR: PLS1 and PLS2 [55; 56]. In PLS1, PLSR was carried out using grain yield or protein content as single response variable; in PLS2, grain yield and protein content were considered simultaneously as multiple response variables.  
VIP statistics were used for variable selection [57]. Since the average of squared VIP scores equals 1 [58], only the variables with a VIP score greater than 1 are generally considered significant. However, thresholds between 0.83 and 1.21 have also been suggested [32]. A value of 0.8 is also considered by [PERSON] [59] for retaining or deleting variables. The soil variables with the highest VIP values were selected. PLS regression was performed using PLS procedure of SAS/STAT [54].