## 2 Materials and Methods
### Statistical Analysis  
We utilized the R statistical environment for comprehensive data analysis. The data were represented as means \(\pm\) standard deviation, and statistical significance was considered at the 5% level. Given that metabolic pathways associated with alternate bearing can be influenced by a multitude of climatic events affecting both vegetative and reproductive aspects of olive trees, especially in traditional groves [116], we conducted an analysis of variance followed by [PERSON]'s test for multiple comparisons. This analysis aimed to explore whether the productivity of centennial olive trees exhibited a biennial fruiting pattern, shedding light on their fruit-bearing behavior. Additionally, we delved into a within-species thermal and humidity pattern variations assessment focusing on the estimated thermal and humidity indices (T\({}_{\text{IQR}}\), T\({}_{\text{OPR}}\), H\({}_{\text{IQR}}\), H\({}_{\text{OPR}}\)), for both sides of each olive tree's trunk. This examination was conducted using \(t\)-tests to ascertain whether significant differences existed between these indices on the opposing sides of the trunk. The identification of such variations bears the potential to provide insights into the tree's health state and any underlying structural issues that may be concealed. Indeed, the evaluation of temperature and humidity distribution on tree trunks assumes substantial importance as an indicative measure of their overall health condition [82]. Subsequently, we investigated the interrelationships between trees' phenotypic information, thermal and humidity trunk and canopy indices, and CWSI using correlation statistics. Furthermore, a series of multiple linear regression analyses were employed, incorporating a backward elimination procedure to systematically dissect the collective impact of all variables on productivity. To ensure the validity of these analyses, we conducted checks for linear dependence by calculating the variance inflation factor (VIF), with a VIF threshold of >3 indicating multicollinearity [117]. Sequential removal of variables with the highest VIF values helped refine the models. Our analyses were divided into four distinct categories: the first three categories evaluated both the individual and combined effects of phenotypic traits and CWSI, as well as the influence of trunk and canopy thermal and humidity indices, on both mean productivity and the productivity for each year. The third category explored the effects of all variables on CWSI. Furthermore, we conducted a relative importance analysis for each model, quantifying the individual contributions of independent variables to the dependent variables (productivity and CWSI). This approach sheds light on the relative significance of these variables, enhancing our understanding of their roles within this ecological framework. We further proceeded to explore the potential influence of productivity, phenotypic traits, CWSI, and canopy and trunk thermal and humidity indices of trees with and without OLS. For this, we developed a series of binary logistic regression models. This exploration involved the utilization of classification tables, which enabled us to compare observed data with model-predicted outcomes for three specific categories: (a) the impact of productivity and phenotypic traits variables, (b) the influence of thermal and humidity indices, and (c) the combination of all variables. Additionally, we conducted receiver operating characteristic (ROC) curve analysis to assess the overall predictive accuracy of our models. To determine the general significance of these models, we applied the Hosmer-Lemeshow goodness-of-fit test, a statistical tool that evaluates the alignment between actual and predicted results. Furthermore, we computed Nagelkerke's R\({}^{2}\), serving as an explanatory metric of model variation and offering insights into the extent to which predictor variables accounted for variance in the presence or absence of OLS.