## 2 Materials and Methods
### Machine Learning Regression Algorithms Evaluated for Digital SOC Mapping  
The selection of machine learning regression algorithms to be evaluated in this study was performed according to total indexing in the WoSCC based on the following topic search: \"TS = (digital soil mapping AND soil organic carbon AND machine learning algorithm)\" (Table 1). The machine learning prediction was performed in R v4.3.2 [25] and the caret library [26]. Prior to modeling, the data were pre-processed using centering and scaling to standardize the variables and reduce the effects of differing scales. All models were tuned using a grid search approach, where 10 different combinations of tuning parameters were evaluated to optimize model performance according to the hyperparameters listed in Table 1. The final model was selected based on its performance on the training data, and its predictive accuracy was evaluated using the specified resampling method. In traditional linear models such as MLR, GLM and GAM, predictions are made by fitting a linear equation to the data, relying on assumptions about the linear relationship between input variables and the response [39]. As the simplest prediction algorithm of those evaluated in this study, MLR estimated the linear relationship between the sampled SOC and environmental covariates by estimating coefficients to compute the predicted SOC value for a new observation. GLM is a generalization of linear regression that allowed for non-normal response variables and non-linear relationships between the SOC values and environmental covariates [40]. GAM estimated the additive relationship between SOC and environmental covariates using smooth functions [41]. Regularization techniques such as LASSO and LAR enhanced these models by introducing penalties, enabling feature selection, and managing overfitting. LASSO is a linear regression model with an L1 penalty term that encouraged sparsity in the estimated coefficients to compute SOC based on environmental covariate data [42]. Similarly, LAR is a linear regression model that estimates the coefficients using a forward stagewise procedure that adds one variable at a time to the model [43]. The last of the traditional prediction methods, PLS concatenated centroids of predictors and responses to effectively explain variance in settings with high-dimensional data, making it suitable in regression contexts where the predictors exceed the number of observations [44]. On the other hand, tree-based methods like RF, CART, and GBM are non-parametric and model interactions between predictors through hierarchical tree structures, as well as by averaging, boosting, or bagging model predictions to enhance accuracy [45]. CART is a decision tree algorithm that recursively partitioned the feature space into subspaces and fitted a simple model to each subspace, with the output as the value of the constant at the leaf node [46]. GBM is an ensemble learning method that built multiple decision trees and combined their predictions using a gradient descent algorithm, with the output as the weighted sum of the predictions from all the trees [47]. Similarly, Cubist is a rule-based regression model that built a series of if-then rules to predict the response variable [48]. It partitioned the feature space into rectangular regions and fitted a linear model to each region. During prediction, a new observation was passed through the rules, and the output was the weighted sum of the linear models that matched the observation. As the most frequently used machine learning method for digital SOC mapping based on WoSCC search results, RF is an ensemble learning method that built multiple decision trees and averaged their predictions to produce a final output, utilizing bootstrap aggregation (bagging) in the process, having a new observation passed through each decision tree, as well as the average of the predictions from all the trees as the output [49].