## 6 Discussion  
A complex interaction of several geo-environmental variables drives the spatial pattern of gully erosion [1; 24; 33; 77]. Consequently, understanding the cause-and-effect of these geomorphic processes and accurately mapping the areas prone to gully erosion can provide valuable insights for identifying appropriate management strategies for a territory [78]. Various statistical and machine learning methods have been applied in the last decade to model and map gully erosion susceptibility [13; 21; 22; 23; 29; 31; 32; 79]. However, no agreement has yet been made on selecting the best model for predicting gully erosion occurrence. This lack of consensus is because the formation of gullies is influenced by the specific topological, geomorphological, geological, pedological, and hydrological settings in each study area [2; 24; 31; 46; 80]. Several scientific papers have asserted that machine learning techniques generally perform better than traditional statistical methods [19; 26; 29; 32; 61]. In this study, we tested the predictive capabilities of the MaxEnt method for mapping the gully erosion susceptibility in a catchment of the Calabria region (South Italy). To implement the MaxEnt algorithm, 12 predisposing factors, such as: lithology, soil texture, soil bulk density, land use, drainage density, slope gradient, slope aspect, plan curvature, LS, TPI, SPI, and TWI, were selected based on the previous scientific literature and detailed surveys in the study area [13; 24; 26; 29; 31; 36; 42; 61]. Using a multi-collinearity diagnosis, the inter-dependence or redundancy between the mentioned factors was analysed [81]. The results showed no multi-collinearity among the 12 factors used to build the susceptibility model. The predictive capability of the trained model, using the 10-fold cross-validation, was evaluated using confusion matrix measures and the AUC-ROC curve. According to the results presented in Table 2, the accuracy measures for all models are very similar in each fold. The model's excellent goodness-of-fit and predictive skill (AUC values well above 0.90) demonstrate the reliability of the method applied and confirm that accurate predictions of gullies' occurrence may be obtained from implementing the MaxEnt method. In addition, the high accuracy of the prediction model also demonstrates the validity of the gully erosion inventory and the geo-environmental variables selected as predisposing factors. Therefore, tiny differences in the predictive capacities were observed during the 10-fold cross-validation, which suggests that the MaxEnt method is able to produce a reliable and robust gully erosion predictive model when changing the calibration and validation sets. Moreover, the very low values of standard deviation obtained for accuracy, kappa coefficient, and AUC (Table 2) confirmed a certain stability of the prediction model. This suggests that the MaxEnt method is particularly promising for mapping the complex spatial pattern of gully erosion-prone areas [52]. The findings also highlight that the 10-fold cross-validation approach is adequate to reduce the negative effects of random sampling on the performance of the machine learning method [81]. Furthermore, the k-fold cross-validation technique can improve the predictive capability of the gully erosion susceptibility model because it helps to generate new accuracy measures and grow the robustness of other conventional ones. The achieved findings agree with those shown in previous studies, which applied the MaxEnt algorithm to assessing gully erosion susceptibility in different geological contexts [21; 26; 29; 47; 52; 61; 82]. Compared to other machine learning methods frequently used to evaluate the susceptibility of gully erosion, such as random forest [20; 83], support vector machine [33; 84], boosted regression tree [21; 22], and artificial neural network [22; 33; 85], the MaxEnt method has the advantage of not requiring a dataset of points corresponding to areas without gullies to use as a dependent variable to run the model.