## 4 Discussion
This suggests that statistics-based models, including machine learning algorithms, commonly predict core habitats around occurrence coordinates, but the areal size can differ according to the specific model. Therefore, appropriate model selection for the purpose of a study is crucial, as is highlighting the current application of ensemble models to project occurrence areas conservatively by extracting consensus areas from each model [27]. In contrast to the areal size by classification, the occurrence possibility by regression was similar between RF and MLP, and they were \(\sim\)2.5 times higher than the occurrence possibility evaluated by MaxEnt. MaxEnt uses the maximum entropy model to calculate the occurrence possibility [2], whereas RF and MLP are universal classifiers that calculate probability based on the weight of modelvariables [3,4]. Different thresholds for classification are necessary for each model to project similar distribution patterns. Recently, a value that maximizes the TSS has been proposed as the threshold value, which is the value used in this study [34]. In addition, MaxEnt requires the determination of optimal model features, and delta Akaike Information Criterion (AIC) has been mostly used for selecting the best model settings. However, threshold-dependent evaluation metrics could be a better option because AIC-based selection can result in low predictive performance due to oversimplification of the model [56]. This suggests the necessity of defining the best model in ecological niche modeling when using the MaxEnt. Therefore, we believe that either classification works better with the simultaneous use of different machine learning-based models than a regression method to evaluate a specific probability. A specific method that can adjust different occurrence probabilities needs to be considered to calculate the occurrence probability [57]. Although the MLP model exhibited the lowest model performance owing to the small number of data points available for model training, its performance for both species was reliable, suggesting its potential for SDM applications [4,58]. When developing an MLP model, one of the most challenging tasks is to determine the hyperparameters necessary for determining the optimal model structure related to the number of hidden layers and neurons. This process mostly depends on the intuition of the researcher based on variations in the loss function; thus, a formalized method that is applicable to SDM is necessary [58]. In this study, the model performance metrics evaluated by the test dataset were used to determine the optimal model structure. All model metrics, including TSS and accuracy, were almost saturated as the number of neurons increased, indicating that there was a minimum threshold value that guaranteed model performance. Therefore, we believe that TSS can be used as an index to objectively determine the structure of the MLP model in the SDM, in addition to the loss function. One of the main purposes of SDM is to derive ecological insights into species distributions. This is generally conducted by analyzing the contribution or importance of model variables, which reflect the environmental characteristics of species' habitat and biology. Variable contribution and mean decrease in accuracy are widely used measures of variable importance in MaxEnt and RF, respectively. In both models, the important variables showed similar trends for both the ant species. Bio1 (annual mean temperature) and bio14 (precipitation seasonality) were the two most important variables suggested by both MaxEnt and RF for _S. invicta_, which is consistent with a previous study that reported bio14 to be the most important variable in RF because variations in soil humidity related to precipitation seasonality affect the survival of _S. invicta_[15,59]. In addition, low and extremely high temperatures are unfavorable for _S. invicta_[16,60], justifying the importance of monitoring annual average temperature in predicting _S. invicta_ occurrence areas. For _A.