## 4 Discussion  
In this study, three different SDMs were developed to implement machine learning algorithms. The AUC exhibited a value near or above 0.9, regardless of the model, which suggests excellent performance of the developed models [44]. Compared to AUC, a relatively lower TSS value was obtained for all models, with the highest result in the MaxEnt model. In contrast, the MLP model showed lower TSS compared to the other models, which is consistent with a previous modeling study for _S. invicta_ and may be due to the amount of data used for model training [15]. This could be observed in the MLP models for both ant species, as \(\sim\)2.5 times more data were used to develop the model for _S. invicta_ than for _A. gracilipes_. In addition, the relatively small amount of data used in the _A. gracilipes_ MLP model exhibited significantly less specificity compared to the sensitivity in the same model, as well as compared to other models. This suggests that insufficient data points may be a source of uncertainty [45; 46]. Compared to the MLP model, the RF algorithm showed only a 0.3% and 0.1% difference in the TSS and accuracy, respectively, between _S. invicta_ and _A. gracilipes_, suggesting robustness even with small sample sizes [15; 47]. This advantage of RF in SDM is consistent with similar performance and spatial projection of _S. invicta_ in a previous study, where a boosted regression tree was used [17]. Finally, there still exists controversy on model performance metrics due to dependency on prevalence, suggesting the necessity of using multiple metrics to confirm the model performance [48; 49; 50]. MaxEnt and RF had similar spatial projection sizes. MaxEnt is a specialized SDM tool [2]; thus, it has an algorithm suitable for data generally used in SDM. The RF algorithm has also been used for ecological modeling to define areas of species occurrence because it can overcome limited data points [46; 51]. However, the MLP model predicted larger presence areas than MaxEnt and RF, suggesting the necessity of sufficient data to train deep learning models [52]. This can be shown by the areal sizes of _S. invicta_ and _A. gracilipes_ predicted by the MLP model. For _S. invicta_, which used 2.5 times more coordinates than _A. gracilipes_, the MLP model projection under the current climate was \(\sim\)1-2% larger than those by MaxEnt and RF. For _A. gracilipes_, the MLP model projection was 14-15% times larger compared to the other models. This suggests that more data points might be necessary to develop an MLP model that is comparable with MaxEnt and RF. Areal variation due to climate change was the least in RF, suggesting that RF was relatively insensitive to model variables, which is consistent with the observation of a previous study showing the least projection areas of _S. invicta_ by RF [15; 53]. In contrast, the MLP model produced the largest variation in projection areas for both species due to climate change, showing a sensitive response to changes in model variables that might be due to a dependency on initial model variable weight [54]. Therefore, a developed MLP model can be an option to record changes in species distribution due to climate change, but cautious interpretation is necessary when considering other comparable models. The CLIMEX model is a mechanistic SDM tool for evaluating the habitats of a species that is climatically suitable for species biology [12; 14]. This model predicted areas for both species that were much larger than those of this study because CLIMEX finds an area where species biology can endure a regional climate [55]. Only MLP showed areal projections similar to the CLIMEX results for _A. gracilipes_, but this might be due to the limited training data. The current results were similar to the projections by the genetic algorithm for rule-set prediction (GARP) and BioClim [13].