## 3 Results
### Spatial Projection Comparison by Models  
The overall global potential distributions of the two ant species were predicted using the occurrence data. _Solenopsis invicta_ was predicted to be densely distributed in North and South America, where most of the occurrence data were concentrated, and showed some potential presence in Africa, Asia, and Australia (Figure 2). Europe was predicted to be an at-risk area for _S. invicta_ distribution in MaxEnt and MLP models, whereas RF expected only a rare chance of its occurrence under the current climate conditions in Europe. The potential distribution areas--the ratio of predicted occurrence area to the whole world calculated by counting the cell numbers in the map--of _S. invicta_ under the current climate for the MaxEnt, RF, and MLP models were estimated to be 5.2%, 4.0%, and 6.5%, respectively (Table 3). When applying the climate change scenario, all the models predicted that the potential occurrence area of _S. invicta_ would expand. The MaxEnt, RF, and MLP models predicted 5.6%, 4.3%, and 16.5% of the ratio of potential occurrence area to the whole world, respectively, and high variation was observed in the MLP model compared to the MaxEnt and RF models. In addition, European regions were vulnerable to significant _S. invicta_ invasions. Similarly, the potential distribution of _A. gracilipes_ was mainly predicted in Southeast Asia, in addition to Central America (Figure 3). Notably, large areas in South America were predicted to be at risk of _A. gracilipes_, although there was no current occurrence data. For _A. gracilipes_, the ratios of potential distribution areas to the whole world were 7.3%, 8.4%, and 21.8%, estimated by MaxEnt, RF, and MLP models, respectively, revealing significantly larger projections in the MLP model. In contrast to _S. invicta_, it was predicted that areas of _A. gracilipes_' potential distribution would not be significantly affected by climate change but rather would be reduced slightly without further habitat expansion. Quantitatively, the potential areas predicted by MaxEnt, RF, and MLP models were 6.1%, 7.8%, and 17.8%, respectively, reducing by 0.5-4% for each model. In general, the MLP model produced the largest area of potential distribution for both species and the highest variations due to climate change, whereas RF exhibited the lowest variations in potential distribution (<1%) for both species due to climate change. The average probability projected by regression differed according to the model, showing similar results for RF and MLP in contrast to MaxEnt (Figures 4 and 5). The average current possibility predicted by MaxEnt was the lowest, at 0.307 and 0.317 for _S. invicta_ and _A. gracilipes_, respectively. The highest average probability was predicted by RF for _S. invicta_, whereas MLP showed the highest possibility for _A. gracilipes_ under the current climate. It is expected that the occurrence possibility of _S. invicta_ will remain relatively unchanged in 2050, with the largest variation in the RF model (1.5%). In contrast, relatively large variations in the occurrence possibility of _A. gracilipes_ were predicted in 2050 compared to the current climate, showing 2-4% variations depending on the model used. In general, MLP predicted a relatively higher occurrence probability, whereas MaxEnt predicted the lowest worldwide occurrence probability, regardless of species and climate change. Figure 2: Conf. Figure 2: Classification of potential presence and absence areas for _S. imitrab_ by each model and climate change scenario.