## 3 Results  
We found that an increase in the number of present records could reduce the accuracy of the SDMs (Figure 2). We found that there were significant relationships between fine scales and coarse scales in the current day and in the future (Table 1). The relationships between 2.5 arcminutes and the other three spatial scales were the largest for the potential of IAPS to invade protected areas and the inequality of IAPS invasion for protected areas (Table 1).  
The most significant relationship was observed between the potential of IAPS to invade protected areas modeled with 5.0 arcminutes and PC1 in the present and future (\(S_{t}\); average R\({}^{2}\) = 95.92%; \(p\) < 0.001; Figure 3). The invasion inequality of IAPS for protected  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multicolumn{6}{c}{**Potential**} & \multicolumn{6}{c}{**Inequality**} \\ \hline  & **2.5** & **5** & **10** & **30** & **2.5** & **5** & **10** & **30** \\ \hline
2.5 & 1 & 0.9987 & 0.9935 & 0.9438 & 1 & 0.949 & 0.7711 & 0.4126 \\
5 & 0.9987 & 1 & 0.9952 & 0.9473 & 0.949 & 1 & 0.7882 & 0.4057 \\
10 & 0.9935 & 0.9952 & 1 & 0.9536 & 0.7711 & 0.7882 & 1 & 0.4616 \\
30 & 0.9438 & 0.9473 & 0.9536 & 1 & 0.4126 & 0.4057 & 0.4616 & 1 \\ \hline \end{tabular}
\end{table}
Table 1: The relationships between the potential presence of IAPS-invaded protected areas and the inequality of IAPS-invaded protected areas; 0.5: 0.5 arcminutes; 2.5: 2.5 arcminutes; 5.0: 5.0 arcminutes; 10.0: 10.0 arcminutes. All the relationships were significant (\(p\) < 0.001).  
Figure 2: The records and AUC values for nine IAPS.  
areas modeled with 5.0 arcminutes was also significantly related to PC1 in the present and future (\(D_{t}\); average R\({}^{2}\) = 89.23%; \(p\) < 0.001; Figure 3 and 2.5 arcminutes also showed a significant relationship with PC1 (average R\({}^{2}\) = 92.75% for potential and R\({}^{2}\) = 86.78% for inequality; \(p\) < 0.001; Figure 3). There was little bias in the invasion inequality of IAPS for protected areas between 2.5 arcminutes and 5.0 arcminutes. The scale of 5.0 arcminutes was the most consistent when using PC1 of these two indicators to evaluate the risk of IAPS for protected areas (Figure 4). However, above all, we used 5.0 arcminutes to evaluate the risk of IAPS for protected areas via the potential of IAPS to invade protected areas (\(S_{t}\); Figure 4). Based on 2.5 arcminutes and 30 arcminutes, most protected areas that were invaded by IAPS were distributed in southern China under climate change (Figure 5; Table S2). The protected areas, including Damingshan, Dayaoshan, Yunkaishan, Maolan, Qianjiadong, and Yongzhoudoupangling, were shown to be significantly invaded by IAPS in the present and the future (Figure 5; Table S2).  
Figure 4: The linear relationships (coefficient of determination; R\({}^{2}\)) between the invasion potential of IAPS and the invasion inequality of IAPS for protected areas across all the scales and PC1. Current: the present day; RCP4.5: low-gas-concentration scenario; RCP8.5: high-gas-concentration scenario.  
Figure 3: The linear relationship (coefficient of determination; R\({}^{2}\)) of risk of IAPS for protected areas, comparing different scales of resolution (i.e., 0.5 arcminutes, 2.5 arcminutes, 5.0 arcminutes, and 10.0 arcminutes) and PC1 in different concentration scenarios. Current: the present day; RCP4.5: low-gas-concentration scenario; RCP8.5: high-gas-concentration scenario; 0.5: 0.5 arcminutes; 2.5: 2.5 arcminutes; 5.0: 5.0 arcminutes; 10.0: 10.0 arcminutes. All the relationships were significant (i.e., \(p\) < 0.001).