## 4 Discussion
Previous studies [17; 18; 33; 34] showed the impact of the scale effect on the results of SDMs (e.g., Maxent) and indicated that the fine scales were fit for modeling the potential distributions of species. However, several studies have also used coarse scales to map the distributions of species [4; 15; 35; 36]. Hence, our suggestion was to use different scales of resolution as the inputs of SDMs, and then a simple method to integrate various scales into SDMs was proposed. We found that 2.5 arcminutes and 5.0 arcminutes were the most appropriate for the evaluation of the risk of IAPS for protected areas (2.5 arcminutes and 5.0 arcminutes for the invasion inequality of IAPS for protected areas and 5.0 arcminutes for the potential of IAPS to invade protected areas). Hence, 5.0 arcminutes could account for most scales and demonstrated the weakest effect of scale on the potential distributions of multiple species. We also found an interesting result in that there was a significant relationship between the potential of IAPS to invade protected areas and the invasion inequality of IAPS for protected areas across all scales, and 5.0 arcminutes was the most consistent with PC1 for these two indicators. To summarize, we used 5.0 arcminutes to evaluate the risk of IAPS in protected areas. Some researchers have used SDMs to model the potential distributions of species in protected areas, including endangered species and IAPS [4; 37; 38; 39; 40]. Here, we predicted the potential distributions of IAPS in Chinese protected areas and found that Damingshan, Dayaoshan, Yunkaishan, Maolan, Qianjiadong, and Yongzhoudoupangling would be significantly invaded by IAPS, which indicates that we need to conduct long-term monitoring of these protected areas, particularly grids with a high possibility for the invasion of IAPS, to prevent the invasive spread of IAPS because of climate change [41; 42]. More importantly, our finding that there was a significant relationship in terms of invasion risk between the present day and the future suggests that we should attach importance to the current risk of IAPS for protected areas. How can we evaluate the risk of IAPS for protected areas under climate change? We used the ability of IAPS to invade protected areas to assess the risk of IAPS for the overall protected area and the invasion inequality of IAPS for protected areas for part of the protected area. A study by [PERSON] et al. (2011), who used SDMs to assess the ability of protected areas to protect endangered species under climate change, provided insights into evaluating the risk of IAPS for protected areas [4; 43]. We regarded a large proportion of suitable habitats of IAPS as having a high risk in the overall protected area. The current level of protected areas invaded by IAPS was consistent with the future when following the patterns of greenhouse gas emissions. However, we also found that greenhouse gas emissions, particularly in the high-emissions scenario, will increase the uncertainty of the change in IAPS risks for protected areas. We should not ignore the differentiation of IAPS invasions into different parts of protected areas. For the protected areas violently invaded by IAPS, the high invasion inequality of IAPS indicated that the difference in habitat quality was large, and vice versa. Hence, the invasion inequality reflected the risk areas of IAPS at some levels. For protected areas with high invasion inequality, we should take conservation actions based on the parts of protected areas while attaching importance to the protected areas invaded by IAPS. If the protected areas have low invasion inequality in terms of IAPS, the regions with high habitat quality are a key consideration for protected areas with high IAPS invasion risks [44]. Greenhouse gas emissions could enhance the relationship between the invasion ability and invasion inequality of IAPS for protected areas [45]. This indicates that future invasions of IAPS will be more intensely focused on protected areas compared to those of the present day.