## 4 Discussion  
We built on a simple method that uses PCA to amalgamate different scales into SDMs when predicting the potential distributions of species and used our method to evaluate the risk of IAPS for protected areas in mainland China. We were able to use the linear relationship between the results of SDMs from different scales to select an appropriate scale to model the potential distributions of species. The results showed that the AUC values were significant, which ensures the accuracy and credibility of the experimental results. Figure 5: The potential of IAPS-invaded protected areas and the inequality of IAPS-invaded protected areas at both 2.5 arcminutes and 30.0 arcminutes under climate change. Current: the present day; RCP4.5: low-gas-concentration scenario; RCP8.5: high-gas-concentration scenario. Here, increasing records may weaken the performance of SDMs, which may be affected by the uncertainties in the GBIF and CVH data. The increase in records could be enriching the distribution in areas where it had not been recorded, and with other environmental conditions that also enrich the bioclimatic profiles of the species. Coarse scales can lead to a small number of occurrence records. Hence, it is possible that coarse scales can lead to high accuracy in SDM for predicting IAPS distributions under climate change. [PERSON] et al. [16] found that the patterns and determinants of species richness vary on different spatial scales. The reasons for this might include (1) the scale effect of large-scale ecology, with the effect of climate change increasing relative to species richness with decreasing scales of resolution [31], and (2) cases in which the power of the climate, including environmental energy, water resource availability, and climate seasonality, increase with geographic expansion while the power of habitat heterogeneity and human activity declines [16]. At small scales, the dispersal of IAPS and human disturbance (e.g., changes in land use) made large contributions to the development of suitable habitats for IAPS. IAPS distributions were more strongly influenced by dispersal limitations. Human disturbance can change global land cover, resulting in ecosystem fragmentation, habitat loss, and consequent changes in the local distributions of IAPS. Hence, we should identify the forms of dispersal of IAPS, and incorporate changes in land use into SDMs [16; 31; 32]. Hence, modeling the potential distributions of multiple species was influenced by the spatial scale. We need to determine the scale units to model the potential distributions of species with a fine or increasingly coarse resolution. [PERSON] et al. [17] studied the impact of using various scales on plant species distributions and proposed that it is necessary to balance fine and coarse scales. Some studies have found that there was a bias in the scale effect for the results of SDMs when using fine scales or coarse scales, and this indicated that the selection of scales may lead to an over- or underestimation of the potential distributions of species [18; 19]. We also found that the extent of the differences in the results of Maxent--namely, the invasion risk--for different scales suggested this pattern in our study. The effect of scale can be solved by applying a scale balance to the SDM results of Maxent based on the relationship between the potential distributions of species on fine scales or coarse scales [12; 30; 31]. Here, we used PC1 as the indicator representing all scales, and PC1 could explain most of the SDM results across all scales. We selected the most appropriate scale related to PC1. Our main objective was to select the scale that could reduce the difference between SDM results across all scales due to the scale effect. Thus, we could select the appropriate scale based on the relationship between the scales and PC1. We used the case of the invasion of IAPS into Chinese protected areas to explore the effect of applying a scale balance to the SDM results of Maxent using fine and increasingly coarse scales.