Darwin's naturalization conundrum provides an important theoretical basis for predicting the invasion of alien species. However, Darwin's naturalization and pre-adaptation hypotheses predicted two different results. Darwin's naturalization conundrum debates whether differences or similarities among species promote the successful invasion of alien species, which may be due to the neglect of the multidimensional nature of functional traits. The multidimensional nature of functional traits implies that different functional traits represent different ecological functional axes. Invasion by alien species is the result of different ecological processes in multiple dimensions. According to the modern species coexistence theory, this study constructed a model framework for invasion prediction based on the two dimensions of environmental filtering and fitness differences. Different dimensions correspond to different functional traits and species-similarity relationships. The prediction model showed that alien species that tended to be similar to native species in terms of environmental dimensions and different from native species in terms of fitness dimensions were potentially invasive species, and their damage mainly depended on the community assembly of native communities. The model framework can provide a theoretical basis for the early warning of alien species invasion and practical guidance for biodiversity protection and management.