Invasive alien species cause major changes to ecosystem functioning and patterns of biodiversity, and the main factors involved in invasion success remain contested. Using the Mediterranean island of Crete, Greece as a case study, we suggest a framework for analyzing spatial data of alien species distributions, based on environmental predictors, aiming to gain an understanding of their spatial patterns and spread. Mediterranean islands are under strong ecological pressure from invading species due to their restricted size and increased human impact. Four hypotheses of invasibility, the “propagule pressure hypothesis” (H1), “biotic resistance hypothesis vs. acceptance hypothesis” (H2), “disturbance-mediated hypothesis” (H3), and “environmental heterogeneity hypothesis” (H4) were tested. Using data from alien, native, and endemic vascular plant species, the propagule pressure, biotic resistance vs. acceptance, disturbance-mediated, and environmental heterogeneity hypotheses were tested with Generalized Additive Modeling (GAM) of 39 models. Based on model selection, the optimal model includes the positive covariates of native species richness, the negative covariates of endemic species richness, and land area. Variance partitioning between the four hypotheses indicated that the biotic resistance vs. acceptance hypothesis explained the vast majority of the total variance. These results show that areas of high species richness have greater invasibility and support the acceptance hypothesis and “rich-get-richer” distribution of alien species. The negative correlation between alien and endemic species appears to be predominantly driven by altitude, with fewer alien and more endemic species at greater altitudes, and habitat richness. The negative relationship between alien and endemic species richness provides potential for understanding patterns of endemic and alien species on islands, contributing to more effective conservation strategies.