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Species distribution modeling aimed at forecasting the spread of invasive species under projected global warming offers land managers an important tool for assessing future ecological risk and for prioritizing management actions. The current study applies Bayesian inference and newly available geostatistical tools to forecast global range expansion for the ecosystem altering invasive climbing fern Lygodium microphyllum. The presented modeling framework emphasizes the need to account for spatial processes at both the individual and aggregate levels, the necessity of modeling non-linear responses to environmental gradients, and the explanatory power of biotic covariates. Results indicate that L. microphyllum will undergo global range expansion in concert with anthropogenic global warming and that the species is likely temperature and dispersal limited. Predictions are undertaken for current and future climate conditions assuming both limited and unlimited dispersal scenarios.