Invasive plant species impact ecosystems by altering native plant community composition and modifying ecosystem properties such as fire and nutrient cycles. We used species distribution models to address both theoretical and applied questions regarding invasive plants in an ecosystem particularly vulnerable to invasion, riparian areas. In our first study, we asked whether a native species is closer to equilibrium than a functionally similar invasive species and determined drivers of invasion for an aggressive invader of riparian areas, Phalaris arundinacea (reed canarygrass). We modeled the presence of P. arundinacea and a comparable native species using four techniques and compared model fit between species and between models with and without dispersal processes incorporated. Non-dispersal model fit for our invasive species was lower than for the native species and improvement in fit with the addition of the dispersal constraint was greater for the invasive species than the native species. These results provide evidence that invasive species are further from equilibrium than native species and suggest that dispersal processes should be considered when modeling invasive species. In our second study, we addressed whether there was a set of site traits that make some sites more prone to invasion by non-native plants than others. We used Random Forests to individually model the presence of 11 invasive plant species that are designated as noxious weeds in our study area. We used model results to identify general patterns of invasion and to provide management recommendations for the study area. We found that a particular site type was more likely to be invaded by the majority of study species: hot, dry sites with high grass or shrub cover near roads with high nutrient levels and high stream baseflow values. Management recommendations to combat invasion by P. arundinacea in particular and invasive species in general are the same: limiting species’ spread along roads, lowering site nutrient levels, and anticipating increased spread with climate change.