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Invasive plant species pose a major threat to wetland ecosystems. One effective way to control the spread of invasive plants is to intercept them early in the invasion process. Species distribution models (SDMs), fit with covariates related to habitat suitability, can predict where new invasions are likely to occur. For species that have not yet filled their niches during early invasions, dispersal dynamics such as proximity to known presences and/or human vectors may control spread as much as habitat suitability. Yet, many SDMs assume that the species has filled its niche, incorporate only biophysical predictors, and do not consider spatial processes. Including dispersal dynamics can account for nonequilibrium processes, thereby improving the utility of invasive SDMs. We quantified the importance of environmental (abiotic and biotic) and dispersal-related drivers (anthropogenic and endogenous) on the occurrence and abundance of Hydrocharis morsus-ranae (European frogbit; EFB), a floating aquatic plant. We fit Bayesian hurdle models with integrated nested Laplace approximations (INLAs) to 2487 quadrat observations recorded across coastal wetlands in Michigan, USA from 2011 to 2021. We found that EFB occurrence was most strongly associated with distance to the nearest known population (m), a proxy of local dispersal. EFB occurrence also exhibited a nonlinear relationship with water depth (cm), demonstrating an optimal range of water depth for EFB. Occurrence was negatively associated with wave energy and positively associated with cattail (Typha spp.) abundance, which we attribute to protection from waves. Surprisingly, none of our predictors had any meaningful associations with EFB abundance, suggesting that it may be too early in EFB's invasion stage to quantify important drivers of abundance once at a site, or we did not include important factors that operate at the scale at which these growth processes occur. Moreover, the dispersal model yielded slightly better predictive capacity of EFB across Michigan. Overall, our results indicate that local dispersal is the primary driver of occurrence for an invasive species that has not yet filled its niche, whereas additional data or SDMs may be necessary to (a) better predict its abundance once established in coastal wetlands and (b) identify susceptible areas to future invasions.