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Aim Geographic variation in dispersal abilities is widespread and likely to affect species' range dynamics in response to climate change. However, distribution models that predict climate-induced range shifts do not account for spatial variation in dispersal. We developed an eco-genetic model to investigate how variation in dispersal distances across a species' range could interact with climate-induced selection and alter predicted range dynamics in a species with documented variation in dispersal traits. Location We investigated the range of an annual plant, Cakile edentula var. lacustris, which occupies beaches spanning a 555 km latitudinal gradient along the Laurentian Great Lakes. Methods We built a hybrid model that combines climatic niche modelling, based on decadal climate projections, with an individual-based model that allows for evolutionary processes to act upon a heritable dispersal kernel. We evaluated how spatial variation in dispersal distance and dispersal evolution influenced range dynamics, spatial and temporal variation in dispersal, and the distribution of neutral genetic variation. The model was parametrized with data on C. edentula's distribution, life history and dispersal characteristics. Results Geographic variation in dispersal distance, adaptive dispersal evolution and dispersal distance increased the potential for local populations of C. edentula to keep pace with changing climatic conditions through range shifts. Dispersal distances always increased at the expanding and contracting range edges when dispersal was allowed to evolve. Furthermore, scenarios where dispersal distances were initially lower at the range edges resulted in the largest evolutionary changes over 105 years (>1.5 km increase in mean distance at northern edge). Adaptive dispersal evolution always reduced neutral genetic diversity across the species' range. Main conclusions Variation in dispersal abilities across C. edentula's range and adaptive evolution led to different predicted outcomes in range dynamics during climate change illustrating the importance of including spatial variation in dispersal into species distribution models.