The regional distribution of a plant species is a result of the dynamics of extinctions and colonizations in suitable habitats, especially in strongly fragmented landscapes. Here, we studied the role of spatial dynamics of the long-lived, clonal pioneer plant Geum reptans occurring on glacier forelands in the European Alps. We used demographic data from several years and sites in the Swiss Alps in combination with dispersal data to parametrize a matrix model for G. reptans to simulate extinctions, colonizations and spatial spread of established populations on glacial forelands. We used different scenarios with varying germination rates, wind and animal dispersal capabilities, and modes of spatial spread (seed-only vs clonal spread), resulting in population growth rates (lambda) ranging from 1.04 to 1.20. Our results suggest that due to the low germination rate (similar to 1%) and the very limited wind dispersal distances (99.8% of seeds are dispersed < 5 m), G. reptans has a low probability of establishing new populations and a very low spatial spread by seed dispersal alone. In contrast to the low rate of establishment, the persistence of established populations is high and even populations of only a few individuals have an extinction probability of less than 25% within 100 years. This high persistency is partly due to clonal reproduction via aboveground stolons. Clonal reproduction increases the population size and contributes considerably to the spatial spread of established populations. Our simulation results together with the known pattern of molecular diversity of G. reptans indicate that the occurrence of populations of this species in the Alps is unlikely to be a result of recent colonizations by long-distance dispersal, but rather a result of post-glacial colonizations by large migrating populations that were fragmented when glaciers retreated. Additionally, our simulations suggest that the currently observed high rates of glacial retreat might be too fast for pioneer plants, such as G. reptans, to keep up with the retreating ice and therefore might threaten existing populations.