The ability of species to track their ecological niche after climate change is a major source of uncertainty in predicting their future distribution. By analyzing DNA fingerprinting (amplified fragment-length polymorphism) of nine plant species, we show that long-distance colonization of a remote arctic archipelago, Svalbard, has occurred repeatedly and from several source regions. Propagules are likely carried by wind and drifting sea ice. The genetic effect of restricted colonization was strongly correlated with the temperature requirements of the species, indicating that establishment limits distribution more than dispersal. Thus, it may be appropriate to assume unlimited dispersal when predicting long-term range shifts in the Arctic.