When plants establish outside their native range, their ability to adapt to the new environment is influenced by both demography and dispersal. However, the relative importance of these two factors is poorly understood. To quantify the influence of demography and dispersal on patterns of genetic diversity underlying adaptation, we used data from a globally distributed demographic research network comprising 35 native and 18 nonnative populations of Species-specific simulation experiments showed that dispersal would dilute demographic influences on genetic diversity at local scales. Populations in the native European range had strong spatial genetic structure associated with geographic distance and precipitation seasonality. In contrast, non...