Species range shifts in response to climate and land use change are commonly forecasted with species distribution models based on species occurrence or abundance data. Although appealing, these models ignore the genetic structure of species, and the fact that different populations might respond in different ways because of adaptation to their environment. Here, we introduced ancestry distribution models, that is, statistical models of the spatial distribution of ancestry proportions, for forecasting intra-specific changes based on genetic admixture instead of species occurrence data. Using multi-locus genotypes and extensive geographic coverage of distribution data across the European Alps, we applied this approach to 20 alpine plant species considering a global increase in temperature from 0.25 to 4 °C. We forecasted the magnitudes of displacement of contact zones between plant populations potentially adapted to warmer environments and other populations. While a global trend of movement in a north-east direction was predicted, the magnitude of displacement was species-specific. For a temperature increase of 2 °C, contact zones were predicted to move by 92 km on average (minimum of 5 km, maximum of 212 km) and by 188 km for an increase of 4 °C (minimum of 11 km, maximum of 393 km). Intra-specific turnover-measuring the extent of change in global population genetic structure-was generally found to be moderate for 2 °C of temperature warming. For 4 °C of warming, however, the models indicated substantial intra-specific turnover for ten species. These results illustrate that, in spite of unavoidable simplifications, ancestry distribution models open new perspectives to forecast population genetic changes within species and complement more traditional distribution-based approaches.