In response to rapid climate change and increasing human pressure, a wide variety of taxa have shifted their distribution in the past decades (range shift), with important consequences for ecosystem services and human health and economy. However, it is not yet clear whether most species will be able to track their favourable habitats or lag behind the climate signal (migration lag). Studying the paleo-vegetation response to past climatic fluctuations may help to understand the ecological processes underlying range shift dynamics. This thesis aims to implement an efficient model to hind- and fore-cast the range shift of the vegetation at large temporal and spatial scales. To this end, we used the dynamic global vegetation model (DGVM) LPJ-GM, which couples a migration module to the widely-used DGVM LPJ-GUESS, thus allowing plant species to migrate while interacting with each other. [...]