AimDespite the recent improvements made in species distribution models (SDMs), assessing species' ability to migrate fast enough to track their climate optimum remains a challenge. This study achieves this goal and demonstrates the reliability of a process-based SDM to provide accurate projections by simulating the post-glacial colonization of European beech. LocationEurope. MethodsWe simulated the post-glacial colonization of European beech over the last 12,000 years by coupling a process-based SDM (PHENOFIT) and a new migration model based on Gibbs point processes, both parameterized with modern ecological data. Simulations were compared with palaeoarchives and phylogeographic data on European beech. ResultsModel predictions are consistent with palaeoarchives and phylogeographic data over the Holocene. The results suggest that post-glacial expansion of European beech was limited by climate on its north-eastern leading edge, while limited by its migration abilities on its north-western leading edge. The results show a mean migration rate of beech varying from 270myr (-1) to 280myr(-1) and a maximum migration rate varying from 560myr(-1) to 630myr(-1), when limited and not limited by climate, respectively. They also highlight the relative contribution of known and suspected glacial refugia in present beech distribution and confirm the results of phylogeographic studies. Main conclusionsFor the first time, we were able to reproduce accurately the colonization dynamics of European beech during the last 12kyr using a process-based SDM and a migration model, both parameterized with modern ecological data. Our methodology has allowed us to identify the different factors that affected European beech migration during its post-glaciation expansion in different parts of its range. This method shows great potential to help palaeobotanists and phylogeographers locate putative glacial refugia, and to provide accurate projections of beech distribution change in the future.