Since the last glacial period forest trees have expanded to their present range very rapidly, with rates up to 500 m yr−1 for oaks in Europe, which can be explained only by the dispersion of acorns over long distances. We used a stratified dispersal model, including both diffusive and long-distance dispersal of seeds, to simulate the colonization of a 100 km×300 km grid by populations of oak trees. An appropriate rate of spread is obtained with rare dispersal at distances of the order of tens of kilometres. We simulated the effect of stratified versus diffusive dispersal of seeds on the spatial genetic structure at a maternally inherited locus. Founding events associated with stratified dispersal generate a high amount of genetic differentiation among populations, which is likely to persist for a long time after colonization. Using autocorrelation methods, we show that diffusive and stratified dispersals create quite different spatial patterns of variation for the maternally inherited locus. Stratified dispersal creates patchy patterns that are concordant with a previous experimental investigation of chloroplast DNA variation at a regional scale in the oaks Quercus petraea and Quercus robur. For plant populations that have passed through recent episodes of range expansion, long-distance dispersal events are probably the most important factors of spatial genetic structuring of maternally inherited genes at small or medium geographic scales.