The Arctic is currently experiencing the strongest temperature changes worldwide, causing a geographic shift in optimal habitats for many species. Trees are projected to advance into treeless tundra with increasing warmth, which will likely cause a positive vegetation-climate feedback due to an albedo decrease. To date, global simulation models generally assume that species follow the changing abiotic environment immediately. However, responses are strongly shaped by species’ traits determining seed dispersal, and the complex process of migration is not well understood. We approached better projections by parameterising dispersal processes in the individual-based spatially-explicit model LAVESI for larches at the treeline in Siberia. To do this, we inferred the effective seed dispersal based on a genetic parentage analysis using an assay of eight highly polymorphic nuclear microsatellite loci. We genotyped a total of 612 individuals from an open forest site, situated close to the border to treeless taiga at the southern Taymyr Peninsula in north-central Siberia. At this remote site, we sampled all mature trees within an area of 100x100 m2, and we sampled all recruits within the central area of the plot. The results indicated a high on-site recruitment rate of ~53%. The effective seed dispersal follows a pronounced Gaussian function with a fat-tail. The median dispersal distance of ~10 m is comparable to results from studies, but this is unexpectedly short for a wind-dispersed species in an open forest. Simulations with the improved model on hypothetical south-to-north transects revealed a slow-moving treeline front, advancing only by ~1.6 m yr-1 into tundra. While the observed colonisation of the tundra is assisted by occasional long-distance seed dispersal events beyond the treeline area, we conclude that the treeline advance in north-central Siberia currently lags behind the current strong warming and will continue to lag in the near future.