This is an ongoing debate and a single study will not decide things one way or the other. In recent years, the evidence has been shifting towards the replacement model. In northern Europe, there seems to have been a genetic divide between late hunter-gatherers and early farmers (although the divide is just as great between the latter and present-day Europeans). In particular, European hunter-gatherers possessed genetic lineages (haplogroup U) that are rare among present-day Europeans.
Now, the pendulum is swinging back. After studying 92 Danish human remains that range in time from the Mesolithic to the Middle Ages, Melchior et al. (2010) have found evidence of genetic continuity from late hunter-gatherers to early farmers.
The extent to which early European farmers were immigrants or descendants of resident hunter-gatherers (replacement vs. cultural diffusion) has been widely debated, and new genetic elements have recently been added. A high frequency of Hg U lineages, especially U5, has been inferred for pre-Neolithic Europeans based on modern mtDNA data, with Hg U5 being fairly specific to Europe.
[…] The present findings indicate that predominantly haplogroup U lineages persist among Neolithic/Bronze Age population samples in Southern Scandinavia and it may point to regional variation in the penetrance rate of these lineages across cultural shifts in different areas of North Europe. Given our small sample sizes from these crucial time periods further studies are certainly required. However, the frequency of Hg U4 and U5 declines significantly among our more recent Iron Age and Viking Age Danish population samples to the level observed among the extant Danish population. Our study therefore would point to the Early Iron Age and not the Neolithic Funnel Beaker Culture as suggested by Malmström et al. (2009), as the time period when the mtDNA haplogroup frequency pattern, which is characteristic to the presently living population of Southern Scandinavia, emerged and remained by and large unaltered by the subsequent effects of genetic drift.
As the authors note, the sample sizes were small. But it is odd that all of the Neolithic and Early Bronze Age samples were either U4 or U5a. These lineages now account for only 1–5% and 5–7% of present-day Europeans.
Melchior, L., N. Lynnerup, H.R. Siegismund, T. Kivisild, J. Dissing. (2010). Genetic diversity among ancient Nordic populations, PLoS ONE 5(7): e11898.