This is a truly great ancient DNA study. I haven't actually read the paper I must confess up front, but just read the review at Dienekes' Anthropology blog.
The researchers analyzed DNA from hunter-gatherer and early farmer burials, and compared those to each other and to the DNA of modern Europeans. They conclude that there is little evidence of a direct genetic link between the hunter-gatherers and the early farmers, and 82 percent of the types of mtDNA found in the hunter-gatherers are relatively rare in central Europeans today.
So it seems that when farming arrived in Europe some 7000-8000 years ago, it wasn't the local hunter-gatherers that learned farming, but rather farmers bringing their new technology. Not that they simply invaded and replaced the local people:
We know that people lived in Europe before and after the last big ice age and managed to survive by hunting and gathering. We also know that farming spread into Europe from the Near East over the last 9,000 years, thereby increasing the amount of food that can be produced by as much as 100-fold. But the extent to which modern Europeans are descended from either of those two groups has eluded scientists despite many attempts to answer this question.
Now, a team from Mainz University in Germany, together with researchers from UCL (University College London) and Cambridge, have found that the first farmers in central and northern Europe could not have been the descendents of the hunter-gatherers that came before them. But what is even more surprising, they also found that modern Europeans couldn't solely be the descendents of either the hunter-gatherer alone, or the first farmers alone, and are unlikely to be a mixture of just those two groups.
The new study confirms what Joachim Burger´s team showed in 2005; that the first farmers were not the direct ancestors of modern European. Burger says "We are still searching for those remaining components of modern European ancestry. European hunter-gatherers and early farmers alone are not enough. But new ancient DNA data from later periods in European prehistory may shed also light on this in the future."