A recent paper in PNAS talks about ancient DNA results in Ireland. The story is getting to be a familiar one: 5000 years ago Ireland was inhabited by a Sardinian-like population, 4000 years ago by people pretty similar to the Irish today. Looks like near-total replacement. Since the Corded Ware culture was in place by 4900 years ago, we know that the replacement process in northern Europe took less than 900 years, maybe a lot less. Ongoing ancient DNA investigations should give us a pretty good chronology in the next few years.
Some questions are going to be harder to answer. Why near-replacement in northern Europe, but not in southern Europe? Obviously Indo-Europeans imposed their languages, lots of Y-chromosomes, and made an autosomal contribution to southern Europe, but it doesn’t look like replacement. Sometimes these things boil down to choices, as when the Mongols started taxing the southern Chinese rather pursuing extermination. Maybe a prehistoric Yelü Chucai convinced the invaders that the EEF population was good for something (pizza?), or on the other hand, maybe some of those southern populations put up stronger resistance. Yet the G2a Y chromosomes, once dominant, are very much reduced in number.