Language Log has a fascinating post up, The Linguistic Diversity of Aboriginal Europe. The distribution of language families, and their relationships, are not arbitrary. They tell us something about human history. Here is the interesting part for readers of this weblog:
It follows that the appearance of IE languages in much of Europe at an early date must reflect a considerable spread of IE languages from their point of origin. Many commentators, for a great variety of reasons, would like to believe that that spread occurred without any significant population movements; but that, too, violates the UP. It has to be remembered that those IE languages spread not as trade languages for some specialized use, but as native languages; and all our contemporary experience shows that a language can acquire new populations of native speakers only if already existing native speakers are in intimate contact with communities speaking other languages. One can imagine an IE language spreading from village to village through intermarriage, but if that's what happened, the spread must have been slow; the frontier of IE-speaking territory might have advanced, say, a depth of six villages per century by such a process--and in the mean time the IE language that was spreading in that area would have been diversifying into dialects and eventually fragmenting into two or more languages (see above). In some areas that could be what happened. But there is no way that such a process could have resulted in a few closely related Celtic dialects or languages being spoken over a large continuous territory from the Atlantic seaboard to Bohemia and beyond--a situation that clearly existed around 500 BCE...We cannot avoid the inference that there were substantial migrations of people speaking IE languages into Europe in the prehistoric period.
What they are referring to here is a wave of advance of some sort. Even if the initial numbers were substantial due to basic Malthusian dynamics, the original "genetic signal" would be vastly diminished over distance. In the late 1990s some researchers concluded that the R1a Y chromosomal haplgroup was exactly that signal, though that seems more doubtful today. Other researchers are looking to other genetic clues which might offer up insight into from where, and how, the Proto-Indo-Europeans spread. H/T Trollblog