I have criticized the “pots not people” paradigm on this weblog before. In short, the idea is that material cultural changes reflected in the archaeological record are an indicator of memetic, not genetic, evolution. So a shift from pottery style X to pottery style Y informs you of an cultural switch. This is not implausible on the face of it. In the year 450 the dominant religion in the Roman Empire was a derived Jewish sect, Christianity. The only other de jure recognized religious organization within the Empire was another derived Jewish sect, an early form of Rabbinical Judaism.* But most people assume that there was far less genetic gains to Jews and Jewish-derived people. Rather, it was Jewish ideas which spread to non-Jews, and superseded non-Jewish ideas.
The German magazine Der Spiegel has a rather thick new article out reviewing the latest research which is starting to reintroduce the concept of mass folk wanderings into archaeology. The title is How Middle Eastern Milk Drinkers Conquered Europe. In the story you get a good sense of the recent revision of the null model once dominant within archeology that the motive forces of history manifested through the flow of pots and not people. This viewpoint came to ascendancy after World War II, and succeeded an older method of interpretation which presumed a tight correlation between race and culture. It repudiated the idea that the flow and change of pottery styles and extant patterns of linguistic dialects may have been markers for the waxing and waning of peoples.
Obviously a pots-not-people model had some major exceptions even during its heyday. The demographic explosion of European peoples after 1492, and especially the Anglo peoples after 1700, occurred within the light of history. Even if it hadn’t it would be ludicrous on the face of it to assert that the modern American population were derived from the indigenous populations, and that they had simply adopted the language, religion and folkways of the British conquerors of North America. But outside the presumed aberration of the European imperialist and colonial venture of the modern era the details on the ground were obscure enough that a model could be imposed from without.