I would like to return to this suggestion, pretty much overlooked. It provides a rational explanation; and if correct, would imply that the level of 'Steppe DNA' in the Iberian late Chalcolithic is probably significantly overstated, with the skeletons found in the cemeteries only being those from the elite Steppic lineages. The samples analysed could be unrepresentative of the general population, with non-Steppic people excluded.
The important question is - is it true? Is this sex-specific pattern replicated in other Steppic populations? If it is, then this would provide convincing circumstantial evidence that what Crazy Donkey suggested is actually what was happening. What does the data have to say about Corded Ware samples, for instance - are the females more Steppic on average? And Yamnayan samples - are the females less CHG-infused?
The "newcomers" are still steppe-admixed, while the "old-timers", if you will, aren't. How much really doesn't matter. There is a clear demarcation. Dilution is to be expected, unless migrating directly, by boat. That the Lower Danube, Carpathian Basin, Hungarian Plains, and Low Countries were ethnic/genetic "mixing bowls" does not mean that elite lineages weren't guarded (by some degree of endogamy), a preferred language was not faithfully transmitted, or closely held cultural traditions were not maintained.
That non-steppic populations persisted as a "ghost" population remains to be seen. I suspect a combination of:
* A depopulating event (drought, famine, plague).
* Intrusion by herders into the vacuum (previously farmed areas turned to "scrub").
* Possible seizure by the invaders of the copper mines, which were the real source of Iberian wealth.
* Breaking of the connection of "town and country", with "cities" (if villes with a thousand residents can be called such) turned into isolated "islands".
* Further population loss due to conflict, warfare, sieges, etc. This could also help explain the even ratio of men/women in the cemeteries, rather than the expected male surplus, in that many bodies of warriors lost in battle might never have been recovered or were buried on the spot.
* Leading to 1) dispersal/emigration to neighboring regions and/or 2) assimilation into the dominant group and economy, resulting in the distribution of steppic genetic admixtures (along with further dilution) across the remaining population. For another example of mass migration/assimilation resulting from "crofters" being replaced by herders, see the Highland Clearances.
Note, however, that this did not lead to language loss/conversion in much of Iberia, despite ruling elites or cliques being replaced, with Iberian surviving along the southeast coast until Roman times and Basque in the north until now.