This whole notion of cultural DNA being passed on from long-ago departed former inhabitants of a place sounds a bit like the popular superstition that ghosts of long-past eras hang around their former home and ''possess'' the people who later inhabit their haunted territory. So if I understand it right, the WASPs and Puritans of old New England are now possessing the bodies of all the diversities who live in Boston and New Haven or Manchester, N.H., and maybe even those Somalis that live in Lewiston, Maine.
I found this observation amusingly apt, having just finished listening to an interview with Colin Woodard in which the following exchange occurs (around 39 minutes into this podcast):
Host: One of the big fears in many countries is how immigration will change the very nature of a city or a state or a place and what's interesting from what you're saying is actually you can be a little more relaxed about that because there's something almost secretive, deep-rooted, almost magical, you can't quite explain it logically that lives on generation to generation, that if you have a sensible immigration policy actually the people who come will be pulled into that story as well, because as you've said before when you go back to look at some of these communities the people for example in New York who trace their roots back to being Dutch is minimal but something from that settlement still affects New Yorkers.
Woodard: You are correct, in that in theory in any country or place in the world if one moves there you would assimilate maybe you personally wouldn't fully successfully do it because you'll always be a foreigner maybe in your own mind or can't master the language completely. But your children will and your grandchildren almost certainly will, if there aren't cultural impediments to being assimilated or allowed to assimilate.