Below I stated:
…until the late 20th century the majority of the ancestry of the white population of the republic descended from those who were counted in the 1790 census.
A commenter questioned the assertion. The commenter was right to question it. My source was a 1992 paper that estimated that only in 1990 did the proportion of American ancestry which derived from those who arrived after the 1790 census exceeding 50%. In other words, if you ran the ancestors of all Americans back to 1790, a majority of that set would have been counted in the 1790 census (so people of mixed ancestry would contribute to the two components are weighted by their ancestry).
The major issue here is that there is a difference between whites, and non-whites, especially before mass Asian and Latin American immigration post-1965, when white vs. non-white ~ white vs. black. Almost all the ancestors of black Americans who were black were already resident in the United States in 1790. A few years ago I read up on the history of American slavery and was surprised how genuinely indigenous the black American, slave and free, population was by the late 18th century (English speaking and Christian). There was an obvious reason why Southern slave-holders went along with the ban on importation of slaves which was due to kick in in the early decades of the republic: American blacks, unlike slave populations elsewhere in the New World, had endogenous natural increase. This explains part of the relative paucity of African aspects in their culture in relation to the blacks of Haiti or Brazil, where African-born individuals were still very substantial numerically at emancipation because of high attrition rates (it is sometimes asserted that the majority of blacks liberated during the Haitian Revolution were born in Africa. Likely a hyperbole, but it gets across the strength of connection).
In any case, to estimate the white proportion attributable to 1790, I have to correct for the black proportion within the total. As an approximation I think it’s acceptable to simply attribute blacks as a whole to the proportion which had ancestors here in 1790 in full. I suspect a greater proportion of the black ancestry which post-dates 1790 would come from the white component of their heritage which simply isn’t of notice in American society for various reasons in any case (Henry Louis Gates Jr. is more white than he is black in terms of ancestry, but he’s the doyen of Africana Studies). So, assuming that blacks contribute to the 1790 and before component in full, I estimate that between 1910 and 1920 the majority of the ancestry of the white population shifted from 1790 and before, to after. Specifically, in 1910 51% of the ancestry could be traced to 1790 and before among whites, and in 1920 49%. In 1950 it was 47% 1790 and before. So I should have said early 20th century, not late. I wouldn’t be surprised though if the balance has started to shift in recent years, as many “white ethnic” groups (Jews, Italians, Irish, etc.) are more heavily concentrated in urban areas, while the most fertile white community in the United States, the Mormons of Utah, are also the most Old Stock Yankee in ancestry (I am aware that many Mormons are descended from European immigrants who converted in Europe and made the journey after conversion, but Mormons are still far more Old Stock Yankee than any group outside of interior New England).