Another reason why I posted that graph was to show that the impact of immigration is overestimated.
High immigration during the period of 1830 - 1914 did not really "totally overwhelm" the 1790-1830 "old stock" Americans, because the U.S. population was growing not only thanks to immigration, but also thanks to very high rates of natural growth.
It seems that the high average rate of natural increase (livebirths minus deaths per 1000 people per year) was driven by good health, relative prosperity based on people owning their own land or running their own businesses, and very high birthrates.
Here is the data on rates of natural increase in the USA during each decade (I used this data to make the graph posted above):
http://www.nber.org/papers/h0056
JohannaK said:
Perhaps one is of Anglo-Irish ancestry and after 10 years decides to identify his ancestry as Irish rather than as English, for whatever reasons.
Or someone is of Romano-Briton ancestry and after 10 years decides to identify his ancestry as Anglo-Saxon or Gaelic Scottish*, for whatever reasons. Or someone is of Breton ancestry and after 10 years becomes a Scoto-Norman and after next 10 years becomes a Gaelic Scot, only to turn into an Inglis-speaking Scot 10 years later, only to emigrate to Ireland and become a Scotch-Irish later, etc. OK, but that was not the main point.
The main point was to show that Americans are not as much a "nation of immigrants" as is usually claimed, because many of them are still descendants of the old "colonial stock" - i.e. those who lived in the English colonies before independence, before the 1790 census.
Of course those people had also immigrated to North America before 1776 - but by that time they were European colonists, not Americans.
*Original people of Scotland were Brythonic-speaking Britons and Picts. Gaelic-speakers came from Ireland and founded the Scottish realm, their Gaelic language replaced Brythonic in most of Scotland. But in Bernicia (Scottish Borders) English was already spoken when Gaels conquered that land.