Concern over surges of immigration by unfamiliar groups is a hardy perennial of American history: Scotch-Irish (1763-1775), Irish and Germans (1846-55), Ellis Island arrivals from Eastern and Southern Europe (1892-1914), Mexicans and other Latinos (1982-2007). That’s the list from Michael Barone, the political sage and immigration expert.

But there’s another phenomenon that comes, quite reliably, a generation later. “After the immigrants more or less blend in—a difficult process sometimes—Americans look back with affection,” Barone says. And they brag about the United States as “a nation of immigrants”—John F. Kennedy’s phrase—with a “melting pot” that assimilates newcomers as Americans.