Clark and Cummins note that their estimates suggest that family background has a much bigger impact on social status than previous studies have found. Another is that genetics likely has little to do with those results. Clark and Cummins studied surnames across eight generations. So, two people with the same surname in 1800 and 2011 would only share 0.58= 0.4 percent of their DNA.For the bulk of those years, 1800 onto about 1960, reasonable people thought about marrying people with good breeding. This is because, before the widespread use of contraception, people generally had harsh cold reality intruding upon their idiotic fantasies. Sex would result in children, and the bad boy on the block wasn't going to provide. So, smart women made more accurate calculations. They did not have DNA testing, but there was a general sense of what made for good breeding, and it is in this way that genetics matters.
Within every single generation, with the decision about who to marry, genetics mattered. Since there was no test, they used signals that would function as proxies- indeed a prominent family name may well be a just such a signal.
So, it doesn't matter that "two people with the same surname in 1800 and 2011 would only share 0.58= 0.4 percent of their DNA" what matters is whether or not the genetic line improved. I suspect, though, a certain level of prosperity functions similarly to the pill, and allows for more fantasy, which would be why many elite names eventually fall.