Assume for simplicity that each man has one son and one daughter. He will have four grandchildren (son’s son, son’s daughter, daughter’s son, daughter’s daughter) of whom just one will carry that grandfather’s Y-chromosome.
After 10 generations, there will be 2[sup]10[/sup] = 1024 descendants, but only one will be an agnatic (Y-chromosome) descendant.
After 36 generations, just enough to take us from William the Conqueror to the present, there will be 2[sup]36[/sup] = 69 billion descendants with, again, just one of them carrying William’s Y-chromosome.
Of course that’s too simplified. The upper castes were much more productive than the lower castes, so William has more than 69 billion living descendant slots. How is that possible, with the total world population much less than 69 billion? We’re counting slots. The numbers would balance if he had just 69 million descendants, but appeared 1000 times in the fully expanded pedigree of each of those 69 million.
And indeed, William probably is the ancestor of most Englishmen. But as far is as known, nobody retains his Y-chromosome. Similarly, Charlemagne and Clovis the Great have billions of descendants but, as far as is known, no agnatic descendants. Most Y-chromosomes die out after a few generations.
But the Y-chromosomes that are successful are very successful. There are several hundred thousand Americans surnamed Stewart and, although most are not agnates of the Lord High Stewards of Scotland, many of them are.
Especially astounding, I think: It is now known that over half the present male population of Western Europe are agnates (Y-chromosome descendants) of a King (now known only as “R-L151”) who lived near Bavaria about 3000 BC. He founded a huge royal dynasty (now named for its Bell Beaker pottery style) that rapidly spread out and conquered Britain, France, Spain, etc. You can see his descendant clades here. In a few years time, expect these clades to be mapped to specific migrations and invasions.
