The only reigning successor or is the head of the House of the Hashemite the most direct male dependency with political power? I thought the House of Saud had a claim, but it wasn't as direct, so may have gone through a female or younger son in the line somewhere.
Then ya got that black turban, white turban deal within the leaders of the faith, with only those claiming to be descendants of Muhammad allowed to wear the black.
To put it into a different perspective, there are supposed to be *millions* of people said to descend from the 102 people on the Mayflower & the trip happened in 1620, well after polygamy was practiced by Christians. In 10 or 11 generations, we have millions of people from 102.