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View Full Version : Common Ancestor -- What Are The Odds?

Contrapuntal
10-24-2007, 06:42 AM
In light of Lynn Cheney's revelation that Barack Obama and VP Cheney are eight cousins, I am wondering how likely it is that any two people in America will share a common ancestor from 400 years ago or so. (Their common ancestor was a 17th Century French immigrant.)

John Mace
10-24-2007, 08:37 AM
Probably pretty good if we're talking about people of Western European ancestry, since the Most Recent Common Ancestor (http://en.wikipedia.org/wiki/Most_recent_common_ancestor) for all Western Europeans is thought to have lived as recently as 1000 years ago.

If you're talking about any two random Americans, the odds are obviously going to go down.

BobLibDem
10-24-2007, 08:51 AM
How reasonable is this computation:

The common ancestor begets siblings in the first generation, cousins in the second generation, second cousins in the third generation, and so on to eighth cousins in the ninth generation. If each of the descendents had 2 children, then the ninth generation is going to have 512 members. Take the 300,000,000 population of the US and divide by 512 and I get something like 1 in 585,000. That seems quite high intuitively but I can't find a flaw in the reasoning. Even if they have 4 children per generation that's still only 1024 in generation 9.

Giles
10-24-2007, 09:03 AM
If two Americans have ancestors back for several generations in the US then the odds will be much higher than if they areboth recent immigrants from different parts of the world. For example, with Barack Obama's father (from Kenya), and Tiger Woods' mother (from Thailand), you would expect to have to go back a lot more generations to find a common ancestor.

WhyNot
10-24-2007, 09:11 AM
Probably pretty good if we're talking about people of Western European ancestry, since the Most Recent Common Ancestor (http://en.wikipedia.org/wiki/Most_recent_common_ancestor) for all Western Europeans is thought to have lived as recently as 1000 years ago.

I'm going to need this in Captain Dummy Speak. You're saying that all Western Europeans are descended from the same person who lived in 1007 CE? But...don't we have books and stuff written from that long ago? There were tens of thousands of people living then, and only one has surviving descendants? I know that can't be right, and the problem must be that I'm misunderstanding the concept of MRCA, but the wiki article isn't helping me here.

Giles
10-24-2007, 09:18 AM
I'm going to need this in Captain Dummy Speak. You're saying that all Western Europeans are descended from the same person who lived in 1007 CE? But...don't we have books and stuff written from that long ago? There were tens of thousands of people living then, and only one has surviving descendants? I know that can't be right, and the problem must be that I'm misunderstanding the concept of MRCA, but the wiki article isn't helping me here.
The MRCA in Western Europeans is the most recent person who is an ancestor of all Western Europeans. Note that there may be more than one MRCA -- it could be that a husband and wife are jointly the MRCA, though it's more likely to be a man with many illegitimate children -- and that the father and mother of the MRCA are also common ancestors, but not most recent CA.

However, many others alive in that generation may have large numbers of descendants. Some might have more that 99% of all Western Europeans as a descendant, but you need 100% to be the MRCA.

BwanaBob
10-24-2007, 09:28 AM
How reasonable is this computation:

The common ancestor begets siblings in the first generation, cousins in the second generation, second cousins in the third generation, and so on to eighth cousins in the ninth generation. If each of the descendents had 2 children, then the ninth generation is going to have 512 members. Take the 300,000,000 population of the US and divide by 512 and I get something like 1 in 585,000. That seems quite high intuitively but I can't find a flaw in the reasoning. Even if they have 4 children per generation that's still only 1024 in generation 9.

It seems high because you're assuming all these ancestors were unique and that's almost never the case. I know from my own family tree that about 6 generations ago, a couple who shared a common great grand father got married.
So the tree just go pruned in half right there. It was very common in the past for 2nd cousins to marry (heck Ithink even first cousins marrying was common); many people lived in small towns and you couldn't avoid meeting "distant" relatives everyday.

John Mace
10-24-2007, 10:21 AM
It seems high because you're assuming all these ancestors were unique and that's almost never the case. I know from my own family tree that about 6 generations ago, a couple who shared a common great grand father got married.
So the tree just go pruned in half right there. It was very common in the past for 2nd cousins to marry (heck Ithink even first cousins marrying was common); many people lived in small towns and you couldn't avoid meeting "distant" relatives everyday.
Yep. If you assumed only unique ancestors, there would have to have been 1B people on the earth 30 generations ago (about 600 years ago). That clearly wasn't the case, since we hit the 1B mark only about 200 years ago. I suspect that very few of us could trace our ancestry back more than 10 generations w/o encountering duplicate ancestors.

BobLibDem
10-24-2007, 02:12 PM
It seems high because you're assuming all these ancestors were unique and that's almost never the case. I know from my own family tree that about 6 generations ago, a couple who shared a common great grand father got married.
So the tree just go pruned in half right there. It was very common in the past for 2nd cousins to marry (heck Ithink even first cousins marrying was common); many people lived in small towns and you couldn't avoid meeting "distant" relatives everyday.

It seems to me that marriage among distant relatives would make the family trees narrower, not wider. In my example of 9 generations with 512 in the latest, would not marriage of relatives merely make some of the people in the ninth generation present more than once? Once as descendent of A, another as descendent of A's relative B.

Hari Seldon
10-24-2007, 02:49 PM
If you take one person and look at his descendants, the probability approaches 1 that he or she will have no descendants in some generation down the line. He may have no children or one or more of his children have no children or.... The result of this is that a relatively small number of people have all the decendants after enough time has passed. Although it is possible that there was someone in the British Isles 1000 years ago from whom every Brit is descended, it sounds unlikely to me because there has been too much immigration (especially in the years following 1066 and all that). Another point to remember, however, is that by the time you get to around 16 generations, it is getting unlikely that you have inherited even one gene from that ancestor. That's because 2^16 is over 65,000, while we have only about 25,000 genes. Perhaps I am descended from Solomon, but you can't explain my intellectual abilities from that.

Pleonast
10-24-2007, 03:14 PM
If you take one person and look at his descendants, the probability approaches 1 that he or she will have no descendants in some generation down the line.This doesn't seem right. What I think you mean, is: If you take one person and look at his descendants, at some generation he will he either be an ancestor to all or none. Thus making this true:The result of this is that a relatively small number of people have all the decendants after enough time has passed.That fraction of people who have all the descendants does not approach zero.

Peter Morris
10-24-2007, 10:55 PM
I'm going to need this in Captain Dummy Speak. You're saying that all Western Europeans are descended from the same person who lived in 1007 CE? But...don't we have books and stuff written from that long ago? There were tens of thousands of people living then, and only one has surviving descendants? I know that can't be right, and the problem must be that I'm misunderstanding the concept of MRCA, but the wiki article isn't helping me here.

No, I don't think it's that none of the others have surviving descendants. I guess the majority of adults back then have surviving descendants. Its just the way the families intermingle.

Our Guy had many children. Lets say he had a harem full of wives and 20 children that survived into adulthood. They married into 20 different families, and had on average 6 children each. Each of those married into a different family, and there we have 120 families descended from Our Guy. Add a few more generations and Our Guy becomes ancestor of everyone.

Darryl Lict
10-25-2007, 07:34 AM
I seem to recall some article which claimed that every Western European was a descendent of Charlemagne . I'm thinking that it was actually some respected magazine like Scientific American or National Geographic. Unfortunately, the only cite I can find is this unimpressive website (http://home.planet.nl/~voort359/home3int.html) which states:

By now, at the dawn of the 21st century, most West-Europeans are descended from Charlemagne, who had at least 25 children. And when the great genetical melting pot keeps working for another 100 years, the majority of the world population will have become Charlemagne's offspring, whether they are aware of it or not.
This site (http://genealogical-gleanings.com/Charlemagne.htm) talks about his known offspring:
Charlemagne had sons: Louis "the Pious" whom he made his heir, Pepin I, and Karl "the Younger" and daughters: Adelheid and Rotrud by his consort, Hildegarde Von Vintzg one of 10 women with which he was reputed to be involved. He had a son, Theodorich with his consort, Adelinde. With his consort, Gerswinda of Saxony, he had a daughter, Gerswinda Adeltrud. Rothilde was his daughter with consort Maldegard. Another daughter, Hruodhaid whose mother's name is unknown, addded to his progeny. Sons Drago and Hugo were the offspring of consort, Regina. Pepin "Der Bucklige" was the son of Hililtrud. With Fastrada, Charlemagne had daughters: Theodrada and Hiltrud. All of Charlemagne's daughters remained with him, unmarried until after his death as he desired their company to be with him.
I guess if his daughters were unmarried at the time of his death, that diminished the quantity of his descendents, but I'm guessing that he was screwing around quite a bit when he was running around conquering all those people.

Tibidabo
10-25-2007, 09:19 AM
Some geneticists believe that everybody on earth is at least 50th cousin

http://www.straightdope.com/classics/a2_083b.html

Er... if that helps with the ol' calcumalations, like.