6th 7th 11th cousins?

[Condition1]

It's been reported that Dick Cheney and Barrack Obama are 8th cousins, having a common ancestor 8 generations ago. Other reports surfaced (most done by the New England Historic Genealogical Society, not sure how credible they are) that stated Obama being related to 8 U.S. presidents including both Bushs, Harry Truman, LBJ, through something ridiculous like "11th cousins 3 times removed" and the youtube community just about lost their minds.

 

Anyways, what are the odds of random people.... well they aren't random people. What are the odds of people of the same race (Obama is biracial, but the rest are white) and similar social status being 6th, 7th, or even 11th cousins twice, three times, or even six times removed and it being some kind of unintentional coincidence?

[Mr Skeptic]

There's pretty good odds of finding such coincidental relationships. To calculate exactly what odds there are you'd have to specify the degree of separation, and then make assumptions about the number of children per couple (or actual data from specific couples). Think of it this way: If everyone has on average 2 children per couple, after 30 generations that is 1 billion 30th generation people, plus another billion of their ancestors, who would be related via direct descent from this couple. Now consider that whenever there is a marriage, this connects the original couple (and their descendants) to a new family, which will likewise have lots of people related to them. For maybe 10 generations you'd have 1000 10th generation descendants at 2 children per couple, plus another 1000 ancestors. Each time there is a marriage you could join together two families with another 1000 or so relatives for the same reasons. So if you have 10 generations and 3 rounds of marriages that's 1 billion relatives again, so long as all marriages are to unrelated people (of course in 10 generations you get 10 rounds of marriages so that would really be 1,000,000,000,000,000,000,000,000,000,000 relatives if the marriages were only between unrelated people, which is impossible -- because, obviously, everyone is already related to everyone). Anyhow, you'd need an estimate of the relatedness of people who get married to get proper numbers, and it will start getting a little too complicated for my liking. But the short answer is, everyone is related to everyone and it's just a matter of what their degree of separation is.

[Sisyphus]

Say the average person has three children - higher than today, but a conservative assumption historically.

 

Then, you have 2 siblings.

You have 4 aunts/uncles, therefore 12 first cousins.

You have 8 great aunts/uncles therefore 24 first cousins once removed, therefore 72 second cousins.

You have 16 great great aunts/uncles, therefore 48 first cousins twice removed, therefore 144 second cousins once removed, therefore 432 third cousins.

 

So, for number of nth cousins, it is 2^(n+1)*3^n. (To change average number of children, just change the 3 in this formula.)

 

So for 6th cousins, that is 93,312.

 

For 11th cousins, that is 725,594,112. (And remember that going back 11 generations, 3 children per couple would be a small family, so it's probably a lot higher than that.)

 

You also have about 1/160000000th of your genes in common as a result of that relation. (Although you would actually have far more than that, obviously.)

 

In other words, that degree of relatedness is meaningless. You and I are probably 11th cousins many times over.

 

As for the probability of each, that would be a lot more complicated to figure out, and have to take into account size of populations, degree of interbreeding, etc. All you can really say about the probability is that it's "a lot higher than you would expect."

[Condition1]

Thanks for the answers. I figured it would be logical considering the race and social class.

[John Cuthber]

Since all humans can breed with all other humans* it's fair to say that we are all related.

Since we are, therefore, all n th cousins m times removed, the question is how big a value of n and m are you prepared to put up with?

 

* there's the requirement that males breed with females but, at worst, that just means skipping a generation..

[ggbonner]

 

So, for number of nth cousins, it is 2^(n+1)*3^n. (To change average number of children, just change the 3 in this formula.)

 

 

This isn't right on three counts:

 

1. This calculation pretends that a person who is a descendant of one pair of nth-great grandparents will NOT be also a descendant of other pairs of nth-great grandparents. This is clearly not the case.

 

Take, for example, the case of 3rd cousins, and where the number of children = 2. The above formula solves to 128 third cousins. But that's not right, because the total number has to be reduced for all the examples of multiple counting. For the 8 breeding pairs of ancestors that would lead to 3rd cousins, the subject would appear in the descendants list of all 8 pairs, not just one. So that total number needs to be reduced by 8-1=7. Similarly the total needs to be reduced by 7 to account for the sibling of the subject. Then there would be 4 first cousins who would appear in 4 of the 8 breeding pairs descendants list, so the total needs to be reduced by 4*(4-1)=12. And finally, there are 16 2nd cousins who would appear in the descendants list of 2 breeding pairs, and so the total needs to be reduced by 16*(2-1)=16. This leads to a correct tally of 128-7-7-12-16=86.

 

2. The calculation does not take into consideration the fact that those descendant will be 3rd cousins OR CLOSER.

 

Of the 86 in the above calculation, not all of them will be exactly 3rd cousins. Some of them will be closer (the person's sibling, for an obvious example).

 

Of the 86 total descendants of 8 breeding pairs leading to families to include relations to 3rd cousins, the breakdown is this:

 

64 3rd cousins

16 2nd cousin

4 1st cousins

1 sibling

1 self

=86

 

3. The calculation given prior only applies to people in the terminal generation. But there are other people who would exist who are related to within 3rd cousinship. An obvious example would be an aunt or uncle, but also should include all 2nd cousins, once removed, and first cousins, once removed, etc.

 

So it is not nearly so simple as just applying an exponential times the numer of breeding pairs.