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chances of being a 10th cousin?

Started by Private User on Friday, December 9, 2011
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Hey guys does anyone know what the chances of any two people in this country being a 10th cousin?

Okay, so you are going to make me do the math, when I should be instead doing my reading now :)

I think you might figure 2.5 children per family - replacement rate of 2.2, plus some historical population growth. This is probably a low estimate, but to keep the numbers manageable, and to minimize the overlap.

10th cousins means that you and your cousins have both of your 9th great grandparents in common, for simplicity.

So, your 9th greats then have 2.5 children, in your 8th great-gr generation.

Each of them has 2.5(2.5)=6.25 cousins in your 7th gr-gr generation
6th gr-gr generation is 6.25(2.5)=15.625 cousins
5th gr-gr generation is 15.625(2.5)=39 cousins
4th gr-gr generation is 39(2.5)=97.66 cousins
3rd gr-gr generation is 97.66(2.5)=244.14 cousins
2nd gr-gr generation is 244.14(2.5)=610.35 cousins
1st gr-gr generation is 610.35(2.5)=1525.88 cousins
grandparent generation is 1525.88(2.5)=3814.7 cousins
parents generation is 3814.7(2.5)=9536.7 cousins
your generation is 9536.7(2.5)=23,842 cousins

But now the real problem comes in to play. You have 23,842 10th cousins, living, from just that single pair of ancestors ten generations back. But, how many ancestors do you and each of those cousins have?

gen 1 (your parents) is 2 ancestors
gen 2 (your grandparents) is 4 ancestors
gen 3 (your 1st gr-grands) is 8 ancestors
gen 4 is 16 ancestors
gen 5 is 32 ancestors
gen 6 is 64 ancestors
gen 7 is 128 ancestors
gen 8 is 256 ancestors
gen 9 is 512 ancestors
gen 10 is 1024 ancestors
gen 11 (your 9th greats) is 2048 ancestors

Then, let's assume we divide by half, to get 1024 unique ancestor pairs.

Each pair then has 2.5 children, so that by the 10th cousin generation, each pair will have 23,842 descendant cousins in your generation.

So, now the math works out as:

1024(23,842)=24,414,208

So, you would have 24 1/2 million living 10th cousins.

Knock that number down by a few million, though, because going back a dozen or so generations, you are going to lessen the number of unique ancestor pairs, as family lines start to merge with common ancestors.

So, say roughly 20 million people are exactly your tenth cousins in the world. Keep in mind that we are excluding any 9th cousins once removed, etc., from the count.

But in a population of 380 million, 20/380 equals 5.3% chance that any given random person in the U.S. population is exactly your tenth cousin.

However, the U.S. population is mostly of immigrant stock in the last couple hundred years in which we are calculatiing, so that complicates the math further. We might have to use a larger world population base, to account for that, which would then make the odds a bit smaller.

Or a larger early birth rate would instead make the number bigger. So say 5-10% odds of finding a random living person with a common ancestor, back to the Revolutionary War era?

Hey I'm not sure that math is totally correct but heres a formula i just discovered: (1-2^C/P)^(2^C) where C is the cousin number and P is the total source population

C is cousin # and P is total world population or country population.

Also i think two things hurt this type of equation. Some of my ancestors had 20 children so that beefs up the #s exponentially, whereas in modern times it was more like 2/3 more like your model. Also theres a lot of inbreeding, so that shrinks the # some of course.

Oh by the way the US population is only about 310 million now.

The inbreeding shrinks the number is the bottom line. There are several articles on this phenomenon. I don't know the odds of being 10th cousins but of course the odds go up if you are both descendants of small, closed populations. Like me and another descendant of the Great Migration (1620-1640 immigration to America) or me and another Litvak Jew (from Greater Lithuania in the 18th and 19th centuries). In both communities, the numbers were small and people tended to marry within the same families.

I’ve actually found my 20th cousin. And come to find out it’s my beat friend of ten years husband.

So if "Niall of the Nine Hostages"(5th century) is in my lineage what does that make us?

What would be 16 cosin ,4 times removed ?

16 th cousin 4 times removed same ansestor

Yes I am . But I do not Know which side either Poteet or Watson or Spears side. My Dad's name is David Lee Poteet and my mom's name is Mary Alice Watson Poteet.

I found an 11th cousin in Norway, where my family and most everyone I've been able to uncover for at least 7 generations has lived. Prior to the early 1900s, few if any left. By the math, it leaves me with at least 40 million living cousins. Problem is, Norway has a population of around 5 million, with around one million having emigrated there during the last generation. That leaves a missing 36 million cousins or makes the chances anyone I meet there is a cousin, like 500%! Something is a bit off here, lol.

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