Re: How many 1st cousins 6x removed?

Wasn't it James Dow Allen who wrote:
>
>The famous abolitionist martyr John Brown
>  http://fabpedigree.com/s032/f250617.htm
>was my 1st cousin 6 times removed.
>
>I mentioned this to someone the other day and they
>laughed, thinking this was a distant relation****p.
>About how many 1st cousins 6x removed does
>an average person have?  How does this compare with
>the number of 6th cousins 1x removed?

There are two flavours of "N cousin Mx removed", those that are removed 
upwards and those that are removed downwards.

In the case of "1st cousin 6x removed", we can ignore downwards for 
living people, because they'd be six generations younger. A "1st cousin 
6x removed upwards" is a 1st cousin of a G(x4)Grandparent. We all have 
32 G(x4)Grandparents. These days, people have an average of about 10 
cousins, but back in my G(x4)Grandparent's day they had more. I'm going 
to guess an average of 20 cousins. Call that "C". So people alive today 
had about 32*C ~= 640 "1st cousin 6x removed", assuming no inbreeding.

In the case of "6th cousin 1x removed", we have to consider upwards and 
downwards, because the 1x removed downwards people are only one 
generation younger, so they could have been born already.

A "6th cousin 1x removed upward" is a G(x5)Grandchild of a "1st cousin 
6x removed". Let G5 be the average number of G(x5)Grandcildren. I'm 
going to wildly estimate 80 because it's about 2.4^5. So the total 
number of "6th cousin 1x removed upward" would be G5 * 32 * C which is 
about 51200.

A "6th cousin 1x removed downward" is a G(x7)Grandchild of a "1st Cousin 
5x removed". Let G7 be the average number of G(x7)Grandcildren. I'm 
going to wildly estimate 460 because it's about 2.4^7. The number of 
"1st Cousin 5x removed" is 16*C, so the total number of "6th cousin 1x 
removed downward" is G7 * 16 * C which is about 147200.

So the total number of "6th cousin 1x removed" is about 198400, assuming 
no inbreeding.

Actually, younger people are likely to have fewer downwards removed 
relatives, so the number is a bit less than that.

-- 
Mike Williams
Gentleman of Leisure