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Vaniver comments on Stupid Questions June 2015 - Less Wrong Discussion
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Suppose A and B are brother and sister. They have a son, C. C and B have a son, D. D and B have a son, E, and a daughter F. How genetically related will be the children of E and F, given they do not interbreed?
(This is actually the history of our cats.)
The simplistic approach is that A and B share 1/2 of their (variable) genes by virtue of being siblings, and so their child C will have that shared half, and half of the remainder (i.e. a quarter) will come from B, so C and B share 3/4 of their genes. By the same approach, D and B will share 7/8 of their genes, and thus E and F will have 7/8 shared for certain and 1/16 shared by chance, and so their children will share about 15/32ths of their genes, i.e. be about as related as actual siblings.
Thank you. (It is odd how difficult it is to suppose that a random cat is the result of sequential inbreeding - they really look no different than random cats.)
In related news, check out MawBTS's comment on this Cochran post on inbreeding, on Cleopatra's ancestry. Yikes.
As I understand it, the reason the simplistic approach doesn't quite work is because the knowledge that a genetic combination produced a functioning adult allows you to update on the total degree of sharing / whether or not any of the ruinous parts were shared.