In the first generation, Craster would have a 50% coefficient of relatedness with his daughters.

In the second generation, this would increase to 75%. In the third, this would be 87.5%, etc.

The second season ofhas started and the series has become the topic of some fun discussion, I thought I'd give my €0.02 on the topic of genetic improbabilities.One of the good things about fiction is that it brings up interesting probabilities that would not often come up in theworld. In the first episode of Season 2, we are introduced to Craster , a character who lives north of the Wall repeating the cycle. Let's examine whether or not this scenario is plausible:What is interesting is that their autozygosity would also increase across the generations.In the first generation, at a random locus the probability that both copies have been inherited from the same ancestor is some random number corresponding to the probability of identity-by-descent in the general population.In the second generation, at half the loci there is a 50-50 chance that the same allele will be inherited from Craster, hence the grand-daughters will be autozygous across at least 25% of the genome. This means that they will be homozygous for about a quarter of Craster's deleterious genetic load.When we first see Craster, he seems to have quite a few "wives", so my guess is that this has been going on for 2-3 generations at least, which seems plausible given the early age of marriage in a quasi-medieval world.However, given the severe abnormalities observed in children of father-daughter incest it will become increasingly difficult for Craster to obtain viable offspring through this practice. Many of his children would be aborted, die, or be severely incapacitated.In order to increase his harem's size (as he seems to be doing) he would need each of his wives to produce 2 daughters for him. This translates to an average of 4 offspring per daughter (since 2 boys will also be born, on average, and exposed).But, due to high levels of autozygosity, many of Craster's offspring would not be viable; hence, each wife must undergo a very large number of pregnancies. And, given that each wife is heavily inbred herself, she is less likely to survive many pregnancies, especially since there's no ob/gyn north of the Wall.In conclusion, the tale of "Craster and his Wives" does seem to fit well in a work of fantasy...