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NancyLebovitz comments on Open Thread - Aug 24 - Aug 30 - Less Wrong Discussion
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Why wouldn't having grandparents from different continents make rare alleles less likely to be reinforced?
There is some reinforcement, but it’s not very significant.
For example, consider an Ashkenazi Tay-Sachs carrier who marries a person from China. If their children mate, the chance that the grandchildren would have Tay-Sachs disease is (1/2)^4=1/16. If instead of a Chinese, this Ashkenazi Tay-Sachs carrier marries another Ashkenazi (who have ~0.03 chance of being a carrier), the chance that the grandchildren would have Tay-Sachs disease is almost the same, ~1/16*1.12. In absence of incest, a grandchild of a Tay-Sachs carrier would have a ~0.03/8 (i.e. ~17 times smaller) chance for getting the disease.
Ashkenazi Jews is too large a category. Try Ashkenazi Jews from a region where Tay Sachs is common for all the grandparents.
I don’t think this is possible.
Tay-Sachs allele used to slightly increase evolutionary fitness in heterozygotes (i.e. people who carry just one Tay-Sachs allele). This allowed the allele to increase in frequency until ~3% of Ashkenazis became its carriers. But once the local frequency becomes high enough the negative effects (the risk that a random couple produces children with two Tay-Sachs alleles) balance the positive effects on fitness. Thus in any region it should be impossible for Tay-Sachs to be common for all the grandparents.