I don’t understand why the origin of grandparents should matter.
To the best of my knowledge, the main problem with incest is recessive alleles. For example, if the grandfather’s genotype is ”aA” (where “a” is a very rare recessive allele) and his children (parents’ generation) mate with each other, then there is a relatively high chance (1/16) that the grandchildren would be of “aa” genotype (which might be extremely deleterious or even lethal). Having another grandparent from a different continent should not change this.
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.
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.
I don’t understand why the origin of grandparents should matter.
To the best of my knowledge, the main problem with incest is recessive alleles. For example, if the grandfather’s genotype is ”aA” (where “a” is a very rare recessive allele) and his children (parents’ generation) mate with each other, then there is a relatively high chance (1/16) that the grandchildren would be of “aa” genotype (which might be extremely deleterious or even lethal). Having another grandparent from a different continent should not change this.
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.