But what should you do if your parents or grandparents come from remote branches of the human species which didn’t have the opportunity to interbreed until fairly recently?
Go with the diet of the majority ancestral group, I think.
Some quick informal arguments: imagine health response to diet is set by many genes of small additive effect. (This is often true for any complex trait; behavioral psychology, and a lot of the heritability of common diseases is being identified in GWASes as that.) Imagine there are population-level differences; this is trivially obvious (lactose and alcohol), but that there’s a lot more than this (probable, since crops differ so much from region to region). Say, 1000. And you inherit genes from 1 of 2 ancestral groups, Red or Green. Each ancestral gene is +1 for that group, 0 otherwise.
Now, if you have 2/3s Red ancestry and you eat a Red diet, what’s your diet score? Well, 666 of your genes are Red, and so you get 1*666=666; 333 of your genes are Green and you get 0*333=0, total 666. If you ate Green, then it’s the other way around, 0*666 and 1*333, total 333. Clearly you want to eat Red. What if you’re 3⁄3 Red? Then 1*1000 vs 0*1000, obviously you still want to eat Red. What if you have a bare majority Red, 501/1000? Well, 501 (Red diet) > 409 (Blue diet). No matter what fraction, you always do better by going with your plurality descent.
Q: what if there’s uncertainty about the fraction of ancestry? A: the binomial around your estimated fraction is going to be pretty tight; randomness means if your family tree is 2⁄3 Red, you’re going to be close to 2⁄3 of your diet genes being Red if there’s more than a few dozen diet genes. And a quick $100 at 23andMe will fix any uncertainty about ancestry anyway.
Q: what if there’s more than one relevant ancestral group and/or diet? A: the reasoning still works even if it’s maximizing the gain from a split of genes like 10%/1%/1%.../1%.
Q: why not ‘match’ fractions of diet with fractions of ancestry, eg. if 1⁄3 Red and 2⁄3 Green, eat Red breakfasts but Green lunches & dinners? A: For the same reason “probability matching” doesn’t maximize your expected-value when the probabilities are known (as they will be in this case); it might work if your genes were changing or there was a lot of uncertainty, but that’s not the case and so ‘pulling the suboptimal arm’ is just suboptimal.
Q: what if I know that I am lactose-intolerant through self-experiment, should I really eat as much cheese as my Dutch ancestors? A: No.
Q: what if I know that I am lactose-intolerant because my 23andMe report shows I didn’t get the relevant SNPs, should I really eat as much cheese as my Dutch ancestors? A: No.
Q: what if there are genes of differing effect sizes, where some seem to have large effects on how diet affects health? A: Well, if you don’t know about them, then you’d expect all ancestral groups to have the same expected-value; and if you do know about specific ones, you can add them to the calculation based on their effect and different prevalences between groups.
Q: what if genes’ effects aren’t additive, but are crazy wild-ass interacting nonlinear networks and stuff like that? Nonlinear nonlinear nonlinear whoooo! A: lots of stuff seems to be additive, and anyway, if your genes are really that hard to predict, why would that make your minority genes outperform your plurality genes? It’s wild stuff either way.
Go with the diet of the majority ancestral group, I think.
Some quick informal arguments: imagine health response to diet is set by many genes of small additive effect. (This is often true for any complex trait; behavioral psychology, and a lot of the heritability of common diseases is being identified in GWASes as that.) Imagine there are population-level differences; this is trivially obvious (lactose and alcohol), but that there’s a lot more than this (probable, since crops differ so much from region to region). Say, 1000. And you inherit genes from 1 of 2 ancestral groups, Red or Green. Each ancestral gene is +1 for that group, 0 otherwise.
Now, if you have 2/3s Red ancestry and you eat a Red diet, what’s your diet score? Well, 666 of your genes are Red, and so you get 1*666=666; 333 of your genes are Green and you get 0*333=0, total 666. If you ate Green, then it’s the other way around, 0*666 and 1*333, total 333. Clearly you want to eat Red. What if you’re 3⁄3 Red? Then 1*1000 vs 0*1000, obviously you still want to eat Red. What if you have a bare majority Red, 501/1000? Well, 501 (Red diet) > 409 (Blue diet). No matter what fraction, you always do better by going with your plurality descent.
Q: what if there’s uncertainty about the fraction of ancestry? A: the binomial around your estimated fraction is going to be pretty tight; randomness means if your family tree is 2⁄3 Red, you’re going to be close to 2⁄3 of your diet genes being Red if there’s more than a few dozen diet genes. And a quick $100 at 23andMe will fix any uncertainty about ancestry anyway.
Q: what if there’s more than one relevant ancestral group and/or diet? A: the reasoning still works even if it’s maximizing the gain from a split of genes like 10%/1%/1%.../1%.
Q: why not ‘match’ fractions of diet with fractions of ancestry, eg. if 1⁄3 Red and 2⁄3 Green, eat Red breakfasts but Green lunches & dinners? A: For the same reason “probability matching” doesn’t maximize your expected-value when the probabilities are known (as they will be in this case); it might work if your genes were changing or there was a lot of uncertainty, but that’s not the case and so ‘pulling the suboptimal arm’ is just suboptimal.
Q: what if I know that I am lactose-intolerant through self-experiment, should I really eat as much cheese as my Dutch ancestors? A: No.
Q: what if I know that I am lactose-intolerant because my 23andMe report shows I didn’t get the relevant SNPs, should I really eat as much cheese as my Dutch ancestors? A: No.
Q: what if there are genes of differing effect sizes, where some seem to have large effects on how diet affects health? A: Well, if you don’t know about them, then you’d expect all ancestral groups to have the same expected-value; and if you do know about specific ones, you can add them to the calculation based on their effect and different prevalences between groups.
Q: what if genes’ effects aren’t additive, but are crazy wild-ass interacting nonlinear networks and stuff like that? Nonlinear nonlinear nonlinear whoooo! A: lots of stuff seems to be additive, and anyway, if your genes are really that hard to predict, why would that make your minority genes outperform your plurality genes? It’s wild stuff either way.