A few days ago Jim Babcock stated
I care about nutrition because I believe it has a very large, very underappreciated impact on individual productivity. Low quality diets make people tired and depressed, so they don't get anything done.
There's obviously a sense in which that is trivially true. If you start consuming no more than zero calories per day, you will get very tired, maybe depressed as well, and you will eventually not be able to get anything done. And getting adequate iodine and other nutrients is very important for children to properly develop their cognition. But Jim Babcock is probably making a stronger claim. I think what he is claiming is something like "going from the 10th percentile in diet quality among Americans to the 90th percentile would have very large, very underappreciated impact on an adult's individual productivity (taking into account that diet quality is almost certainly at least partially dependent on individual factors)."
I'd like to know what evidence we have for that claim. The strongest piece of evidence I can find is Rae et al., 2003, which showed that creatine supplementation increased the average IQ of their sample of vegetarians by 12 points, but that hasn't been replicated, and it seems extremely hard to substantially improve the cognition of adults. And, when it comes to depression, people have been trying really hard to show that omega-3 supplementation has substantial effects on it, but it's dubious that it does. L-methylfolate is a nutrient that is apparently effective enough that someone convinced the FDA to approve it to treat depression (as an add-on to treatment to another antidepressant), but only in quantities that far exceed those that anyone gets from their diet.
So I have a fairly low credence that his claim (as I formulated it) is true. But I was wondering if there were any major pieces of evidence I have completely missed.
Update from the future (1/16/2023): iron deficiencies are really bad, worse than I thought when I wrote this.
 Apparently some rationalists planned to try to replicate this, but there seemingly hasn't been an update to that in three years.