If two populations have moderately different means for some quantitative trait, for example differing by one standard deviation, the fraction that exceeds a high threshold is very much larger in the population with the higher mean.

I have mentioned this once or twice before, but it’s worth explaining in some detail. It has some important consequences, and I have the feeling that there are actually a fair fraction of Harvard graduates who aren’t familiar with it.

This is a natural consequence of the shape of the distribution function. It certainly happens with a Gaussian distribution (and many traits are roughly Gaussian), but it will be true for any distribution function that declines more and more rapidly as you get farther from the mean.

In practice, this means that if population A is significantly taller than population B, people from population A will account for a surprisingly large fraction of people taller than 7 feet. The effect is particularly strong for the tallest people, the farthest outliers – they may all be from group A, even when there are far fewer people in A.

There are quite a few cases in which we care a lot about outliers. In athletic competitions, you’re not really interested in the strong & the fast – you’re interested in the fastest, the strongest. In research, it helps to be able to solve puzzles that others can’t: being the smartest, rather than just smart, improves your odds.

Because this effect is so strong at the highest levels, you can run it backwards to come up with useful inferences. A priori, anything that screwed up the brain enough to misdirect sexual orientation might well decrease average intelligence as well: but the existence and accomplishments of Alan Turing and G. H. Hardy strongly suggest that this is not the case. Running it forwards, you would expect to see very few, maybe zero, top-flight mathematicians (the top 1000) from populations that have low average IQs – and that is the case. You would also expect to see a vast over-representation in mathematics from a population with a significantly higher-than-average IQ, such as the Ashkenazi Jews – and again that is so.

In another application – if the average genetic IQ potential had decreased by a standard deviation since Victorian times, the number of individuals with the ability to develop new, difficult, and interesting results in higher mathematics would have crashed, bring such developments to a screeching halt. Of course that has not happened.

At the limit, this means that families that score high on some quantitative trait, who are from a group with high mean values of that trait, live in a suitable environment, and whose high scores happen to be almost entirely due to genetic factors rather than good developmental luck, can be competitive, at the highest levels, with entire continental races. For example, there’s the Bekele family, from Bekoji, Ethiopia. Kenenisa Bekele holds the world record at 5,000 and 10,000 meters, while his little brother is the 3,000 meter world indoor champion. That one family is competitive (in running) with China, population 1.35 billion.