Assortative mating and the far tail of intelligence

A Fermi estimate of the increase in the tail population due to elitism, mobility and assortative mating. My conclusion is that there has been a significant increase in the number of kids in the far tail relative to, say, just one or two generations ago. I think my assumptions below are fairly realistic. (Note to non-scientists: this is only an order of magnitude calculation!)

My original estimate was off -- see erratum 2 below and this updated post

US birth cohort roughly 4 million.

Roughly few hundred kids at +4 SD ability (taking into account an excess over the normal distribution prediction; past assortative mating is probably one of the main causes of this excess ;-). What are these kids like? See here or here.

Number of +3 SD graduates per year from elite universities (average at these universities is above +2 SD): 10,000
(Note: a significant chunk of the roughly 40k +3 SD population!)

Plausible additional number of +3 SD / +3 SD marriages due to elitism and assortative mating, relative to one or two generations ago: + 1000 per annum

Number of additional +4 SD children produced, assuming, e.g., heritability of .8 (so, +4 SD kids are +1.6 SD from parental midpoint adjusted for regression): + 100 per annum

This ignores any environmental advantage to a child from having two +3 SD parents; but that effect might be small.

This enhancement of the tail population doesn't imply anything about the average intelligence of the overall population -- it is due to a concentration of good genes in a small sub-population that has been filtered by psychometric exams like the SAT, GRE and LSAT. I suspect that immigration (e.g., foreign graduate students at top programs, engineers coming to Silicon Valley, etc.) produces an effect of similar or even larger size.

Erratum 1: I kept screwing up the most important part of the calculation: what the mean IQ of children of +3/+3 SD parents would be. (See comments below from Carson Chow and Henry Harpending.)

Rather than continuing to try to do it in my head I looked up the result in Gillespie's Population Genetics (p.113) and the result is that the correlation between offspring and midparent is h^2 = heritability.

If the parental midpoint is +3 SD, then the children are distributed around an average of +3 h^2.

I had originally assumed h^2 = .8 which leads to +3 (.8) = +2.4, which requires a +1.6 fluctuation to produce a +4 kid. The odds of that are about 1/20.

If heritability is much lower, like .5, then it requires a +2.5 fluctuation to get a +4 SD kid and the effect of assortative mating is small.

Note, I have also been assuming that the residual variance among the +3/+3 kids is the full 15 point SD of the general population distribution. Probably the variance should be lower, but this requires us to go beyond the simplest models of additive genetic variance. ...


Erratum 2: After a bit more research, I would guess that the additive portion of genetic variance is no more than .5 or so. The high values of heritability typically quoted (e.g., .8) are broad sense heritabilities which include both additive and non-additive variance. The non-additive part results from dominance, gene interactions, etc. and does not allow a simple prediction of offspring qualities from the parental midpoint. So the result given above for h^2 = .5 is probably the largest effect we can expect from assortative mating, and it is not as large as I originally thought. A second point is that the residual variance once parental midpoint is fixed (i.e., exhibited by siblings) is probably smaller than 15 points. If narrow sense (additive) heritability is .5 then the remaining variability would have SD of about 11 points. This further reduces the chances of getting a +4 SD kid.

For parental midpoint n (in SD units), the probability of a child who exceeds this midpoint is

1 - erf( n sqrt ( 1 - h^2) )

where h^2 is the narrow sense or additive heritability. To see this, note that the mean among the offspring would be n h^2 , so the required upward fluctuation is n ( 1 - h^2 ) , but relative to the remaining variance, which has SD = sqrt ( 1- h^2 ). The probability of a child surpassing superior parents gets smaller the more exceptional the parents, however the probability is much higher than for a random child selected from the general population: 1 - erf(n). This would also be the result for any choice of parents if narrow sense heritability is zero. On the other hand if h^2 = 1 then all children would equal their parental midpoint: 1 - erf(0) = 1.

Note, throughout this discussion I have assumed no environmental boost from being raised by exceptional parents.