In an earlier

post I did a lousy job of trying to estimate the effect of assortative mating on the far tail of intelligence.

Thankfully, James Lee, a real expert in the field, sent me a current best estimate for the probability distribution of offspring IQ as a function of parental midpoint (average between the parents' IQs). James is finishing his Ph.D. at Harvard under Steve Pinker -- you might have seen his

review of R. Nesbitt's book Intelligence and how to get it: Why schools and cultures count.

The results are stated further below. Once you plug in the numbers, you get (roughly) the following:

Assuming parental midpoint of n SD above the population average, the kids' IQ will be normally distributed about a mean which is around +.6n with residual SD of about 12 points. (The .6 could actually be anywhere in the range (.5, .7), but the SD doesn't vary much from choice of empirical inputs.)

So, e.g., for n = 4 (parental midpoint of 160 -- very smart parents!), the mean for the kids would be 136 with only a few percent chance of any kid to surpass 160 (requires +2 SD fluctuation). For n = 3 (parental midpoint of 145) the mean for the kids would be 127 and the probability of exceeding 145 less than 10 percent.

No wonder so many physicist's kids end up as doctors and lawyers. Regression indeed! ;-)

Below are some more details; see

here for calculations. In my earlier post I arrived at the same formulae as below, but I had rho = 0.

Assuming bivariate normality (and it appears that IQ has been successfully scaled to produce this), the offspring density function is normal with mean n*h^2 and variance 1-(1/2)(1+rho)h^2, where rho is the correlation between mates attributable to assortative mating and h^2 is the narrow-sense heritability.

I put h^2 between .5 and .7. Bouchard and McGue found a median correlation between husband and wife of .33 in their review many years back, but not all of that may be attributable to assortative mating. So anything in (.20, .25) may be a reasonable guesstimate for rho.

In discussing this topic with smart and accomplished parents (e.g., at

foo camp, in academic science, or on Wall Street), I've noticed very strong interest in the results ...

See related posts

mystery of non-shared environment ,

regression to the mean**Note**: Some people are confused that the value of h^2 = narrow sense (additive) heritability is not higher than (.5 - .7). You may have seen *broad sense* heritability H^2 estimated at values as large as .8 or .9 (e.g., from twin studies). But H^2 includes genetic sources of variation such as dominance and epistasis (interactions between genes, which violate additivity). Because children are not clones of their parents (they only get half of their genes from each parent, and in a random fashion), the correlation between midparent IQ and offspring IQ is not as large as the correlation between the IQs of identical twins. See

here and

here for more.