Offspring IQ vs parental midpoint IQ

We had Alex and Adrian with us over the Easter and fell to talking .. as you do .. about the correlation between parental IQ and the intelligence of their offspring. I was trying to recall this post, from Steve Hsu, from which I reproduce the key material below.

There are three key ideas in Steve's post:

• You start from the parental midpoint IQ (the average of father and mother)
• To get the mean, or expected value of the offspring IQ multiply by h²  (Breeder's Equation)
• The distribution of offspring IQ has a tightened standard deviation, 12 rather than 15 IQ points.

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"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! ;-)
 ...
"Assuming bivariate normality (and it appears that IQ has been successfully scaled to produce this), the offspring density function is normal with mean n*h² and variance 1-(1/2)(1+ρ)h², where ρ is the correlation between mates attributable to assortative mating and h² is the narrow-sense heritability. *

"I put h² 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 ρ.
...

"Note: Some people are confused that the value of h² = narrow sense (additive) heritability is not higher than (.5 - .7). You may have seen *broad sense* heritability H² estimated at values as large as .8 or .9 (e.g., from twin studies). But H² 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."

* Putting in the numbers: σ = 15 √(1 - 0.5 * 1.225 * 0.6) = 12.
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The other discussion we had was how to estimate the IQ of my parents, now both dead.

Neither ever took an IQ test as far as we know. We have my mother's DNA with 23andMe so eventually with full genome sequencing we may expect to read this off (when the research ...).

We don't have my father's DNA although we might forensically get it one day via his belongings.

Still, all is not lost. Life is an IQ test and we have the biographies. We can also do some reverse correlations from the children, (my brother, sister and myself). IQ test data is not available here either, but we can still make biographical estimates.