46andMix – The smartest kid you could have

What is the smartest kid you could have, compared to your and your spouses mean IQ of X? That is, if you could pick one out of each of your chromosome pairs such that the genetic endowment for intelligence of the resulting collection is maximized and your partner does the same, how high would we expect the IQ of the resulting kid to be?

Now, this isn’t even going to be the maximal possible IQ for your offspring, because we ignore recombination, which in principle allows the selection of sections of chromosomes instead of full chromosomes. It’s just a lower bound, what I call an insanity check, for what emryo selection, chromosome selection, DNA synthesis or Crispr/CAS9 might one day make possible.

First we have to take regression to the mean into account. Regression to the mean happens, because outliers are created by extraordinary genes and luck. Luck in this case may be special environmental factors (like unusually few early childhood infections) or non-linear interactions between your chromosomes (like certain negative mutations occurring unusually often only on one chromosome, allowing the other one to jump in). Afaik in IQ it amounts to 20% of the deviation from the population mean. So if your and your spouses mean IQ is $100+x$ , we’ll discount (or raise) that number to $100+0.8 \cdot x$ . That is the expected mean IQ of your children.

One way to look at our question is: If you had an infinite number of children, where would you max out? We need two pieces of information for our calculation: How many is “infinite” and what is the standard deviation in siblings. It turns out that if you ignore recombination, which is what we do, “infinite” amounts to $2^{46}$ , after that we run out of chromosome combinations and we’ll start to repeat ourselves with genetically identical kids. We expect the standard deviation in siblings to be $\sqrt{\frac{15^2}{2}}=10.6$ . How much of an outlier is one in $2^{46}$ ? Well, the Z-score for $(1/2)^{46}$ is 7.605, which multiplied with the siblings std.dev. of 10.6 equals 80.613 IQ points out from the siblings mean. No matter what kind of parents you start out with, that’s one smart kid.