Sunday, April 07, 2013

Extreme assortative mating and IQ

People assortatively mate on traits such as intelligence. Does this make a difference to the usual bell-shaped curve for IQ? Surely it ought to increase the spread, the standard deviation?

Take a European Caucasian population with mean IQ of 100 and standard deviation 15. Now suppose the right-hand side of the population with IQ > 100 reproduce assortively only amongst themselves. The mean of the new population is at the 75th percentile of the original bell-shaped curve,  at 0.67 sigma or approx 10 IQ points above the old mean.

This new distribution,  the right-hand side only of the original curve, is far from normal .. but by the magic of the central limit theorem, over some number of generations, random mating will result in a new bell curve centred on IQ 110 with a sigma, as before, of 15.

(Update: Oops!  The distribution has been pulled in; the standard deviation is actually reduced to 9 points. This counteracts the increased mean as far as very intelligent offspring are concerned,  absent continued selective pressure for increased intelligence and time for advantageous mutations.)

The situation for the reproductively-isolated left-hand side is symmetrical: they end up as a normally-distributed population with mean IQ 90.

If the environment is systematically culling the less-intelligent, as in our evolutionary history, then this analysis - simple as it is - applies.

It would be shocking to suggest that advanced societies today are culling the right-hand side of the bell-curve - as smart professionals decline to have offspring!