Monday, October 06, 2014

Smart genes from stupid people?

Intelligence, as measured by IQ, is largely - but not completely - under genetic control. For example, this from Wikipedia:
"There are some family effects on the IQ of children, accounting for up to a quarter of the variance. However, adoption studies show that by adulthood adoptive siblings aren't more similar in IQ than strangers, while adult full siblings show an IQ correlation of 0.6.

"Conventional twin studies reinforce this pattern: monozygotic (identical) twins raised separately are highly similar in IQ (0.86), more so than dizygotic (fraternal) twins raised together (0.6) and much more than adoptive siblings (~0.0)."
This means that when you meet someone smart they're likely to have the benefit of a good set of genes (for IQ) and some lucky environmental input. Apart from basic stuff like good nutrition, lack of serious diseases and a non-traumatic upbringing, no-one is too clear what a 'lucky environment' actually is. However, only the genes-part makes it through to the next generation so without the luck the kids are likely (but not certain) to be a little less bright than their luckier parent.

Equally, someone a little bit dim is likely to have been dealt a poor hand in the genes-for-high-IQ department, but also to have had ill-luck environmentally speaking. Their kids will not inherit the bad luck, on average, and will therefore tend to be brighter.

This phenomenon is called regression towards the mean.

We can put some numbers behind all this, as Steve Hsu explains. Recall that IQ is conventionally standardised (for European Caucasians) as mean = 100 and standard deviation (SD) = 15 IQ points.
"Assuming parental midpoint of n SD above the population average, the kids' IQ will be normally distributed about a mean which is around +0.6n 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 4 x 15 = 160 -- very smart parents!), the mean for the kids would be 100 + 0.6 x 4 x 15 = 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! ;-)"
This gives us a chance to revisit Cinderella.

Prince Charming is, frankly, not the sharpest tool in the box. More a lover than a fighter, his IQ is around 105 - below average for someone of his royal socio-economic status.

Cinders, naturally, lives amongst the dregs of society. She is part of half the population with below average IQ. In fact, when she was tested, her IQ was only 90. However, she is known as the pretty-but-dim one of the family so there is hope that she just got unlucky: perhaps those evil step-sisters deprived her of essential nutrients as a child.

So, prince and poor-girl get together. What can we say about the likely IQ of their kids?

Their parental midpoint IQ is (105 + 90)/2 = 97.5 which is 2.5/15 = 1/6 of a standard deviation below population average: this is the 'n' in the formula above. The mean IQ for their kids is therefore predicted to be 100 - 0.6 x (1/6) x 15 = 98.5 with a standard deviation of 12 IQ points. There is a 45% chance that a child of this fairytale marriage will have an IQ of 100+.

Reasonable odds of not being a dreg .. even a royal dreg!


Table of IQ requirements for various jobs (not including royalty).