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For instance, if two parents have IQs of 160, can one calculate the probability that their child has an IQ over 160?

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    $\begingroup$ This is a very broad question that is briefly introduced in a long wikipedia entry. Is there a specific aspect that you are interested in? $\endgroup$ – StrongBad Sep 26 '17 at 14:42
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This is precisely the question Galton had in mind when he invented regressions. He tested it with heights. Given parents heights, their children height is actually more likely to be closer to the population mean. So high parents tend to have smaller children, and short parents taller children (hence the term "regression"). To answer your question, a children of parents with high IQs (160 is very high), is likely to have a higher IQ than the average population, but lower than the parents. This is even more true than for height as IQ is a lot less heritable. The precise likelihood can be calculated given some assumption.

Galton, F. (1886). Regression towards mediocrity in hereditary stature. The Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246-263.

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  • $\begingroup$ I do not understand. Does it mean that son's height is more likely to be closer to population mean than father's? And daughter's compared to mother's? Or calculation is somehow dependent on heights of both parents? $\endgroup$ – rus9384 Oct 7 '17 at 15:36
  • $\begingroup$ Gender is encoded in only 1 gene. Only phenotypes encoded in the same gene are gender dependent. Height is not. Neither, as far as we know, IQ (if it even makes sense to talk about IQ as a phenotype). So height depends on both parents. An example of gender-dependent phenotype is deuteranopia (one kind of colorblindness). It is encoded in the X gene and is about 8% in males, but only about 0.6% in female (0.08^2), as they have 2 X-genes thus are less likely to have both of them "deficient" (as deuteranopia is recessive). $\endgroup$ – baca Oct 7 '17 at 17:52
  • $\begingroup$ Not the "gene", but the "chromosome". Mean (also, what "mean" does mean? Is it mean across humans living in the same area or worldwide?) female height and male height differs. Other parameters (including IQ) also can do. So, if test only took into account only the parent of the same gender, there could be another explanation. But if it took both it should've taken into account that men are ~6-8% taller than women. $\endgroup$ – rus9384 Oct 7 '17 at 18:03
  • $\begingroup$ Can you put sources to your answer? $\endgroup$ – AliceD Oct 8 '17 at 18:38
  • $\begingroup$ Yes, chromosome, not gene. Gender plays a small role in height. It's not properly Mendelian so there are presumably a large number of genes contributing to it. But to a first approximation you can treat inheritance of height as a sum of random variables. For intelligence, it's a highly controversial issue. Besides the thorny question of how you define it, it is still unclear how inheritable it is. $\endgroup$ – baca Oct 9 '17 at 2:13

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