The page you linked only gives a weak argument (3 genes to give a normal distribution of colour in maize?) and no references to empirical observations of the distribution. The video on the page, talking about skin colour, does not claim anything about the distribution, beyond the fact that there is a continuous range. Even with all of the mixing that has taken place in the last few centuries, the world does not look to me like skin colour is normally distributed.
Even Fisher’s original paper on the subject says only “The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors” near the beginning, then proceeds with pure mathematics.
I can think of several ways in which a polygenic trait might not be normally distributed. I do not know whether these ever, rarely, or frequently happen. Only a small number of genes involved. Large differences in the effects of these genes. Multiplicative rather than additive affect. The central limit theorem doesn’t work so well in those situations.
And the graph of raw scores in the OP is clearly not a normal distribution. Would you justify transforming it into a normal distribution because that is how the “real” thing “must” be distributed? That would render the belief in normal distributions untestable.
Research on heritability of IQ implies, from the similarity of IQ in closely related persons, the proportion of variance of IQ among individuals in a population that is associated with genetic variation within that population. This provides an estimate of genetic versus environmental influence for phenotypic variation in IQ in that population as environmental factors may be correlated with genetic factors. “Heritability”, in this sense, “refers to the genetic contribution to variance within a population and in a specific environment”.[1] In other words, heritability is a mathematical estimate that indicates an upper bound on how much of a trait’s variation within that population can be attributed to genes. There has been significant controversy in the academic community about the heritability of IQ since research on the issue began in the late nineteenth century.[2]Intelligence in the normal range is a polygenic trait, meaning that it is influenced by more than one gene,[3][4] specifically over 500 genes.[5]
So while what you say is true, we cannot know that general intelligence is polygenic because this is once again talking about IQ. Of course IQ will imply intelligence is polygenic, because IQ itself has a normal distribution. We are once again putting the cart before the horse.
If general intelligence is a polygenic trait it will be normally distributed.
https://ib.bioninja.com.au/higher-level/topic-10-genetics-and-evolu/102-inheritance/polygenic-traits.html
To what extent has that been empirically tested?
The page you linked only gives a weak argument (3 genes to give a normal distribution of colour in maize?) and no references to empirical observations of the distribution. The video on the page, talking about skin colour, does not claim anything about the distribution, beyond the fact that there is a continuous range. Even with all of the mixing that has taken place in the last few centuries, the world does not look to me like skin colour is normally distributed.
Even Fisher’s original paper on the subject says only “The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors” near the beginning, then proceeds with pure mathematics.
I can think of several ways in which a polygenic trait might not be normally distributed. I do not know whether these ever, rarely, or frequently happen. Only a small number of genes involved. Large differences in the effects of these genes. Multiplicative rather than additive affect. The central limit theorem doesn’t work so well in those situations.
And the graph of raw scores in the OP is clearly not a normal distribution. Would you justify transforming it into a normal distribution because that is how the “real” thing “must” be distributed? That would render the belief in normal distributions untestable.
Wikipedia says:
So while what you say is true, we cannot know that general intelligence is polygenic because this is once again talking about IQ. Of course IQ will imply intelligence is polygenic, because IQ itself has a normal distribution. We are once again putting the cart before the horse.