In two earlier posts I mentioned one problem in GWAS of educational achievement when used to compare national IQs. This problem is that PGS (polygenic score) is not a genotypic measure but it gets the numeric value from educational achievement scores. It is a score formed by first discovering from a discovery sample a set of gene alleles that correlate with educational achievement and then, in the prediction stage, weighting them in a suitable way to create a predictor that gives a minimal prediction error for a prediction sample. Thus, when plotting the subpopulation PGS against the subpopulation average IQ for subpopulations that are included in the prediction sample we actually only compare one predictor of subpopulation educational achievement (PGS) against another predictor of subpopulation educational achievement (IQ). The result should be a rather good straight line.
In this approach the average PGS score of a subpopulation is the same as what we get if each individual of a subpopulation is assigned the average educational achievement score of the subpopulation the individual belongs to, meaning that the predictor is equivalent to a predictor that only finds a best match of an individual to the subpopulations used in the study. The predictor only selects a subpopulation (a real subpopulation in the prediction sample or a constructed admixture, usually a linear combination of subpopulations). The educational achievement score of a nation is what gives the numeric value of the national PGS score. It does not have any direct connection with the real effect of the gene alleles in the PGS.
As can be seen, this is an error: two good predictors of the same property do correlate very well but the result is framed as showing that a phenotypic trait, intelligence measured by IQ, is explained by a purely genotypic measure of gene allele frequencies in the PGS. Well, it is not at all so.
This error appears in Dunkel et al (2019) and in Piffer (2019) because both papers plot data points of subpopulations that were included in the prediction sample of the used PGS from a GWAS study of Lee et al (2018). (As these three papers make this quite serious error, I omit precise references and links to them, but for interested readers google finds them easily.)
This problem I already discussed in two earlier posts and the error is real, but does not mean that Piffer’s correlation of national PGS versus national IQ is completely without any basis. His straight line fits well also for populations that were not in the prediction sample, and this requires some explanation. Yet, it is not so clear that the correlation is that good. For instance, Rushton’s estimation of Sub Saharan African (SSA) IQ was 15 points over the measured value 70. Should Piffer’s correlation then predict SSA IQ as 85, not as 70? I will not try to explain why Piffer’s correlation seems to work. Instead, in this post I will look at an issue that is more interesting and may partially explain why Piffer’s correlation seems to work for nations that were not in the prediction sample.
The question of interest is the additive nature of the PGS as in Lee et al (2018) and other similar studies. It is very possible that some traits do depend on gene alleles in an additive manner, but it need to be so for intelligence. Height is a polygenic trait and it can rather well be described by an additive PGS.
Humans have bred dog races where the trait height is maximized. Puppies of dogs from these very tall races are also very tall. The variance of height for these tall races is small. It must be so if the effect of genes is additive and polygenic. The sum of a set of small independent random variables converges to the normal distribution. This means that there is reduced variation at the both ends of the distribution. As a simple case, the binomial distribution B(p,n) converges to N(np,npq), q=1-p, and the variance npq gets smaller when p is close to 1, but this effect happens with any trait that is caused by a large number of additive genes, the additive property implying that the effects of the genes are independent.
We do not see this effect in the trait intelligence: children of parents with IQ over 150 do not typically have IQ very close to 150. The average IQ of the children is indeed very high, but the variance does not go to zero when the intelligence of the parents approaches the upper limits. The higher variance is not caused by occasional mutations as mutations are too rare.
But if gene alleles for intelligence were additive, the variance must go to zero at both ends. If the action is additive, alleles of different genes can be taken as independent random variables and the genetic intelligence of the children would be normally distributed with the average (about) np, where n is the number of IQ related genes and p is the average from the parents. Then the variance of the intelligence of the children should be (about) npq, a small number. This is not the case.
Do not confuse this issue with regression to the mean. In regression to the mean we select parents with high scores in a trait from a population with a smaller average score of the trait. The children will have smaller average score of the trait than the parents. This happens also with dogs: if we select very tall dogs from a population where the height is normal, puppies will not be as tall as parents. Here this is not the situation. The case is that we have by a long time selection produced a breed that has genes for great height. The population average has this large height, so puppies have the same average as the parents. The question is why this has not happened in some human population. Why is there nowhere a human population with the average IQ of 150? There is no, and surely there would be if it were possible. Intelligence is a positive trait and positive gene alleles tend to get fixed.
The natural explanation is that the trait intelligence is not determined by additive alleles of genes but by combinations of alleles of several genes. If there are several alleles of intelligence related genes, the children do not always inherit IQ increasing alleles for all genes that are required for increased intelligence. The result is that the variance of the IQ of children is larger.
If two different populations are mixed, a trait depends on more than one gene, and in both populations the trait has been increased by selection, then mixing the populations decreases the average value of the trait.
I will not produce a rigorous proof, but demonstrate this claim by a simple example. Let intelligence be a trait where particular alleles of two genes are needed for increased intelligence and we focus only on these two genes at the moment.
Let there be two populations and in each population there are two alleles of both genes, and each gene has the frequency of 50% in the population. Thus, in the first population there is a gene with two alleles A,a and another gene with two alleles B,b and the combination AB increases intelligence. In the other population these genes have different alleles C,c and D,d where CD increases intelligence. In each population 1/4 of the population has the intelligence increasing combination. An equal admixture of these two populations gives a population where these two genes have 16 different combinations and only two of the combinations (AB or CD) give an increased intelligence. Thus, 1/8 of the mixed population has an intelligence increasing combination of these two genes.
For a more rigorous proof, just notice that the sum of advantageous combinations grows linearly as a function of admixed populations while the sum of all combinations grows much faster.
This observation explains why human populations tend to be ethnocentric. As long as genetic diversity of the population is small, it can develop advantageous non-additive traits. Mutations in different genes can occur towards the same goal because only one or very few alleles of each gene are present in the population. Under these conditions, a population can in a short time develop a higher intelligence, or any other trait, be it support of own people or greed, or whatever.
But it genetic diversity is large and there are many alleles of each gene, then heritability of non-additive traits from parents to children is weaker. The result is that the trait is not seen as a heritable trait and it loses importance. The average value of the trait will be low because advantageous contributions from any original subpopulation in the mixture are rare. This leads to a prediction:
If a population has several alleles of intelligence affecting genes, then we should expect that the average IQ of the population is lower. We should also find most ethnocentricism from populations with low genetic diversity as they have the most to lose from admixture.
This prediction fits well to the fact that Sub Saharan African populations have the largest genetic diversity, while East Asians have small genetic diversity, even smaller than Europeans. Middle Eastern and most South Asian people are admixed less than Sub Saharan Africans but less than Europeans, while South and Central Americans are native American Indians with European and African admixture. Ethnocentricity is high in East Asia, where genetic diversity is small, and also among some hunter-gatherer tribes, where genetic diversity is very low and who may have special traits that are not yet well studied.
We get another easy result:
Assuming that genetic intelligence is a non-additive trait, we can elaborate Richard Lynn’s Cold Winter Theory of IQ. According to this theory higher IQ of East Asians and Europeans is a result of natural selection for higher intelligence in Northern latitudes because survival in a cold climate was more demanding. One problem if this theory is that survival in many other environments, like in a desert, should not be much easier.
A better explanation comes from the amount of genetic diversity in different populations. We can assume that a new human population started from a small number of founders and in a short time advantageous gene alleles had become fixed in the small population. Occasional mutations created new combinations, mostly deleterious but sometimes advantageous, and the population adapted to the environment. This also implied that it improved in intelligence, as it is a positive trait. This would have happened in Northern latitudes after the Last Glacial Maximum. It would also have happened in many other places in some different times. For instance, Australian aborigines have improved skills of finding a route in a desert. This is what we should expect: in a hunter-gatherer society mental challenges included better memory and better skill of orientation. We may assume that similar developments occurred in all early populations. Inheritance of genetic traits was easier because there were no additional alleles, thus natural selection could work rather fast.
The Northern population, including East Asians and Europeans, probably developed very recently, after the end of the Last Glacial Maximum. The population started as a small group with few founders. It developed light skin color and, as all early populations, genes for intelligence adapted to the environment. In this particular case there may have been special features, such as (very early, 50,000 BP) admixture with Neanderthal people, but probably there were special features in each case and the only really special feature with the Northern population is that this population developed so recently that it has not yet had time to degenerate.
That is, the original hunter-gatherer societies got into contact with each other and mixed. Mixing populations with different types of improved intelligence caused a drop of intelligence and stopped improvement of intelligence because with many alleles of the genes, natural selection is ineffective as children usually do not inherit the phenotype of parents. This admixture happened earliest in Sub Saharan Africa. Spreading of Europeans over the world in recent times has caused admixture in local populations. Unlike it is presently though, this admixture may have been mostly negative.
Plotting genetic diversity against IQ may give a rather similar plot as Piffer’s plot of population average PGS against population average IQ.
A related observation is that one can make a PGS from skin color genes and train it with a prediction sample of educational achievements. Plotting national averages for such a skin color PGS against national IQs should give a rather similar straight line as Piffer’s correlation. The best correlation is not obtained from the observable skin color hue but from training the prediction with gene frequencies: the skin tone of East Asians is about the same level as in Europeans, but gene frequencies are different and because of this difference, PGS can be weighted to give a higher average IQ for East Asians.
This observation is related to genetic diversity because skin color is a visible indicator of admixture with more southern populations, light skin color being the result of lower levels of sun light. Admixture with other populations indicates lower average IQ, which explains why e.g. East Asian populations value light skin color: it is an indicator that there is no admixture.
So far we see that non-additive effect of intelligence genes can explain ethnocentricity, preference for white skin in some populations, lower IQ of Sub Saharan Africa, and throw some light on the Cold Winter Theory, namely that it was nothing unique: similar raises of intelligence had happened elsewhere but finally admixture nullified them.
Today it is fashionable to argue that low genetic diversity is negative. It is true that low genetic diversity is associated with inbreeding and accumulation of mainly recessive deleterious gene alleles in a population, but it has a negative effect only in more modern societies. Let us remember that barbarians were barbarians. In the hunter-gatherer stage these negative aspects of low genetic diversity did not cause much harm since the tribe killed undeveloped children, mentally ill people, and other deviants. A low genetic diversity was a direct consequence of sparse population and certain mechanisms, like infanticide, were able to cope with the negative effects, while the positive effect was an ability to improve non-additive traits.
There is another mechanism that must be mentioned: wide scale polygamy. Hunter-gatherer groups often practice small scale polygamy, where more important men have two or three wives, but typically these societies cannot support a system where the king, chieftain or other big man, had a large number of wives. Such societies become possible only after the shift to agriculture or animal husbandry. The king would have a much larger number of wives than the other men in the population and his genes would spread in the population. The king would like his sons to continue in his position, and most naturally it would be the eldest son. The problem of such a society appears rather soon: mutations increase the genetic load and finally the population becomes infertile and dies. This seems to have happened with the earliest European agriculture: many local societies showed reduced Y-DNA diversity and they collapsed.
Probably as a countermeasure to genetic load Levantine cultures developed the sacrifice of the first born son. Sacrifice of the eldest son makes it possible for the other sons to compete for the father’s position. This gives more chances that at least one son is healthy and competent. Such a competition helps not only in avoiding single deleterious recessive genes, but also with finding a son with advantageous non-additive traits, like intelligence. The societies in Levant were mixtures of many original societies, thus we can assume they had diverse genes for non-additive traits, such as intelligence. If the population has many alleles of relevant genes, then a man needs many children in order to have a sufficient chance of having a son who has inherited desirable traits from the father. As kings and other big men contributed more to the gene pool than less important men, this mechanism can sustain desirable traits in a population for some time.
The intelligence measured by IQ is specific type intelligence. It is suitable for reading, writing and mathematics. It does not measure the ease of finding a route in a desert, thus Australian aborigines get low scores in IQ though they have intelligence that is adapted to their environment. Traits should develop only when there is the need for them, thus intelligence of the type that IQ measures cannot be very old. It must have developed in societies that needed such skills.
But the important thing is that a new trait develops faster in a population if there are only few alleles of relevant genes. Higher intelligence of the type measured by IQ could develop only after the shift to agriculture and animal husbandry, but this trait of intelligence could develop faster in Northern populations with their hunter-gatherer low diversity genes than in the South where genetic diversity was larger.
So, this is my minor contribution to the field of IQ research in this post. Minor, but not zero, that’s enough. There should always be some small contribution.