In 2016 psychologist Jennifer Delgado made it into news by writing a post to the blogsite Psychology Spot informing the great public that according to recent research intelligence is in the X chromosome, which men inherit from their mothers. The news was fast “debunked” by well-meaning, but not quite knowledgeable, bloggers, who pointed out that the IQ of natural children correlates about 0.4 with either of parents. That is true but it is a different issue. Another Jennifer, Jenni Graves, claimed that the Y chromosome will finally disappear and that is the end of men. Being a man, I finally had to check if the women are really taking over.
The case is quite simple and it is strange that some people try to confuse things.
The X chromosome is incorrectly called the female chromosome while it is a sex chromosome for both men and women. X has genes for ovaries and other female organs, but also for prostate and other male specific tissues. The small Y chromosome is correctly called a male sex chromosome, as it contains genes for sperm production and no female specific genes. Y has some 70 genes, while X is estimated to have over 900 genes. In the early stage of the XY sex chromosome system both chromosomes probably were of roughly equal length, one containing genes for egg production and the other one for sperm and most of the X chromosomes had a corresponding part in the Y chromosome and these parts underwent meiosis, but Y lost most of the genes that have correspondence in X. There still are left 12 genes in the PAR-region (actually there are two of them PAR1 and PAR2) which undergoes meiosis. These genes may disappear in the future as Graves thinks, but the remaining genes in Y are needed for sperm production and cannot easily disappear or jump to X. Y will stay, though it may get still shorter.
The reason for the shortening of Y is that evolution is speeded up if men have only one copy of some genes. Most mutations are recessive and if there always are two copies, recessive mutations are mostly hidden and easily lost in the evolution. As men have only one copy of X, all mutations in X are expressed in men. Women have two copies of X but most of the genes in the X chromosome are inhibited. It means that in each cell of a woman’s body only one X chromosome is active. The active one is usually selected randomly, but there are some X chromosome genes, where the selection is based on the origin of the X chromosome, paternal or maternal (this way of selection is called imprinting). Finally, there are genes in the X chromosome, where the other X copy is not inhibited. They include the 12 genes in the two PAR regions and some 10-25% of other genes. X inhibition in women means that a woman’s body is a mosaic where roughly every second cell uses the maternal and every second the paternal X copy. If one X copy contains a harmful mutation, its effects are expressed in men. If the mutated allele is a fully recessive, it is expressed in women only in homozygotes. If the allele is partially dominant, its effects are much mitigated by the X inhibition mechanism in women. A fully dominant allele can only happen in genes that escape X inhibition.
This situation is the rational for the Ricci hypothesis, which predicts that the X chromosome collects recessive and partially dominant mutations that are advantageous for men and disadvantageous for women. Such mutations in X are much more often expressed than recessive mutations in autosomal chromosomes, where they influence the phenotype only for homozygotes. Consequently, natural selection works much faster on these mutations. If there is no harmful effect to women, these mutations become fixed in the population. If the mutations are harmful, or even lethal for women in the evolutionary sense by causing infertility, X inhibition masks the effect, but in that case the mutated allele cannot become fixed since it would imply that all women are homozygotes. The mutation remains rare.
If the mutation is harmful for men and women, for instance by causing mental retardation, it will mostly be expressed in men. It will finally be pruned out of the population, but new harmful mutations are being created all the time and this is the confirmed explanation for the higher rate of mental retardation in men. In 2004 there were known 1237 mutations causing mental retardation. On them 27%, 333, were in the X chromosome. This agrees very well with the theoretical calculations by Morton in 1978:
http://www.pnas.org/content/pnas/75/8/3906.full.pdf
He estimated that in a group of 100 there are 1.6 new recessive mutations, which cause mental retardation for a homozygote and derived the result that mental retardation in inbreeding is caused by rare recessive genes at about 325 loci. Today his conclusions are essentially verified.
https://genome.cshlp.org/content/10/2/157.full
This is then the reason why men are over represented in the lower end of the IQ distribution.
A natural extension of this idea is to propose that the reason why men are over represented also in the high end of the IQ distribution is also caused by the X chromosome. It is mentioned in Morton’s paper, but it could not be demonstrated for a long time. Finally, in 2017 appeared a paper by Zabaneh et al:
https://www.nature.com/articles/mp2017121
They made a GWAS study on people with IQs in the 0.03% (over 151 with 15 SD, though the paper says IQ 170). The results of this paper were for some reasons not fully understood. They actually were exactly what could be expected. They did not notice any new high-IQ genes. Instead they found out that high-IQ people have many IQ raising genes and fewer rare alleles, which mostly are IQ lowering, as most mutations are harmful. No IQ raising genes were found from the X chromosome.
This is what should be expected and it explains the important role of the X chromosome in male intelligence. Why I say so? Firstly, of the 406 known brain specific genes only 14 are linked to the X chromosome and the 72 known IQ genes are rather evenly distributed to all chromosomes. It initially seems that the X chromosome has not special role in high IQ, but this initial impression is easily shown wrong: as a large portion of genes causing mental retardation are X-linked, X is indeed essential to intelligence. It is only not so closely linked to IQ differences inside a population.
How can this be so? It is quite logical. Advantageous genes in X become fixed in a short time and they do not appear in a GWAS study, which locates SNPs that have more and less advantageous variants in the population. The SNPs that can be found from X have not become fixed and therefore they usually are recessive harmful mutations. We could find a few mutations, which are advantageous for men but harmful for women, e.g., causing women infertility, but there is no reason to assume they boost man’s IQ. If they are brain specific, they most probably influence the male brain structure and as IQ-tests try to minimize the sex differences in thinking, they will not be seen as IQ-genes but as genes influencing male specific capabilities. They are balanced in the tests by female specific capabilities and the IQ is not affected. Thus, we find only the recessive X-linked genes that lower the IQ and mostly in men.
The autosomal IQ-genes influence both men and women. Evolution acts slower on these genes, since they are recessive or partially dominant, and many of these genes have not become fixed. Autosomal genes often have multiple effects to many organs and they may have balancing negative effects keeping them from becoming fixed. Thus, the GWAS finds these SNPs. They are responsible for the IQ distribution seen in women.
These IQ-genes are mostly autosomal and they should act in a similar way with men. Remembering that X-linked genes lowering intelligence are expressed in men but usually not in women, men should have lower IQ. It is known that the average IQ is very much the same for both sexes. Consequently, men’s IQ distribution without the X-linked IQ-lowering genes must be some points higher. Scientific studies suggest that in the high IQ end men’s distribution is 5 points higher. In one such study the average IQ of women was 1.67 points lower than that of men’s and women’s standard deviation was 13.55 versus 14.54 for men. The point IQ 151 (3.4 SD) can be chosen as a marker of the high IQ end. For men 3.4 SD added to the slightly higher average (1.67 points) gives 151, but for women the corresponding point is 146. That suggests that there is 5 point difference in the higher IQ end. Then we add the effect of IQ-lowering X-linked genes. They lower men’s average IQ to be very close to that of women but they also stretch the distribution wider without moving the high IQ end, where these IQ-lowering genes are absent. This stretching extends men’s IQ distribution symmetrically, as IQ distributions are normal distributions, and men’s distribution had the -3.4 SD point (about IQ 50) 5 points lower than in women’s distribution. This means that the level IQ 151, which for men is 3.4 SD, 1/3,000 is for women 3.8 SD, 1/13,800. There are 4.6 as many men over this level that there are women.
Thus, I think, is the explanation for the over representation of men at both ends of the IQ distribution. There is an alternative view, expressed for instance by David Lykken, which proposes that a genius-level IQ is caused by non-additive factors. While genius in this sense does not mean a specific IQ range, it can be said that the GWAS of people with IQ over 151 did not find such effects. Twin studies have found that the top 15% of the IQ-distribution shows about the same heritability as the whole distribution arguing against non-additive effects for high IQ. Some studies have pointed out to non-additive factors in men’s intelligence, but the prevalent view seems to be that most of the IQ variation will be explained by small additive effects of a large number of IQ-genes, which can be IQ-increasing or decreasing. In calculation of Polygenic Scores these genes are assumed (for simplicity) to be partially dominant by assigning a weight 1 to a heterozygote and weight 2 to a homozygote of an IQ-linked allele. It is not to be expected that GWAS studies can explain all IQ variation. For other traits SNP studies reveal about half of heritability by twin studies. This should be the case also for IQ. From twin studies heritability (genetic origin) of IQ is low in childhood but raises to 80% in adulthood. Thus, GWAS on IQ may eventually capture 40% of IQ variation.
The average of the men’s distribution will be the same, or only a few points higher that women’s distribution. This is because of assortative mating. Assortative mating has been confirmed as the reason why the IQs of spouses correlate about 0.4. It is selection of spouses primarily by women, who for reasons of marriage happiness (evolutionally, for successful procreation) want to find a man, who is at least as intelligent as the woman is. This intelligence is not male or female specific and it is about the same what is measured by verbal IQ tests. As verbal IQ correlates highly with general intelligence factor g, the spouses will mostly have roughly the same IQ-level, with men a bit superior in the selection criteria, verbal IQ, and women in female specific IQ, the spelling subtest.
Men’s intelligence could be lowered to any given number by allowing more mutations to stay in the population, as most mutations are harmful, but this mechanism removes too low IQ men from the genetic pool and the average IQ of both genders will be very closely the same.
If can be said that men suffer from a larger load of IQ-lowering mutations, but women also suffer: from the effect of female hormones and female brain structure. The boost that X-linked advantageous mutations give to men is exactly here: their brain has become more focused by mutations that were disadvantageous for a woman’s task of caring for children. A man can concentrate on an interesting problem and forget to take care of the child. It is this difference what we mean by the over representation of men in the high-IQ levels. Women think more of people. They remember better birthdays of relatives, while men are leading in both the number of Nobel Prize winners and the number of mentally retarded.
Men get their only X chromosome from their mother. In this way men do get the male intelligence from their mothers, but what most people think as intelligence is the variation of IQ in a population. This variation is determined mainly by the autosomal IQ-genes and a man, like a woman, gets these autosomal genes from both parents. The male intelligence that men inherit from their mother is seen in the difference between a male brain and a female brain. Each sex has its own strengths and weaknesses in cognitive capabilities and the male brain must give great advantages for the survival of the offspring since the X chromosome has accumulated mutations that are, in the evolutionary sense, lethal for a woman.
This is seem from the Turner syndrome, where a woman lacks the second X chromosome leading into haploinsufficiency. Most women with the Turner syndrome are infertile. Infertility is evolutionarily equivalent to lethality. I made a model again using population genetics equations. This time I will write the equations without Microsoft’s equation editor so that they easily go to the blog and in do not need to include a pdf. Of course there must be an easy way to insert equations, other people do it, but so far I have not found it. I want this to be a blog post since I want to make some speculations from the results, and it is not good to speculate too much in something that looks like a scientific paper.
Now, to make a model that can describe harmful and even lethal genes for a homozygote, I make the following definitions. Let there be two alleles, a is the mutated and A is the original. They are in the X chromosome, so men are of type a or A and women are of types AA, aA and aa. Let x denote the probability of a man having the allele a. Then 1-x men have the allele A. Let y and z denote the probabilities that a woman is of type aA and aa respectively. Then the probability of a woman being AA is 1-y-z.
The pair a-AA produces only A men and aA women. I give a men an advantage α, thus from the pair a-AA comes α men, all of type A, and α women, all of type aA. The probability that a and AA are a pair is in random mating x(1-y-z) as the probability of an a-type man is a and the probability of an AA woman is 1-y-z.
Similarily, the pair a-aA has the probability xy and half of the boys (α /2) are of type a, half (α /2) are of type A. Girls are half of the type aA and their number is α /2, but half are of the type aa. As this aa type is to have a disadvantage, for instance to die too young to procreate, I will denote the number of these girls by β/2 where β is at most α.
The pair A-AA has the probability (1-x)(1-y-z). Boys are all of the type A. I give A men the weight γ for having children grow to the age to have own children. We cannot set this γ directly to one, indeed it is not one, since doing so would require normalizing the total probability to 1. This way γ will normalize the probability automatically. Thus, this couple produces γ boys of type A. It also produced γ girls of type AA.
The pair A-aA has the probability (1-x)y. It produces boys γ/2 of type a and γ/2 of type A. The girls are γ/2 of type aA and γ/2 of type AA.
The pair a-aa has the probability xz. Boys’ number is α, all of type a and girls’ is β, all of type aa.
Finally, the pair A-aa has the probability (1-x)z, boys γ all of type a and girl β, all of type aA.
In order to find a steady state, we write down the equations that boys of type a also have the probability x, that boys of type A have the probability (1-x), that girls of type aa have the probability z, girls of type AA have the probability 1-y-z and that girls of type aA have the probability y. The first two equations are
x=(α /2)xy+ (γ/2)(1-x)y+ αxz+ γ(1-x)z=( γ+( α – γ)x)((y/2)+z)
1-x=α x(1-y-z)+ (α /2)xy+ γ(1-x)(1-y-z)+ (γ/2)(1-x)y=( γ+( α – γ)x)(1-(y/2)-z)
Eliminate from these ( γ+( α – γ)x), so you get z=x-y/2 and x=(1- γ)/( α – γ). Then take the third equation
z= (β/2)xy+ βxz= βx((y/2)+z)= βx2
from which follows that y=2(x-z)=2x(1- βx). Now to the fourth equation
1-y-z= γ(1-x)(1-y-z)+( γ/2)(1-x)y.
It can be manipulated to the equation
(β-γ) x2-2(1- γ)x+1- γ=0.
Provided that (β-γ) is not zero we can solve this equation for x. If (β-γ) the equation is satisfied for any x. The last equation is
y=αx(1-y-z)+(α/2)xy+γ(1-x)(1-y-z)+(γ/2)(1-x)y=( γ+( α – γ)x)(1-(y/2)-z)
Inserting ( γ+( α – γ)x) that we just solved simplifies the equation to y=1-x. As we also obtained that y=2x(1-βx), equating these two yields
2βx2-3x+1=0.
This can be solved as a second order equation if β≠0:
x=(3±√(9-8β))/(4β).
From these two second order equations we can eliminate x. After some work we get a second order equation for γ
γ2(4β2-24β+28)+ γ(-4β2-7β+3)-β2+β=0.
This is the complete solution. There are two special cases which are easy to derive:
If β=0, then α=3/2, γ=3/4, x=1/3, y=2/3, z=0.
If β=1, then α=1, γ=1, x is arbitrary, y=2x(1-x), z=x2.
For other choices of β, solve γ from the second order equation, then solve x from the equation of β above, then solve y=1-x, z=βx2 and α=(1-γ)/x+γ.
So, that model was not so difficult to solve. Let us now go to the speculation. There is reason to suspect that the X chromosome contains gene alleles, which make women infertile and in this sense are lethal. In the model such a case has β=0. In order there to be a steady state, there must be a corresponding advantage, else the mutation is pruned out of the population and could exist in measurable frequencies only if it is created all the time by in situ mutations. Let us assume that this is not the case. The mutation stays in the population because it is advantageous for males (α›1) while it is lethal for females.
Now, look at the solution for β=0, it is quite interesting and notice that it is the correct and only solution for this quite realistic system for the choice β=0. That is, it is not a nonsense model. That is exactly what you get if there are alleles lethal for a homozygote aa and there is a very good reason (the Turner syndrome) to think this is the case.
In the solution for β=0 one third of men have the mutated allele a, which we will assume gives them advantage α, which I propose is the special male structure of the brain. The reason for suggesting this is that many mutations in the X chromosome cause mental retardation in men. Consequently, the chromosome is strongly connected with the brain. As X does not feature prominently in GWAS of IQ, advantageous IQ mutations in X must be fixed in the population. This very clearly suggests that X has alleles, which create the male brain structure. Let us assume this mutation is lethal for women (β=0) but so advantageous for men (α=3/2) that the system is in a steady state.
Let us assume that the population is in a steady state. One third of men have allele a and two thirds of women are of the type aA. An A man has fertility γ=3/4 with women of any type (aA or AA, as aa is infertile or dead). An a man has higher fertility, α=3/2, but with aA women half of the children are of type aa. That means that 22% of children are of type aa (i.e., the probability of a-aA pairs if β=0 is (1/3)(2/3)=2/9 and half of these children are aa, that is 1/9=22%.) We do not hear of 22% of women being infertile. From all causes, genetics being only one of the causes, about 10% of women have problems of getting pregnant. Yet, there is the Turner syndrome, which gives enough reason to suggest that the case β=0 is realistic. Let us assume that the aa women get spontaneously aborted very early long before birth. This means that a-aA couples are only ¾ fertile, as half of the pregnancies do not go beyond early stages. Thus, a-aA couples are just as fertile as A-AA or A-aA couples.
But there are the a-AA couples, which produce only aA females. They have the full fertility of α=3/2. They produce twice as many children to the reproductive age.
What does this mean? If a-men are more cleaver than A-men because of their brain is boosted by the X chromosome mutation, we may assume that aA women are also more intelligent, less than a-men, but more than AA-women. These aA women are also less fertile. With A-men both have the same success, ¾, but with a-men the AA-women have twice as many children. As the aa-women are aborted before birth, this means that the a-AA couples have twice as many children born. Intelligent women are then less fertile and have more problems getting pregnant.
What could be the traits associated with the mutation a? It could be something similar to autism, but not autism as autism is a serious drawback and probably partially caused by harmful mutations. It could be the MBTI type N (Intuition). About 1/3 of the population is typed as N. (A note, some skeptics consider MBTI as pseudoscience, but the more “scientific” Big Five is almost the same dimensions, I think that the N-type of MBTI has enough justification to be taken into a scientific debate.) N-type people get often scores that are close to the autistic spectrum, while not ill in any sense. It captures much of what is the male brain in its best, as compared to the female brain, which is also very good but different. Let us assume that the a-allele is the reason for the brain structure of the N-type. It appears clearly in men. It also appears in women, but not so clearly: these women are of the type aA.
As a side comment, let us notice that scientists have been suspecting a link between autism and the X chromosome:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2555419/
So, it is quite in line of present research to look for something autistic in the X chromosome, but I prefer the MBTI N-type to a serious mental drawback.
What should happen if such an a-allele enters a population, which so far has only had A-men and AA-women? Regardless of it the gene arises from men or women, there are born some a-men. They have twice as many children with AA women than an average A man. The population of aA women grows. Indeed, the population may grow very fast because of this and it may twist other gene distributions. When aA-penetration in women has reached the steady state of 2/3 of women being aA, the population growth stabilizes, but still one can notice that the less intelligent AA women contribute an twice as many children. Yet, this is not directly connected with the IQ, as the IQ distribution is largely determined by autosomal IQ-genes. This is of the brain structure, whether MBTI-type N or S. N-type women, who actually are diluted N as being aA, have less children. Still the population is in a steady state and nobody needs to worry that the N-type would disappear. There are just as many of those as is needed.
These were just speculations. Maybe somebody wants to study the problem more deeply starting from these. I can only say that my calculations of the equations are certainly correct and that the references to literature are also correct and correctly understood, more I prefer not to claim. But there is much more that the X chromosome can give. A promising area, I think, also for applied mathematics. There are many rather complex mechanisms. It is possible to make nontrivial models and in this topic it is easy to create quite interesting hypothesis.