I had already estimated the African genotypic IQ from my principal component scores extracted from allele frequencies (Piffer, 2013) for different populations. If we take the factor score of people living in equal environmental conditions (Europeans and Japanese), we can figure out how many IQ points each unit score corresponds to. The factor score of Europeans is 0, that of the Japanese is 1.23. The average IQ of Europeans is 99 and that of the Japanese is 105.Thus, 6 IQ points equal a difference of 1.23 factor scores. The factor score of sub-Saharan Africans is -1.73, which is 1.41 times greater than the difference between Europeans and East Asians. Thus, the genotypic IQ difference between Africans and Europeans must be 6*1.41= 8.46. Thus the real African genotypic IQ is 99-8.46= 90.54

You're assuming that there is no interaction between these derived alleles. In other words, if allele A raises mean IQ by 2 points and allele B raises mean IQ by 2 points, the combined effect of both alleles is 2 + 2 = 4. Is that a reasonable assumption? You also seem to be assuming linearity in these effects, i.e., the same allele would have the same IQ-boosting effect on someone with an IQ of 90 as it would on someone with an IQ of 110. I suspect any effect would be greater at lower ranges of IQ (because of ceiling effects). Conversely, the absence of such alleles should have a greater effect at lower ranges of IQ.

Perhaps most, but a significant proportion appears to be non-additive:

"The search for genes associated with variation in IQ will be made more difficult, to the extent that genetic effects on IQ are not additive. We used earlier the illustrative possibility that IQ was affected by 25 genes, each with an equal, additive effect (paragraph 7.15). But some genetic effects, dominance and epistasis, are not additive.

[...] For example, it might be the case that allele 5 of the IGF2R gene is associated with high IQ only if it is accompanied by particular alleles at other loci. In their absence, it is accompanied by normal or even low IQ. If that were true, it would clearly be difficult to detect, and replicate, substantial effects.

[...] Is the genetic variance underlying variation in IQ mostly additive? We noted in Chapter 4 that much research in behavioural genetics assumes this to be the case. But two relatively sophisticated attempts to model IQ variation, while both concluding that the overall broadsense heritability of IQ is about 0.50, also argue that additive genetic variance accounted for no more than about 30% of the overall variation in IQ, while non-additive effects accounted for some 20%."

http://www.nuffieldbioethics.org/sites/default/files/files/Genetics%20and%20behaviour%20Chapter%207%20-%20Review%20of%20the%20evidence%20intelligence.pdf

Perhaps most, but a significant proportion appears to be non-additive:

"The search for genes associated with variation in IQ will be made more difficult, to the extent that genetic effects on IQ are not additive. We used earlier the illustrative possibility that IQ was affected by 25 genes, each with an equal, additive effect (paragraph 7.15). But some genetic effects, dominance and epistasis, are not additive.

[...] For example, it might be the case that allele 5 of the IGF2R gene is associated with high IQ only if it is accompanied by particular alleles at other loci. In their absence, it is accompanied by normal or even low IQ. If that were true, it would clearly be difficult to detect, and replicate, substantial effects.

There are scarcely any genes with replicated additive effects. And there are no genes with replicated interactive effects.

Emil,

The methodology of that study (genome-wide complex trait analysis) ignores non-additive effects. This point is made in a later paper (which was written by some of the same authors):

"GCTA estimates additive genetic influence only, so that non-additive effects (gene–gene and gene-environment interaction) are not captured either."

Trzaskowski, M., O.S.P. Davis, J.C. DeFries, J. Yang, P.M. Visscher, and R. Plomin. (2013). DNA Evidence for Strong Genome-Wide Pleiotropy of Cognitive and Learning Abilities, Behav Genet,43(4): 267–273.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3690183/

Again, I'm not arguing that most of the genetic variance is non-additive, only that some of it is. If intelligence is determined by small effects at large numbers of genes, it seems to me that some of those genes should display non-additive effects. Is there a reason why they should not?

Again, I'm not arguing that most of the genetic variance is non-additive, only that some of it is. If intelligence is determined by small effects at large numbers of genes, it seems to me that some of those genes should display non-additive effects. Is there a reason why they should not?

This point has no relevance to my estimate of the African IQ, or any other racial genotypic IQ. My principal component reflects the strength of selection for a given trait, and there since selection acts on phenotypes and only indirectly on genotype, there is no reason why we should get a different picture by analyzing non additive genes.

Duxide,

On the basis of differences in allele frequencies, the IQ difference between Europeans and Africans should be 10 points. Yet, on IQ tests, the difference seems to be approximately 25 points. How do you explain this discrepancy? The only explanation I can think of is that some of the derived alleles display additive effects, i.e., a single copy has the same effect as two copies (dominance) or one derived allele tends to increase the effect of another derived allele.

Perhaps you have another explanation.

I think all the alleles I used were found to be additive in their effects, so this seems to rule out the non-additive explanation.
My explanation is in terms of epigenetics, which does not involve changes in the DNA code. I may remind you of Adrian Bird's experiments on rats whose DNA methylation (the most well studied epigenetic effect) induced neurobehavioral deficits. However, once the relevant gene was switched on, the rats reverted to the normal behavior, becoming more exploratory. Several videos explaning this can be found on Youtube: https://www.youtube.com/watch?v=CFfx5wNvCT0

The alleles you examined are a very small sample of the many alleles that influence intellectual capacity. There are probably hundreds if not thousands of such alleles. It may be that your alleles don't display non-additive effects (although this would be difficult to prove one way or the other, given the small effect of each allele on IQ). I certainly would not make that assumption for all of the alleles that influence intellectual capacity. In fact, given the prevalence of non-additive effects (notably allele dominance), I have trouble believing that a significant proportion of these alleles don't display such effects.

I am not denying that there are alleles with non additive effects. Rather, I believe that this is irrelevant to the estimation of the African genotypic IQ, as selection acts on the phenotype and the differences revealed by the additive alleles which I examined reflect the differences in selection across populations.

I had already estimated the African genotypic IQ from my principal component scores extracted from allele frequencies (Piffer, 2013) for different populations.

I commented on this over at Peter Frost's blog:

Hi Pete,

I'm surprised that you commented on this. I was afraid that you would when I saw your discussion over at open psychology. A few points:

(1) Piffer's factors scores are unreliable given the low number of alleles used. Also, most alleles were for educational achievement, which taps into more than g.

(2) Piffer anchors his estimate in the Japanese national IQ, on the assumption that the Japanese phenotypic differences (+5) indexes true genetic differences, while the African estimate (-25, Rindermann) indexes true differences + bias. But one can just as validly use the African phenotypic scores as the anchor and reason that the Japanese score is depressed relative to the genotype.

(3) Instead of trying to anchor allele score using one pair of regions (Europe and East Asia or, worse, Europe and Japan), an alternative is to plot the regression for regional IQs on allele frequency when excluding Africa and then see what regional IQ the African allele score would predict. Wicherts et al. discusses this method with regard to national IQ. When this is done, the African scores is well below 80.

(4) Piffer used dubious immigrant substitute IQs in his paper (immigrant selection is a problem). For example, he used a South Asian IQ of 97 based on some Uk Scores; his regional IQ- allele score correlation can't be taken at face value.

I attached an SPSS file with Piffer's frequencies and three regional IQ estimates: L&V2012, Christainsen's 2013 regression results, Piffer's selected IQs. You can just plot the regional IQ x allele association without the African IQ and then see what regional IQ the African allele score would predict.

Is the genetic variance underlying variation in IQ mostly additive? We noted in Chapter 4 that much research in behavioural genetics assumes this to be the case. But two relatively sophisticated attempts to model IQ variation, while both concluding that the overall broadsense heritability of IQ is about 0.50, also argue that additive genetic variance accounted for no more than about 30% of the overall variation in IQ, while non-additive effects accounted for some 20%."

http://www.nuffieldbioethics.org/sites/default/files/files/Genetics%20and%20behaviour%20Chapter%207%20-%20Review%20of%20the%20evidence%20intelligence.pdf

When I saw that, it picked my curiosity. But in fact the references referred above are those 2 studies were :

LISREL Modeling - Genetic and Environmental Influences on IQ Revisited (Chipuer 1990)
The heritability of IQ (Devlin 1997)

Both determine not the GE correlation per se, but more precisely the "passive" rGE. The problem is that they don't use adult sample. It's important because from childhood to adulthood we should expect passive GE to shift to active GE. And some others found different results. Rice et al. (1988) and Alarcon (1998, 1999) said in the CAP there is no passive GE after age 4. And van Leeuwen (2009) also did not find evidence of it (which they call cultural transmission). Jensen (1976) evalutes it at 0.07. But now you have Loehlin who said that measurement errors lower GE correlation estimations, that he evaluate at around 0.30 if IQ tests have reliability of 0.83 for children.

But these were not the most important. It's unlikely that passive GE applies to GWAS estimates. Because in the paper cited by Emil, we can read this :

Can the results reported here be explained by population stratification or a correlation between environmental and genetic similarity? A number of reasons suggest strongly that these explanations are unlikely. The results were consistent when we estimated genetic variance within sub-populations and when we adjusted for up to 20 principal components (Supplementary Table 2). The observation that individual cohorts do not show an inflation of the test statistic, but the combined sample does, would require undetected spurious phenotype–genotype associations due to stratification in all cohorts to be in the same direction, which seems very unlikely. We recently showed that when investigating a trait under polygenic inheritance, increasing the sample size would indeed be expected to increase the inflation factor. A correlation between environmental and genetic similarity might occur if similarity due to environmental factors between relatives segregates with the degree of separation. For example, cousins five times removed might be more similar than cousins six times removed because they have a more similar environment. This argument applies to single SNP associations with any complex trait, and there is no evidence that the robustly associated variants from GWAS are spurious in this respect. Moreover, we estimated the actual amount of genome sharing between very distant relatives, which is different from the expected amount of sharing if we knew the entire pedigree of all individuals. In fact, the more distantly related a pair of individuals is from the pedigree, the larger the amount of variation in actual genome-wide sharing around this expectation (see Supplementary Information for further detail).

[...] Our estimates are based upon realized relationships between very distant relatives and not on pedigree relationships between close relatives. This breaks up a possible correlation (confounding) between genetic and environmental factors, since the variation in realized relationships given pedigree relations is large for distant relatives. Our estimates of the phenotypic variance explained by all SNPs are ~0.4–0.5, and we therefore conclude that the narrow-sense heritability for human intelligence is large and consistent with the inference from twin and family studies.

(4) Piffer used dubious immigrant substitute IQs in his paper (immigrant selection is a problem). For example, he used a South Asian IQ of 97 based on some Uk Scores; his regional IQ- allele score correlation can't be taken at face value.

I attached an SPSS file with Piffer's frequencies and three regional IQ estimates: L&V2012, Christainsen's 2013 regression results, Piffer's selected IQs. You can just plot the regional IQ x allele association without the African IQ and then see what regional IQ the African allele score would predict.

I looked at your file, but what is the "Christainsen's IQ regression results" ? Also, can you be more explicit on your (4) point ? I remember you have written something about it in your blog, but I can't remember the details and I think others would like to see it. Thanks. (note that i don't necessarily want to waste your time on it)