Allele dominance (source). A single copy of a dominant allele is as effective as two copies of a recessive allele. The current thinking is that intellectual capacity has increased in humans through new alleles that cause small positive effects at a large number of gene loci. It now seems that some of these new alleles display non-additive effects.
How has intellectual capacity increased in the course of human evolution? The current thinking is that natural selection has favored new alleles that cause small positive effects at a large number of gene loci. Over the human genome, these little effects have added up to produce a large effect that distinguishes us from our predecessors.
But are these effects simply additive? Many alleles are dominant, i.e., a single copy has the same effect as two copies. Many alleles also interact with alleles at other gene loci. It would be strange if none of the many gene loci involved in intellectual capacity showed no dominance or interaction. This point was made over a decade ago:
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%. (Nuffield Council on Bioethics, 2002)
Yet many researchers still argue for a simple additive model. Davies et al. (2011) estimated additive genetic variance at 40-51%. As some of the same authors later pointed out, however, the methodology of that study (genome-wide complex trait analysis) ignores non-additive effects: "GCTA estimates additive genetic influence only, so that non-additive effects (gene–gene and gene-environment interaction) are not captured either" (Trzaskowski et al., 2013).
Differences among human populations
Davide Piffer (2013) has studied geographic variation in alleles that influence intellectual capacity. He began with seven genes (SNPs) whose different alleles are associated with differences in performance on PISA or IQ tests. Then, for fifty human populations, he looked up the prevalence of each allele that seems to increase performance. Finally, for each population, he calculated the average prevalence of these alleles at all seven genes.
The average prevalence was 39% among East Asians, 36% among Europeans, 32% among Amerindians, 24% among Melanesians and Papuan-New Guineans, and 16% among sub-Saharan Africans. The lowest scores were among San Bushmen (6%) and Mbuti Pygmies (5%). A related finding is that all but one of the alleles seem to be specific to humans and not shared with ancestral primates.
Davide Piffer has now used these geographic differences in allele frequencies to estimate the corresponding geographic differences in “genotypic IQ”, i.e., the genetic component of intellectual capacity:
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 (source)
This estimate of 91 seems to contradict the IQ literature, although there is still disagreement over the mean IQ of sub-Saharan Africans. In their review of the literature, Wicherts et al. (2010) argue for a mean of 82, whereas Lynn (2010) puts it at 66. Rindermann (2013) favors a “best guess” of 75. There is some fudging in all of these estimates, since no one really knows how much adjustment should be made for the Flynn Effect. Indeed, what is the potential for IQ gains in societies that are still becoming familiar not only with test taking but also with the entire paradigm of giving standardized answers to standardized questions?
We are on firmer ground when estimating the mean IQ of African Americans, which seems to be around 85, i.e., 15 points below the Euro-American mean. We can argue back and forth over the cause, but the same gap comes up time and again, even when black and white children are adopted into the same home environment. This was the finding of the Minnesota Transracial Adoption Study: a longitudinal study of black, biracial, and white children adopted into white middle-class Minnesotan families, as well as the biological children of the same families (Levin, 1994; Lynn, 1994; Scarr and Weinberg, 1976; Weinberg, Scarr, and Waldman, 1992). IQ was measured when the adopted children were on average 7 years old and the biological children on average 10 years old. They were tested again ten years later. Between the two tests, all four groups declined in mean IQ. On both tests, however, the differences among the four groups remained unchanged, particularly the 15-point gap between blacks and whites. Whatever the cause, it must happen very early in life. Could it be in the womb? We would then have to explain the consistently halfway scores of the biracial children, who were born overwhelmingly to white mothers.
In any case, whether we accept the African American mean of 85 (which is influenced by some admixture with other groups) or the upper estimate of 82 for sub-Saharan Africans, we are still well below the “genotypic” estimate of 91. Is this an indication of non-additive effects? Do some of the intelligence-boosting alleles display partial dominance? Do some of them interact with other such alleles?
References
Davies, G., A. Tenesa, A. Payton, J. Yang, S.E. Harris, D. Liewald, X. Ke., et al. (2011). Genome-wide association studies establish that human intelligence is highly heritable and polygenic, Molecular Psychiatry, 16, 996–1005.
http://www.nature.com/mp/journal/v16/n10/abs/mp201185a.html Levin, M. (1994). Comment on the Minnesota transracial adoption study, Intelligence, 19, 13-20.
http://www.sciencedirect.com/science/article/pii/0160289694900493 Lynn, R. (1994). Some reinterpretations of the Minnesota Transracial Adoption Study, Intelligence, 19, 21-27.
http://www.sciencedirect.com/science/article/pii/0160289694900507 Lynn, R. (2010). The average IQ of sub-Saharan Africans assessed by the Progressive Matrices: A reply to Wicherts, Dolan, Carlson & van der Maas, Learning and Individual Differences, 20, 152-154.
http://www.sciencedirect.com/science/article/pii/S1041608010000348 Nuffield Council on Bioethics. (2002). Genetics and human behaviour: The ethical context. London
http://www.nuffieldbioethics.org/sites/default/files/files/Genetics%20and%20behaviour%20Chapter%207%20-%20Review%20of%20the%20evidence%20intelligence.pdf Piffer, D. (2013). Factor analysis of population allele frequencies as a simple, novel method of detecting signals of recent polygenic selection: The example of educational attainment and IQ, Interdisciplinary Bio Central, provisional manuscript
http://www.ibc7.org/article/journal_v.php?sid=312 Rindermann, H. (2013). African cognitive ability: Research, results, divergences and recommendations, Personality and Individual Differences, 55, 229-233.
http://www.sciencedirect.com/science/article/pii/S0191886912003741 Scarr, S., and Weinberg, R.A. (1976). IQ test performance of Black children adopted by White families, American Psychologist, 31, 726-739.
http://www.kjplanet.com/amp-31-10-726.pdf 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, Behavior Genetics, 43(4), 267–273.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3690183/ Weinberg, R.A., Scarr, S., and Waldman, I.D. (1992). The Minnesota Transracial Adoption Study: A follow-up of IQ test performance at adolescence, Intelligence, 16, 117-135.
http://www.sciencedirect.com/science/article/pii/016028969290028P Wicherts, J.M., C.V. Dolan, and H.L.J. van der Maas. (2010). A systematic literature review of the average IQ of sub-Saharan Africans, Intelligence, 38, 1-20.
http://mathsci.free.fr/survey.pdf 
