Dear Prof Posthuma,
Thank you for your comments. These comments are not new, and that is not necessarily a bad thing. Actually, it works to my advantage because over the years I have had the opportunity to develop ways to rebut these criticisms.
One of the ways of answering your criticisms, and the one which convinces me the most about the validity of my findings, is the new Monte Carlo approach I developed. I show that thousands of unlinked random SNPs (matched for Minor Allele Frequency using the SNPSNAP algorithm) rarely (p<0.01) achieve the same predictive power as the polygenic scores built from GWAS hits. The issues of Linkage Disequilibrium decay, different causal variants, etc, mentioned by you simply create noise, they do not bias the results in one direction. There is no reason why Linkage Disequilibrium decay should produce the pattern we observe, and magically match the IQ scores of populations so closely. As the paper you cite (Martin et al., 2017) explains: “We demonstrate that scores inferred from European GWASs are biased by genetic drift in other populations even when choosing the same causal variants, and that biases in any direction are possible and unpredictable”.
But genetic drift has been controlled for and ruled out in my papers by two different and complementary methods. First, a Mantel-like test, based on regressing phenotypic values on Fst distances and polygenic score distances, showing that polygenic scores predict average intelligence above and beyond Fst distances (i.e. drift and all that is not directional). Second, a method that shows the unviability of drift to explain my results is a Monte Carlo simulation with several thousands of SNPs, whose correlation to population IQ is outperformed 99% or more by the GWAS hits (for a demonstration, see my paper: https://www.preprints.org/manuscript/201701.0127/v3).
The factor analysis of GWAS hits produced even better results, outperforming 99.8% of the random SNPs. For a report, check: https://rpubs.com/Daxide/279148
What is remarkable is that height GWAS hits fail to predict population IQ. Guess what they predict? Height. The East Asian advantage we observe for education or intelligence-related SNPs disappears and turns into a lower score for the notoriously not gigantic Chinese, Vietnamese and Japanese. A demonstration of this can be seen here: https://f1000research.com/articles/4-15/v3. Look at table 1 and compare the polygenic scores to those for intelligence such as my table2 of my 2015 Intelligence paper http://www.sciencedirect.com/science/article/pii/S0160289615001087 or the more recent scores: (https://topseudoscience.wordpress.com/2017/06/02/new-genes-same-results-group-level-genotypic-intelligence-for-26-and-52-populations). They almost look like their mirror image, with ranks reversed.
An issue I see in the Martin et al. paper is that the polygenic scores were created using a very liberal p-value for inclusion thus pulling in a lot of false positives. False positives are expected to work like random SNPs, hence it is not surprising that they could not reproduce the results in non-Europeans.
When we home-in on the causal variants by picking the right alleles, instead of using a brute-force approach, we tend to see that the same genes have the same effects across different super-populations. For example, countless studies showed that the APOE4 allele is involved in Alzheimer’s disease and has a variety of health-related effects. This allele confers risk on African Americans and European-Americans alike (http://www.nytimes.com/2013/04/10/health/african-americans-have-higher-risk-of-alzheimers-study-shows.html). Accidentally, I should mention that this variant also has a population pattern closely mirroring the intelligence polygenic scores, perhaps due to the general effect on cognition.
The strength of my approach is in using the SNPs that replicated across many GWAS studies, increasing the chance of dealing with true causal variants or SNPs in close Linkage Disequilibrium with them, hence reducing the effect of Linkage Disequilibrium decay.
And Europeans are not even the top scorers, as the “reference-population-bias” hypothesis would predict. This hypothesis is widespread but lacks any logical rationale. In fact, I consistently observed higher polygenic factor scores for East Asians than for Europeans. If there had been a pro-European (i.e. pro GWAS-reference population) bias built into the cross-population comparison, this would imply that my method underestimates all non-European scores, not just Africans. I am so amused that the debate is fixated on the lower African scores, and nobody notices the East Asian advantage. You cannot have it both ways: if my method had a pro-White bias, then the East Asian scores would also be underestimated. This would actually imply that the East Asian advantage is even bigger than that which I have found. This reduction ad absurdum shows the absurdity of claims against my method.
Finally, a paper published this week, using GWAS hits, replicates the East Asian advantage on educational attainment found by several of my papers (although funnily they do not acknowledge my studies, although one of the authors is familiar with my results, because a while ago I had shared my results with him via email): http://biorxiv.org/content/early/2017/06/04/146043
This paper strengthens the argument that SNPs which predict within-population differences can be used to predict between-population differences.
I recently published a paper where I put together all my main findings to date: https://www.preprints.org/manuscript/201706.0039/v1
That paper should be able to answer general questions about my findings and my methods.
In summary, within-population differences can be used to predict between-population differences.