Gregory Connor

Yale has changed its mission statement, rolling back the language that was adopted in 2016

Piffer has a beautiful new substack post about polygenic score trends in European data (full disclosure, he cites one of my tweets in passing). He has a new POV to population structure and how to correct for/measure/interpret its impact. Required reading. @pifferpilfer/p-195843604" target="_blank" rel="nofollow noopener">substack.com/@pifferpilfer/…

This is a technical tweet about statistical methodology in the important recent paper by Akbari et al.; if you are not interested in this narrow topic please skip this long tweet. As I stated in my last tweet, there is a potential bias and inconsistency in the Akbari et al. PGS trend estimates in the presence of group selection via internal European migration. The potential (not proven) bias and inconsistency problem arises from their use of a random effects model. The random effects model assumes independence between the random effects and the explanatory variable (death dates) and for some traits, notably height, this assumption is likely violated. It is not difficult to test this assumption using a Mundlak test and/or a Hausman test. Although neither test is given in the paper, there is enough information in the paper when combined with the earlier findings of Piffer and Kirkegaard to conjecture that their model might fail the Mundlak test. The random effects model gives more precise parameter estimates and unbiased coefficient standard errors when there are random, not explanatory-variable-related, effects across groups. It does not attempt to eliminate parameter estimation bias but rather gives more precise parameter estimates and eliminates bias in the standard errors. Piffer and Kirkegaard find a substantial positive time trend in height PGS, and Akbari et al. also mention that they find a strong and significant trend when they use OLS rather than a random effects model. Akbari et al. state “we carried out ordinary linear regression searching for evidence of a change in the polygenic predictor of height over time and found a significant signal without correction for structure (p=7*10^−159), which disappeared after our correction: (p=0.21).” Such a big change in p-value does not sound reasonable to me from just adding random effects; they are more likely detecting independent-variable-related effects. One defence of the Akbari et al. random effects methodology regarding height is that they get a null result. All statistical models contain false assumptions, so it only matters if the false assumptions have an important impact on the findings. Since it is a null result for height one could argue that it is just an abundance of caution designed to only detect individual not group selection. Even if one accepts this defence in the case of height, it would be valuable to see the results of a Mundlak test, which would show whether group selection via internal migration explains the difference from Piffer and Kirkegaard (see table). It is not clear if the same problem with random effects impacts the other trait estimates, so it would be worthwhile to estimate all of them with a fixed effects model (lower precision but still consistent) and also to perform a Mundlak test on the random effects model, for all the traits. If a fixed effects model is used it is important to do a second step regression of the fixed effect estimates on group death date averages. The Akbari et al. paper deserves many follow-up studies.

I should have pasted in the comparison table:

This is a technical tweet for those interested in the estimation methodology in the recent and important Akbari et al. (2026) paper, and how this methodology might explain the differences between their findings and those of Piffer and Kirkegaard (2024). Most of the findings in the two papers are quite similar, but they differ on whether height PGS increased in Europe since 14,000 years BP. Piffer and Kirkegaard find an increase whereas Akbari et al. find no significant increase after correcting for population structure. This population structure correction seems to be the source of the disparity. In Europe, we know for example that post-800 CE average-tall population clusters, e.g., Scandinavians, outcompeted average-short population clusters, e.g., Celts, as intra-European mobility increased. Statistically, this potential model misspecification is manifested as a possible violation of an independence assumption in the main trend estimation equation (6), which includes random effects for the 2,000 population clusters in the sample. A random effects model is mis-specified if the random effects variable is correlated with the explanatory variable (death date), and I suspect that perhaps the zero correlation assumption is violated for height PGS. At least for data after 800 CE, clusters which load positively on the “Scandinavian” principal component in the clustering algorithm will be on average taller and also on average newer (death dates). Clusters which load positively on the “Celtic” principal component in the clustering algorithm will be on average shorter and also on average older. This will be missed in the height PGS trend coefficient estimate with random cluster effects since the cross-cluster difference will be mostly absorbed into the cluster random effects. The solution I think is the Mundlak procedure where average death date within each cluster is included as an explanatory variable in the random effects model. If the coefficient is significant it indicates that this random effects model assumption is violated. I hope that this is a helpful comment and not too critical of the superb paper by Akbari et al., which I continue to read and re-read.

Increased height due to migration from outside the chosen observation set (West Eurasia) does not fall into the first category, but increased height due to more reproductive success from within the chosen observation set (West Eurasia) is natural selection. Taller Europeans produced more surviving children within Europe with European partners who were not genetically close using the Akbari et al. filter (but were West Eurasian).

@gregoryconnor11 They are testing for natural selection not an increase. Increased height due to migration does not fall into the first category, although it does fall into the second

The Akbari et al. paper is an impressive achievement, but it misses the component of European genetic evolution over the last 14,000 years caused by intra-European migration flows. This is most obvious in the case of height. For most traits, the Akbari et al. (2026) findings replicate those in Piffer-Kirkegaard (2024) but the height polygenic score (PGS) trend is an exception. Akbari et al. state that they find no height PGS increase, but actually they do. They state: “we carried out ordinary linear regression searching for evidence of a change in the polygenic predictor of height over time and found a significant signal without correction for [population] structure (p=7×10^−159), which disappeared after our correction: (p=0.21).” This is because their population-structure-corrected estimate misses the large height PGS increase due to intra-European migration flows. This is observable even in the short historical record. Height PGS increased in the British Isles after the 8th century CE due to Viking in-migration. The Abkbari et al. methodology neutralizes out this component of height PGS increase. Does this methodological difference also somehow explain the non-overlap of estimate confidence intervals for the Years of Schooling PGS?

Thanks very much for the comment, but I think that you have missed that this is a PGS trend due to intra-European migration and the paper is about European PGS trends. Taller (positive height PGS individuals) had more surviving descendants than shorter individuals, within Europe. That these descendants were outside a narrow genetic relatedness subset within Europe (the chosen observation set) does not invalidate the selection effect. Taller individuals had less closely related reproduction partners, but both partners were European. Taller Europeans produced more surviving children than shorter Europeans, without any or negligible in-migration to Europe.

@Imirrr422294 @IanBurkePerry @gregoryconnor11 Yep, the idea behind controlling for genetic relatedness is to discount the observed changes being driven by changes in ancestry. True selection should be independent of this. Changes via ancestry are also interesting but a separate (and less biologically interesting!) question

@IanBurkePerry @WilliamBarrie @gregoryconnor11 Yeah but do they have a way to ascertain if these changes also don't occur due to population movement (itself might be a product of selection if the population that expands has advantageous traits in the selection event, thereby confounding the selection with the migration)?

It's just a realpolitik reality: The only HBD works that the left reads are ones by accepted liberals who tiptoe through the tulips. That's the reason Steve Pinker didn't deal candidly with the state of knowledge about race in The Blank Slate. The payoff was wide readership of his documentation of heritability for a wide variety of traits and for gene-related sex differences. Unlike Reich, Pinker did not unjustly diss other researchers by name, but the tiptoeing was for the same purpose in both cases. And I'm glad they did it for the same reason @jamespsychol is (albeit while continuing to be dismayed by Reich's covering his ass by throwing others under the bus).

A paper whose central claim depends on separating selection from population history should make site-level archaeological metadata available. A 15-year embargo on the full metadata limits independent checks of geographic and sampling confounding. nature.com/articles/s4158…

@akarlin David Reich has been a positive and extremely powerful liberalizing influence on genetic-related research on human traits and migration. I agree with everything you say -- the Piffer citation oversight was probably weak tactical political cover. We all make mistakes.

I do not know if Reich et al.'s studied refusal to cite or acknowledge Piffer's precedence is ideological aversion or a tactical gambit to avert a Woke backlash in light of Piffer's open HBD realm, or both, but I am quite sure it is intentional. Sadly this is typical of this field and its obsession with maintaining "respectability". When I mentioned @DavidePiffer's work to a person somewhat famous in "superbabies" discourse in response to him asking whether anyone has done work on historical genomic IQs, he Googled Piffer up on the spot, scrunched up his face, and said, "Isn't he one of those race/IQ people? Not interested." And subsequently continued to pretend that this is a question "no one is asking right now."

When academia was blocked by woke ideology, researches outside progressed science. They should get credit.

I'm still stunned by how successfully the left has managed to feed the Western public a steady diet of nonsense on anything related to population genetics. They've literally succeeded in making people reject the theory of evolution in their own minds. Yet the reality is so simple and logical: - Europeans and Africans are populations that followed different evolutionary paths, which led them to develop different traits. - These traits are both physical (the most obvious example being skin color) and psychological (intelligence, personality, behavior). Evolution doesn't stop at the neck. - Differences in psychological traits between populations can be substantial, leading to significant differences in behavior and "performance" within a developed society. - The most striking difference is the gap in average intelligence between African and European populations. Absolutely every cognitive test (especially IQ tests) shows that the average intelligence of Africans is significantly lower than that of Europeans. This explains why African immigrants in Europe massively underperform compared to natives in every cognitive domain, from school performance to professional outcomes. - This straightforward observation explains the vast majority of outcome disparities in our societies and completely undermines the claim that "racism" is responsible. For example, African immigrants in Europe are on average poorer because they have, on average, lower IQs. It has nothing to do with some supposed European racism against them. Same for blacks in the US. - Another major behavioral difference between populations concerns the propensity for crime, as well as pro-social or anti-social tendencies. Anyone who's looked even briefly at European crime statistics knows that Africans (and other non-European populations) are massively overrepresented in crime. And once again, the explanation lies in genetic differences between populations. In the coming weeks and months, I'll try to get back into writing well-sourced, scientifically grounded summaries on all these topics. Because this is the great taboo of our time, and it's our duty to smash it to pieces.

Davide, you have been prematurely right and lack the proper academic respectability. Academia will never give you credit. I've had the same problem. How many people have used the arguments about a cognitive elite from TBC without citing the book? Or there's Robert Putman's Our Kids, with several graphs that were virtually identical to ones in Coming Apart and a substantial overlap in themes, and yet Coming Apart wasn't even in his bibliography, let alone cited. But thanks for giving me an excuse to kvetch.

Akbari et al. correctly note (p. 34 of Supplementary Information) that imputed variants can possibly introduce a bias in the time series model parameters. That is a controllable problem, and the bias in hard-call PGS is likely worse. (They do not use hard-call PGS for their time series model parameters, they just display it in the figure.) Better to show imputed PGS even if they do not want to use it for their time series model estimation.

I think those PGS in Akbari et al. Figure 4 are hard-call polygenic index scores without imputation of missing variants. That is fine, but someone needs to go to the trouble of imputing missing variants and putting in probabilistic estimates for them in computing the polygenic index scores.

The Akbari et al. paper is a massive accomplishment, but I do have some quibbles. Their statistical methodology appears to me to be a bit over-engineered and over-complex. They go to enormous trouble to remove any impact of migration and population structure on the estimated polygenic score increases. In doing so, they probably weaken the statistical signal in the time series data of polygenic scores. Their statistical methodology looks like a horse designed by a committee, which turns out to be an elephant. As an important example, Kirkegaard and Piffer found an increase in educational attainment (EA) polygenic scores of well over 1 standard deviation for two EA measures (see their Figure 2). Akbari et al. calculate gamma (the estimated 10k year increase in average standardized scores) of 0.63 +/- 0.13 for EA. I suspect that the larger Kirkegaard and Piffer estimates are more accurate. Someone from the big group who wrote this paper should take the raw genotype data, impute polygenic scores using standard methods, and simply show the time series graphs of the migration-and-population-structure-uncorrected polygenic scores computed in this way. That would be a great follow-up paper. I suspect that by excluding migration effects and employing this very indirect estimation methodology Akbari et al. have underestimated some polygenic index score increases.