No evidence for positive selection for human height

Have humans gotten taller? Yes, there is evidence that contemporary people are much taller than their ancestors. This phenomeon is known as secular trend in height and has been particularly marked in the 20th century in Western countries, possibly as a result of improved health care and access to food (https://en.wikipedia.org/wiki/Human_height). Such a fast increase in height is usually taken to show the importance of the environment in physical growth because the timescale of DNA evolution is much larger and cannot take place in a few decades.

However, there is evidence for a reduced mating and reproductive success of shorter males, together with a preference for average height and tall men (Stulp et al., 2014), indicating that sexual selection is at work. This fact would lead us to think that there has been (sexual) selective pressure for taller stature, hence leading to an increase of height-increasing allele frequencies in contemporary human populations.

In a recently published paper, my colleagues and I (Woodley et al., 2017) found a higher frequency of IQ/educational attainment-increasing alleles in contemporary European individuals than in a sample of Bronze Age people from Europe and Western Asia, with odds ratios (for proportion of alleles in ancient vs modern) ranging from 0.8 to 0.9.

Wood et al. (2014) discovered 697 SNPs that were significantly associated with human height. I decided to look up the counts of these SNPs in modern and ancient populations using the same sample of Bronze Age people that was employed for the IQ/educational attainment study.  A 2 x 2 contingency table shows the counts of positive and negative alleles for ancient and contemporary genomes.

Table 1. 2 x 2 contingency table with Positive and Negative GWAS Effect Allele Counts for Ancient and Modern Genomes.

Positive allele count Negative allele count
Ancient Genomes 19283 19277
Modern Genomes 324781 332137

It can be seen that the counts are equally distributed among contemporary and ancient populations. An odds ratio was computed, yielding a null effect (O.R.= 1.022). Fisher’s exact test yielded significance, but this is due to the huge sample size as over 600 SNPs were employed. The magnitude of the effect is very small (and actually favoring ancient populations).

This null finding is paradoxical and hard to interpret in light of the evidence for lower mating reproductive success of shorter males in contemporary populations. It is possible that human stature did not affect reproductive success in traditional societies where female choice was very limited and marriages were arranged by families. Hence the higher attractiveness of taller males (or lower attractiveness of shorter men) might not have translated into different fitness levels.

Indirectly, this finding also strengthens the effect that my colleagues and I found for the educational attainment/IQ alleles because it shows that the method we employed does not have a systematic bias towards modern populations for alleles that have positive GWAS beta. In other words, this finding rules out the possibility that our results were due to an artifact.

All we are left with is a very puzzling finding. One possible explanation is balancing selection, where average height men enjoy higher reproductive success than short or very tall men, as suggested by Stulp et al. (2014). Another balancing force could be male preference for shorter females, counterbalancing the female preference for taller males. Finally, an advantage in times of resource scarcity for smaller bodies requiring less food might have also played a role in producing balancing selection. I am sure endless other interpretations are possible you are welcome to offer yours.

Update: A paper was published in Nature Genetics last week (Capellini et al., 2017) showing selection on alleles reducing height among Eurasians around the GDF5 gene. Hence, whatever sexual selection pressure for larger height might have been counterbalanced by other selective pressures.

References:

Capellini, T.D. et al. Ancient selection for derived alleles at a GDF5 enhancer influencing human growth and osteoarthritis risk. Nature Genetics (2017) doi:10.1038/ng.3911

Stulp, Mills, Pollet, Barrett (2014). Non-linear associations between stature and mate choice characteristics for American men and their spouses. Am J Hum Biol. 2014 Jul-Aug;26(4):530-7. doi: 10.1002/ajhb.22559.

Michael A. Woodley of Menie,1,2 Shameem Younuskunju,3 Bipin Balan,4 and Davide Piffer (2017).  Holocene Selection for Variants Associated With General Cognitive Ability: Comparing Ancient and Modern Genomes. Twin Research and Human Genetics Volume 20, Number 4, doi:10.1017/thg.2017.37

New genes, same results: group-level genotypic intelligence for 26 and 52 populations

Davide Piffer

pifferdavide@gmail.com

I recently posted a pretty detailed account of my analysis of the new intelligence GWAS, based on the latest GWAS of intelligence. (Un)surprisingly, the estimates of genotypic intelligence (or actually to be precise, of polygenic selection strength, because genotypic intelligence also includes non-additive components) are almost identical to those from my previous 2013 and 2015 studies. By this, I mean that the factor and polygenic score I had estimated for 26 populations in 2015 are almost identical (r=0.96-0.99) to the factor extracted from the new intelligence GWAS (18 SNPs) and from a factor extracted by pooling together the hits from two educational attainment GWAS published after my 2015 study (9 replicated genomic loci), see my paper for more details. This is called a successful replication. Since the old and new results are almost identical, I report the post-2015 factor scores. Robustness of the findings is supported by Monte Carlo simulation using REAL SNPs (not computer-generated junk), which is the best technique to test the robustness of these findings, since it includes all possible sorts of confounding factors (LD decay, spatial autocorrelation, etc.) in one omnibus test.

Table 1. Factor scores for educational attainment and intelligence

Population G Factor score (18 SNPs) EA  factor score (9 SNPs)
Afr.Car.Barbados -1.276 -1.351
US Blacks -0.961 -1.177
Bengali Bangladesh -0.075 -0.209
Chinese Dai 1.35 1.017
Utah Whites 0.844 0.471
Chinese, Bejing 1.109 1.511
Chinese, South 1.208 1.382
Colombian 0.357 0.01
Esan, Nigeria -1.66 -1.453
Finland 0.771 0.702
British, GB 0.797 0.745
Gujarati Indian, Tx -0.049 0.271
Gambian -1.358 -1.397
Iberian, Spain 0.631 0.35
Indian Telegu, UK -0.074 0.049
Japan 0.878 1.342
Vietnam 1.267 1.346
Luhya, Kenya -1.599 -1.488
Mende, Sierra Leone -1.444 -1.403
Mexican in L.A. 0.215 0.056
Peruvian, Lima -0.06 0.05
Punjabi, Pakistan 0.066 0.24
Puerto Rican 0.375 -0.004
Sri Lankan, UK -0.391 0.134
Toscani, Italy 0.764 0.248
Yoruba, Nigeria -1.684 -1.443

 

Some may remember I also published factors derived from ALFRED, whose sample is bigger than 1000 Genomes (50-75 populations), but the coverage is much weaker.

I looked up the 18 intelligence GWAS SNPs and the 9 EA quasi-replicated SNPs and could find 4 in ALFRED. Factor analysis was run on them, producing a very interesting factor. For ease of interpretation, I report results ranked from highest to lowest:

Continent Population Factor
EastAsia Tujia 1.507
East Asia Mongolian 1.358
EastAsia Daur 1.246
EastAsia Yi 1.19
EastAsia Koreans 1.127
EastAsia Miao 1.078
EastAsia Japanese 1.018
EastAsia Dai 0.987
EastAsia Hezhe 0.98
EastAsia Han 0.936
EastAsia Lahu 0.877
EastAsia Tu 0.828
EastAsia Xibe 0.802
Europe Orcadian 0.753
EastAsia She 0.737
EastAsia Uyghur 0.566
Asia Hazara 0.506
Asia Kalash 0.475
Asia Oroqen 0.445
Europe Italians_N 0.437
Europe Italians_C 0.404
SE Asia Cambodians, Khmer 0.34
Siberia Yakut 0.311
Europe Adygei 0.257
Asia Druze 0.254
Europe French 0.217
Asia Burusho 0.151
EastAsia Naxi 0.113
Europe Russians 0.073
Asia Balochi 0.055
Asia Palestinian -0.071
Europe Basque -0.088
Asia Bedouin -0.156
Europe Sardinian -0.225
Asia Brahui -0.334
Asia Pashtun -0.426
Asia Sindhi -0.438
Oceania Melanesian, Nasioi -0.533
Oceania Papuan New Guinean -0.569
Africa Mozabite -0.768
Africa Mandenka -1.153
Africa Yoruba -1.27
NorthAmerica Maya, Yucatan -1.3
NorthAmerica Pima, Mexico -1.312
SouthAmerica Amerindians -1.366
Africa Biaka -1.369
Africa Bantu Kenya -1.381
SouthAmerica Surui -1.382
Africa Mbuti -1.415
Africa Bantu SA -1.454
Africa San -1.488
SouthAmerica Karitiana -1.53
     

We see the that East Asians are at the top. Mongolic tribes from the north, such as Mongolians and the Daur, occupy the top positions. These populations live in really cold climates, and would provide suggestive evidence to the cold winter theory. The Siberian Yakut however, do not fare as well as the East Asians, despite living in cold climates. However, the Yakut are not a Mongolic tribe, but they belong to the Turkic ethnic group.

ALFRED has data from groups not present in 1000 Genomes, such as the Amerindian tribes or the Oceanians.

Let’s have a look at the sub-continental average factor scores:

Continent Factor
E Asia 0.959
SE Asia 0.34
Siberia 0.311
Europe 0.293
M East 0.009
W Asia -0.002
Oceania -0.551
North Africa -0.768
Sub-S. Africa -1.287
America -1.378

Native Americans and Africans occupy the lowest places, despite being genetically very different. The Native American result is a huge problem for people who want to explain the pattern in term of drift or migrations, because despite being the closest genetically to the East Asians, they are at the opposite of the spectrum in terms of factor scores.

This also suggests that whatever created the East Asian advantage happened after 15kya (the earliest estimate of a migration across the Bering strait into the Americas).  It is possible that the extremely low population density in the Americas reduced intraspecific competition, hence selection pressure on higher intelligence was lower.

I calculated the correlation between distance from Eastern Africa (Addis Ababa) and factor scores and this was negative (around -0.45), not supporting the novel environment hypothesis a la Kanazawa.

It seems that what caused different selection pressures on different populations is a mix of cold winters, population size and gene-culture co-evolution.

 

LD and its impact on cross-population correlations of allele frequencies

Linkage disequilibrium is the correlation between allele frequencies within a population and is quantified by the coefficient of linkage disequilibrium:

D_{AB}=p_{AB}-p_{A}p_{B}.

where A and B are two alleles at two different loci.

However, there is another kind of correlation between alleles, and that is the correlation of allele frequencies between populations.

The cross-population correlation between two unliked alleles will be r= 0. However, linkage disequilibrium will increase the cross-population correlation. Two alleles that are perfectly linked should have a cross-population correlation of 1, that is equal to their within population LD. However, there is a phenomenon known as “linkage breakdown”. As far as I know, there are no publications trying to quantify linkage breakdown in human populations.

Linkage breakdown reflect the extent to which the correlation between true and predicted values decays approximately linearly with respect to genetic related between the training and the target populations, due to different linkage disequilibrium patterns (Marigorta & Navarro, 2013). That is, if an association between gene X and phenotype Y is found in a population (training population), its replicability in other populations will depend on their genetic distance from the training population. This is because SNPs that are found by GWAS are usually not directly causal variants but instead are “tag” (proxy) SNPs, in LD with the real causal variants. If LD breaks down, this will affect also the frequencies distributions. Hence, tag SNPs will not necessarily have the same allele frequencies as the causal SNPs in all populations.

In order to estimate the level of LD breakdown in a way that also would affect the validity of my method based on factor analysis of allele frequencies, I computed the correlation between frequencies of SNPs in LD. Moreover, this was compared to the frequencies of random SNPs (with LD<0.5).

LD was calculated using the R package “rsnps”, with the CEU panel.

The frequencies of SNPs in LD (N=93) with a GWAS hit (rs301800) by Okbay et al. (2016) were downloaded from 1000 Genomes. The correlation between each SNP’s minor allele and and rs301800 was computed. The average correlation was r=0.815.

Conversely, the average correlation between an SNP from the set of random SNPs and all the other SNPs was as expected not significantly different from zero (0.053).

This simulation is not exhaustive nor conclusive but it shows that LD decay is unlikely to be a big problem because LD decay isn’t strong across 26 populations. Further analysis limited to populations from some continents would show if LD breaks down in some continents more than in others. For example, do SNPs in LD among Europeans show more linkage breakdown among East Asians or Africans? One could look at the correlation between allele frequencies in East Asian and African sub-populations separately. If the correlation is stronger among East Asians, this would suggest that LD patterns among Africans are more different.

 

 

References:

Marigorta, U.M., Navarro, A. (2013). High Trans-ethnic Replicability of GWAS Results Implies Common Causal Variants. PLOS Genetics 9, http://dx.doi.org/10.1371/journal.pgen.1003566

 

 

 

Height, IQ,polygenes: selection signal or noise?

Okbay et al. (2016) reported 162 independent SNPs that reached genome-wide significance (P < 5*10-8) in the pooled-sex EduYears meta-analysis of the discovery and replication samples (N =405,072). 161 SNPs were found in 1000 Genomes.  These were divided into 32 subsets of 5 SNPs and factor analyzed. The correlations of factor loadings and corr x pop IQ with p value were r= -0.273 and -0.008, respectively. Moreover, the two vectors (factor loadings and corr x pop IQ) were intercorrelated (r= 0.223), implying that the internal coherence of the factors is correlated to their predictive validity.

The scatterplot is shown in figure 1.

mcvokbay

The top 4 significant SNPs sets (N=20) were used to compute a polygenic score and the 4 factor scores were averaged. These were chosen because they had the highest loadings, highest correlation to population IQ and lowest p value (respectively, 0.383 and 0.83, compared to an average of 0.22 and 0.11 for the entire dataset), hence suggesting more signal in the data.

The largest GWAS to date (Wood et al., 2016) identified 697 SNPs which reached statistical significance for their association with human height. Factor analysis was carried out on 69 sets of 10 SNPs.

The top 10 significant SNPs for height were chosen because they had a higher average factor loading (0.419) than the entire set (0.166), actually the third highest among 69 sets of 10 SNPs. Polygenic and factor scores are reported in table 1. The latter are also reported in table 2 and 3, in descending order.

Table 1. Factor and polygenic scores. Top significant SNPs for height and educational attainment (IQ) GWAS.

Population PS_IQ IQ_Top_4_Fs_Mean Height_PS F_Height
Afr.Car.Barbados 0.339 -1.124 0.636 1.342
US Blacks 0.358 -0.904 0.612 0.662
Bengali Bangladesh 0.368 -0.051 0.503 -0.349
Chinese Dai 0.43 0.736 0.417 -1.381
Utah Whites 0.412 0.838 0.569 0.483
Chinese, Bejing 0.471 1.175 0.419 -1.456
Chinese, South 0.45 1.058 0.418 -1.504
Colombian 0.374 0.201 0.515 -0.103
Esan, Nigeria 0.345 -1.307 0.653 1.629
Finland 0.43 0.76 0.417 0.524
British, GB 0.421 0.832 0.551 0.299
Gujarati Indian, Tx 0.386 -0.059 0.524 -0.333
Gambian 0.342 -1.196 0.61 1.33
Iberian, Spain 0.419 0.728 0.552 0.245
Indian Telegu, UK 0.372 -0.127 0.521 -0.475
Japan 0.459 1.235 0.419 -1.568
Vietnam 0.435 0.845 0.417 -1.321
Luhya, Kenya 0.338 -1.306 0.618 1.263
Mende, Sierra Leone 0.332 -1.475 0.624 1.278
Mexican in L.A. 0.36 0.143 0.502 -0.561
Peruvian, Lima 0.304 -0.28 0.496 -0.803
Punjabi, Pakistan 0.39 0.091 0.519 -0.402
Puerto Rican 0.374 -0.012 0.525 0.254
Sri Lankan, UK 0.373 0.025 0.5 -0.576
Toscani, Italy 0.415 0.511 0.562 0.238
Yoruba, Nigeria 0.343 -1.338 0.638 1.285

Table 2. IQ factor scores sorted in descending order.

Population IQ_Top_4_factors_Mean
Japan 1.235
Chinese, Bejing 1.175
Chinese, South 1.058
Vietnam 0.845
Utah Whites 0.838
British, GB 0.832
Finland 0.76
Chinese Dai 0.736
Iberian, Spain 0.728
Toscani, Italy 0.511
Colombian 0.201
Mexican in L.A. 0.143
Punjabi, Pakistan 0.091
Sri Lankan, UK 0.025
Puerto Rican -0.012
Bengali Bangladesh -0.051
Gujarati Indian, Tx -0.059
Indian Telegu, UK -0.127
Peruvian, Lima -0.28
US Blacks -0.904
Afr.Car.Barbados -1.124
Gambian -1.196
Luhya, Kenya -1.306
Esan, Nigeria -1.307
Yoruba, Nigeria -1.338
Mende, Sierra Leone -1.475

 

Table 3. Height factor scores in descending order

Population Factor_Height_10SNPs
Esan, Nigeria 1.629
Afr.Car.Barbados 1.342
Gambian 1.33
Yoruba, Nigeria 1.285
Mende, Sierra Leone 1.278
Luhya, Kenya 1.263
US Blacks 0.662
Finland 0.524
Utah Whites 0.483
British, GB 0.299
Puerto Rican 0.254
Iberian, Spain 0.245
Toscani, Italy 0.238
Colombian -0.103
Gujarati Indian, Tx -0.333
Bengali Bangladesh -0.349
Punjabi, Pakistan -0.402
Indian Telegu, UK -0.475
Mexican in L.A. -0.561
Sri Lankan, UK -0.576
Peruvian, Lima -0.803
Vietnam -1.321
Chinese Dai -1.381
Chinese, Bejing -1.456
Chinese, South -1.504
Japan -1.568

 

There is a strong negative correlation between height and intelligence factor scores (r=-0.778).

The correlation between population IQ estimates (Piffer, 2015) with the average factor score and the polygenic score were r=0.923 and  0.867. The very high correlation of the factor score exceeds the 99% C.I. produced with a simulation using 200 iterations on random SNPs.

East Asians top the IQ rankings but are at the bottom of the height rankings. The opposite is true of African populations. Europeans have mid-high scores for both IQ and height, whereas South Asians and Hispanics/Latinos have mid to low scores on both traits.

The higher internal (i.e. factor loadings) and external (i.e. corr x IQ) coherence of factors extracted from more significant SNPs and the different patterns observed for height and IQ suggest that these SNPs represent signal of polygenic selection and not merely phylogenetic autocorrelation. Another important finding is that the signal is restricted to the most significant hits of each GWAS.

The individual scores are dependent on the choice of SNPs and the computational method (e.g. polygenic vs factor scores) but the overall pattern isn’t affected, since it is pretty consistent across GWAS samples and publications.

 

 

References

Okbay, A., Beauchamp, J.P., Fontana, M.A., Lee, J., Pers, T.H., et al. (2016). Genome-wide association study identifies 74 loci associated with educational attainment. Nature, doi:10.1038/nature17671

Piffer, D. (2015). A review of intelligence GWAS hits: Their relationship to country IQ and the issue of spatial autocorrelation. Intelligence, 53, 43-50.

Wood AR, Esko T, Yang J, et al.: Defining the role of common variation in the genomic and biological architecture of adult human height. Nat Genet. 2014; 46(11): 1173–86

Derived alleles,corrected polygenic scores for IQ and height

Email: pifferdavide@gmail.com

I have recently updated the new version of my paper about polygenic selection pressures on human stature published in f1000research. I chose stature not because it’s a particularly interesting trait but for the simple reason that it’s very straightforward to measure and has the largest sample size available for genome-wide association studies. Its genetic architecture is also very similar to IQ because it’s highly polygenic and normally distributed.

As far as I know, f1000research is the only other journal in the world to be “twice open” : open access and open peer review. The journal I founded (OpenPsych.net) is twice open but also free and is more interactive, besides being based on a bottom up process in the sense that reviewers choose the paper instead of the editor choosing reviewers. Apart from this, let’s come to my study.

The biggest novelty is a correction I have introduced to deal with different population frequencies of derived alleles. Derived alleles are basically human-specific mutations that are assumed to have arisen after the chimp/homo lineages split. Of course these are not the only mutations that arose during human evolution. Remember that we are talking about polymorphisms, hence this automatically excludes all mutations that are fixed  in the human population (no polymorphism, no SNP). The latter are substitutions ascertained via comparison with the chimp genome. Fixed mutations were once polymorphisms (a jargon term for SNP, which is even more alien for some people), but not all SNPs became fixed as some were lost due to random drift or purifying selection (the process that eliminates deleterious alleles).

There is a big controversy going on as to the causes of these: are they the result of relaxed puryfing selection due to population bottlenecks and decreased effective population size? (Henn et al, 2015) Or are they a result of increased mutation rate after a bottleneck? (Do et al., 2015) Were all (or almost all) mutations deleterious or were many of them adaptive? (Harris, 2010).

Besides demographic histories, there is also the problem that GWAS are usually carried out on Europeans, hence they tend to pick up derived alleles at higher frequency among European populations.

Be it as it may, I had to find ways to correct for this bias. In the case of the height GWAS (Wood, 2014), this was rather straightforward. There were 697 SNPs reaching genome-wide significance so this is a pretty big sample but 691 could be aligned for ancestral/derived status using 1000 Genomes. Among the positive effect alleles, there were slight more of the derived kind (370:321). Hence I computed two polygenic scores (mean population frequencies): ancestral and derived. Then I created a composite score by averaging them. This gives equal weight to ancestral and derived alleles (Piffer, 2015b).The end result is that populations with higher baseline frequencies of ancestral alleles (such as Africans) obtain a higher score after this correction, because more weight is given to ancestral alleles.

A corrected score of IQ increasing derived alleles was also computed and averaged across the four polygenic scores (two from Rietveld et al., 2013; one from Rietveld et al., 2014 and one from Davies et al., 2015), affecting educational attainment or fluid intelligence.

Table 1. Polygenic scores.

Corrected Height Uncorrected Height Corrected IQ Uncorrected IQ
Afr.Car.Barbados 0.487 0.473 -0.009 0.374
US Blacks 0.490 0.476 0.018 0.400
Bengali Bangladesh 0.485 0.476 0.002 0.406
Chinese Dai 0.479 0.469 0.078 0.484
Utah Whites 0.511 0.503 0.102 0.511
Chinese, Bejing 0.479 0.470 0.087 0.501
Chinese, South 0.482 0.472 0.075 0.483
Colombian 0.493 0.484 0.062 0.478
Esan, Nigeria 0.485 0.470 0.011 0.386
Finland 0.505 0.497 0.122 0.531
British, GB 0.508 0.499 0.114 0.524
Gujarati Indian, Tx 0.486 0.476 0.031 0.434
Gambian 0.486 0.471 -0.001 0.375
Iberian, Spain 0.500 0.491 0.121 0.534
Indian Telegu, UK 0.488 0.478 -0.032 0.370
Japan 0.477 0.468 0.057 0.463
Vietnam 0.480 0.470 0.105 0.507
Luhya, Kenya 0.483 0.468 -0.014 0.358
Mende, Sierra Leone 0.487 0.472 0.026 0.396
Mexican in L.A. 0.488 0.479 0.004 0.418
Peruvian, Lima 0.484 0.475 -0.043 0.378
Punjabi, Pakistan 0.491 0.482 -0.004 0.406
Puerto Rican 0.493 0.484 0.066 0.482
Sri Lankan, UK 0.487 0.478 -0.024 0.384
Toscani, Italy 0.501 0.492 0.128 0.537
Yoruba, Nigeria 0.484 0.469 0.012 0.384

The correlation between the uncorrected scores (0.602) is slightly higher than between the corrected scores (0.487).

The scores were ranked in descending order and reported in table 2.

Table 2.  Corrected polygenic scores reported in descending order.

Corrected Height Corrected IQ
Utah Whites 0.511 Toscani, Italy 0.128
British, GB 0.508 Finland 0.122
Finland 0.505 Iberian, Spain 0.121
Toscani, Italy 0.501 British, GB 0.114
Iberian, Spain 0.500 Vietnam 0.105
Puerto Rican 0.493 Utah Whites 0.102
Colombian 0.493 Chinese, Bejing 0.087
Punjabi, Pakistan 0.491 Chinese Dai 0.078
US Blacks 0.490 Chinese, South 0.075
Mexican in L.A. 0.488 Puerto Rican 0.066
Indian Telegu, UK 0.488 Colombian 0.062
Sri Lankan, UK 0.487 Japan 0.057
Afr.Car.Barbados 0.487 Gujarati Indian, Tx 0.031
Mende, Sierra Leone 0.487 Mende, Sierra Leone 0.026
Gujarati Indian, Tx 0.486 US Blacks 0.018
Gambian 0.486 Yoruba, Nigeria 0.012
Bengali Bangladesh 0.485 Esan, Nigeria 0.011
Esan, Nigeria 0.485 Mexican in L.A. 0.004
Yoruba, Nigeria 0.484 Bengali Bangladesh 0.002
Peruvian, Lima 0.484 Gambian -0.001
Luhya, Kenya 0.483 Punjabi, Pakistan -0.004
Chinese, South 0.482 Afr.Car.Barbados -0.009
Vietnam 0.480 Luhya, Kenya -0.014
Chinese, Bejing 0.479 Sri Lankan, UK -0.024
Chinese Dai 0.479 Indian Telegu, UK -0.032
Japan 0.477 Peruvian, Lima -0.043

We can see that the ranking of corrected polygenic scores for height and IQ gives higher scores to Africans compared to the uncorrected scores, as predicted on the basis of their lower background derived frequencies. The bottom place for height is occupied by East Asian populations (Japan, Chinese, Vietnamese), and the top place by North Europeans (White Americans, Finns, British) matching anthropometric descriptions and available statistics (https://en.wikipedia.org/wiki/Human_height). The bottom places of the IQ polygenic scores are occupied by South American, South Asian and African populations. It must be noted that the South Asian populations (Indian Telegu, Sri Lankan) are living in the UK and I am not aware of the existence of any reliable studies on their average IQ.

These results are encouraging because they provide discriminant validity (only a moderate correlation between the height and IQ polygenic scores, which can be explained by phylogenetic autocorrelation) and predictive validity (a moderately good fit with phenotypic population averages (IQ and height). A less than perfect fit is expected given that we have not sampled all the SNPs, that these represent only signals of polygenic pressure (thus not including all the non-additive effects) and the importance of environment for these variables, as showed from the dramatic secular trend in height and IQ observed within Western countries.

A Piffer-Mantel test (Piffer, 2015) was carried out by calculating the distances between all pairs of populations for the polygenic scores. The height polygenic score was used as the dependent variable and Fst distances + the IQ score as the independent variables.

There was a slight positive Beta coefficient for the IQ PS (0.387) but Fst was close to 0 (0.06) (Piffer, in press). The average value obtained using 100 polygenic scores from the SNPs (2+ millions) contained in Rietveld et al. (including the non-significant ones) is 0.06 with SD=0.176.if we assume that the tiny deviation from 0 (0.06) was a result of chance or residual signal contained in some of the Rietveld hits, we can calculate the deviation from null expectations: 0.387/0.176= 2.19 Zs.

A partial correlation (height ps, IQ ps, Fst) gave almost identical result (r=0.386).

To confirm that this is a sign of common selection pressures we’ll need more population samples but this is still a suggestive finding.

Conclusion

This article shows that it’s necessary to control for background frequencies of derived and ancestral alleles when computing population-level polygenic scores.

References:

Davies, G., Armstrong, N., Bis, J. C., et al. (2015). Genetic contributions to variation in general cognitive function: a meta-analysis of genome-wide association studies in the CHARGE consortium (N=53949).Molecular Psychiatry, 20:183-192. doi: 10.1038/mp.2014.188

Do, R., Balick, B., Li, H., Adzhubei, I., Sunyaev, S., & Reich, D. (2015). No evidence that selection  has been less effective at removing mutations in Europeans than Africans. Nature Genetics, doi:10.1038/ng.3186

Harris, E.E. (2010). Nonadaptive processes in primate and human evolution. Yearbook of Physical Anthropology, 53: 13-45.

Henn, B.M., Botigué, L.R., Peischl, S., Dupanloup,I.,  Lipatov,M., Maples,B.K., Martin, A.R., Musharoff, S., Cann, H., Snyder,M.P., Excoffier, L., Kidd, J.M.,  Bustamante, C.D. (2015). Distance from sub-Saharan Africa predicts mutational load in diverse human genomes. PNAS ; published ahead of print December 28, 2015, doi:10.1073/pnas.1510805112

Piffer, D. (2015a). A review of intelligence GWAS hits: Their relationship to country IQ and the issue of spatial autocorrelation. Intelligence, 53, 43-50.

Piffer D. (2015b). Evidence of polygenic selection on human stature inferred from spatial distribution of allele frequencies. F1000Research, 4:15

Piffer, in press. Polygenic selection of cognitive ability: polygenic scores predict average group intelligence. Is selection signal a function of GWAS significance?

Rietveld, C.A., Medland, S.E., Derringer, J., Yang, J., Esko, T., Martin, N.W., et al. (2013). GWAS of 126,559 individuals identifies genetic variants associated with educational attainment. Science, 340, 1467-1471. doi: http://doi.org/10.1126/science.1235488

Rietveld, C.A., Esko, T., Davies, G., Pers, T.H., Turley, P., Benyamin, B., et al. (2014). Common genetic variants associated with cognitive performance identified using the proxy-phenotype method. Proceedings of the National Academy of Sciences, USA, 111, 13790-13794. doi:10.1073/pnas.1404623111

Wood AR, Esko T, Yang J,et al.: Defining the role of common variation in the genomic and biological architecture of adult human height. Nat Genet. 2014; 46(11): 1173–86.

 

 

 

 

 

 

Similar selection pressures on fluid g and educational attainment-related SNPs

Author: Davide Piffer. Email: pifferdavide@gmail.com

A recent GWAS has examined the additive genetic variance accounting for variation in general cognitive function or fluid g (Davies et al., 2015)These were assessed using a battery of information-processing tests including memory, block design, matrix reasoning, reaction time, letter-number sequencing (Davies et al. , 2015).

Since my use of an educational attainment GWAS has been criticized for being affected by environmental variables and for not being strictly an intelligence measure, I decided to see if I could replicate this result on an independent sample and using different measures, hopefully tapping into a more “culture-free” construct, such as fluid g. The typical reaction to using educational attainment is that it could be influenced by environmental variables correlated to genetic variation (see for example the comments by this reviewer: http://openpsych.net/forum/showthread.php?tid=262&pid=3737#pid3737).

13 SNPs with genome-wide significance (p<5*10-8) were identified (Davies et al., 2015).  10 hits (i.e. the allele with a positive effect on the phenotype) were derived and 3 were ancestral alleles. Table 1 reports the average frequency of the 13 SNPs for the 26 populations in 1000 Genomes  and the frequency of the top 10 SNPs with an effect on years on education from Rietveld et al. (2013) . The correlation between the two polygenic scores (e.g. average population frequency of GWAS hits) is very high: r= 0.964. Their correlation to population IQ is also substantial: r= 0.817 and 0.715 for Davies et al, 2015 and Rietveld et al, 2013, respectively.

Table 1. Average frequency of intelligence (fluid g) and education (years of education)-increasing alleles from two independent GWAS.

Population  Davies et al, 2015. Top 13 SNPs Rietveld et al., 2013. Top 10 SNPs IQ
Afr.Car.Barbados 0.262 0.317 83
US Blacks 0.320 0.360 85
Bengali Bangladesh 0.371 0.368 81
Chinese Dai 0.498 0.463
Utah Whites 0.521 0.534 99
Chinese, Bejing 0.509 0.468 105
Chinese, South 0.477 0.448 105
Colombian 0.471 0.476 83.5
Esan, Nigeria 0.286 0.341 71
Finland 0.556 0.573 101
British, GB 0.529 0.548 100
Gujarati Indian, Tx 0.391 0.403
Gambian 0.262 0.325 62
Iberian, Spain 0.533 0.566 97
Indian Telegu, UK 0.280 0.293
Japan 0.425 0.399 105
Vietnam 0.511 0.491 99.4
Luhya, Kenya 0.228 0.292 74
Mende, Sierra Leone 0.311 0.355 64
Mexican in L.A. 0.358 0.370 88
Peruvian, Lima 0.300 0.288 85
Punjabi, Pakistan 0.324 0.357 84
Puerto Rican 0.476 0.483 83.5
Sri Lankan, UK 0.308 0.323 79
Toscani, Italy 0.553 0.562 99
Yoruba, Nigeria 0.270 0.340 71

As overrepresentation of derived alleles among GWAS hits is a potential counfound (due to different frequencies of derived alleles among population caused by drift and bottlenecks or GWAS artifacts: see my previous posts for an explanation), a baseline frequency of derived alleles (DAF) was estimated using the 693 SNPs significant for human stature in the largest GWAS to date (Wood et al, 2014).

A multiple regression was ran with population IQ and the two variables (baseline DAF and polygenic score) was ran for the two GWAS hits.

Table 2. Standardized beta coefficients. DAF= derived allele frequency. DP (derived alleles with positive effect on the trait).

  Baseline DAF Davies DP
Rietveld et al., 2013 0.406 0.464
Davies et al, 2015 0.307 0.587

Both polygenic scores emerged as better predictors than baseline DAF. A DAF-calibrated score was calculated by subtracting baseline DAF from the frequency of derived hits. This likely represents selection signal on derived alleles as it controls for evolutionary dynamics such as random drift and population bottlenecks. Since the two population-level polygenic scores were highly correlated (r= 0.953), an average score was computed and is reported in table 3, ranked in descending order. This score is highly correlated to the average of the two polygenic scores obtained using all the SNPs (table 1), r= 0.971. However, the correlation with population IQ is slightly lower, at r= 0.687.

Table 3. DAF-calibrated polygenic scores for derived alleles and average polygenic score. Ranked in descending order. DAF= derived allele frequency.

Population DAF-free Derived hits. Rietveld et al, 2013 DAF-free Derived hits. Davies et al, 2013 Average
Toscani, Italy 0.186 0.178 0.182
Finland 0.188 0.173 0.180
Iberian, Spain 0.188 0.155 0.171
British, GB 0.171 0.149 0.160
Utah Whites 0.160 0.140 0.150
Vietnam 0.114 0.160 0.137
Chinese, Bejing 0.092 0.155 0.123
Chinese Dai 0.087 0.145 0.116
Puerto Rican 0.104 0.116 0.110
Colombian 0.103 0.107 0.105
Chinese, South 0.064 0.127 0.096
Japan 0.025 0.072 0.049
Gujarati Indian, Tx 0.033 0.038 0.036
Mende, Sierra Leone 0.021 0.038 0.029
US Blacks 0.014 0.026 0.020
Esan, Nigeria 0.007 0.013 0.010
Bengali Bangladesh -0.011 0.022 0.006
Yoruba, Nigeria 0.005 0.002 0.004
Mexican in L.A. -0.007 0.000 -0.003
Gambian -0.022 -0.015 -0.018
Afr.Car.Barbados -0.036 -0.022 -0.029
Punjabi, Pakistan -0.036 -0.028 -0.032
Luhya, Kenya -0.046 -0.050 -0.048
Sri Lankan, UK -0.057 -0.042 -0.050
Peruvian, Lima -0.087 -0.045 -0.066
Indian Telegu, UK -0.090 -0.064 -0.077

Conclusion

We can see that genetic variants increasing fluid intelligence and educational attainment are highly correlated at the population-level, suggesting two things: 1) there are common selection pressures on the two phenotypes or 2) educational attainment is a good proxy for g and the SNPs found by Rietveld et al., 2013 are actually g-related (as was suggested by their replication on g in a sub-sample). The findings in the present study debunk two criticisms of my work: 1) That the observed allele frequency differences were “specific” to educational attainment and not really about intelligence and 2) that derived allele differences caused by GWAS artifacts or random drift could mediate the effects. I showed that the observed effects are not due to different baseline derived allele frequencies, thus ruling this out as a possible confound. A discrepancy with IQ estimates is that East Asians lag behind Europeans and that South Asians and Hispanics don’t perform better than sub-Saharan Africans, a finding that is difficult to explain at present.

Again, we observe a tendency for derived alleles (human-specific mutations or not shared with non-human primates) to be overrepresented among the most significant intelligence GWAS hits, confirming the prediction stemming  from the evolutionary fact that intelligence has dramatically increased during human evolution.

References:

Davies, G., Armstrong, N., Bis, J. C., et al. (2015). Genetic contributions to variation in general cognitive function: a meta-analysis of genome-wide association studies in the CHARGE consortium (N=53949).Molecular Psychiatry, 20:183-192. doi: 10.1038/mp.2014.188

Rietveld, C.A., Medland, S.E., Derringer, J., Yang, J., Esko, T., Martin, N.W., et al. (2013). GWAS of 126,559 individuals identifies genetic variants associated with educational attainment. Science, 340, 1467-1471. doi: http://doi.org/10.1126/science.1235488

Wood AR, Esko T, Yang J,et al.: Defining the role of common variation in the genomic and biological architecture of adult human height. Nat Genet. 2014; 46(11): 1173–86.

 

 

 

 

 

 

Using derived alleles to amplify selection signatures on intelligence

Author: Davide Piffer

The aim of this study is to identify polygenic selection signatures on intelligence across 26 populations from 1000 Genomes. In the next post, I will expand on this to include more populations (at the expense of SNPs number and reliability)!

Derived allele frequencies and background calibration

At a theoretical level, an ancestral allele is the allele that was carried by the last common ancestor between humans and other primates whereas an allele is derived when it arose in the human lineage after the split from other primates. In practice, this allele is usually ascertained via comparison with chimpanzees. One limitation of this procedure is that if a mutation arose in chimpanzees after the split from humans, then the ancestral allele is not the chimp allele. Thus, 1000 Genomes infers ancestral alleles via alignment with 6 primate species (Ensembl, 2015).

Frequencies of derived alleles are not the same for all populations. Substantial DAF (derived allele frequency) differences across populations have been found, largely due to random drift and population bottlenecks but in part also shaped by different selection pressures (Henn et al., 2015). Non-African populations tend to have higher frequencies of derived alleles, and DAF is positively correlated to distance from Africa (Henn et al., 2015). There are also potential issues with GWAS. For example, a reviewer of a previous submission (https://topseudoscience.wordpress.com/2016/01/10/the-forbidden-paper-on-the-population-genetics-of-iq/) suggested that the minor alleles picked by the GWAS (carried on European subjects) tend to have higher frequencies among the GWAS reference population (i.e. Europeans) than the average genome-wide frequencies of minor alleles. Minor alleles are more likely to be derived alleles, hence these derived alleles will have higher frequencies among Europeans compared to other populations. If derived alleles tend to have a positive effect, the frequency of alleles with positive effect may be higher among Europeans than other populations.

A novel methodology suggested here to deal with this confound is to create a variable which represents a good approximation to the average frequencies of derived alleles picked up by GWA studies. For this purpose, the significant hits (N= 693) from the largest GWAS of human stature to date (Wood et al., 2014) were grouped by allele status. The average frequency of derived alleles (including both alleles with a positive and a negative effect) was computed and then averaged into a single variable, henceforth the DAF index (table 1). Negative and positive alleles were given equal weight to avoid positive selection bias on the index.

Table 1. Mean derived allele frequencies and country IQ.

Population Height Derived IQ
Afr.Car.Barbados 0.298 83
US Blacks 0.309 85
Bengali Bangladesh 0.363 81
Chinese Dai 0.359
Utah Whites 0.382 99
Chinese, Bejing 0.365 105
Chinese, South 0.362 105
Colombian 0.372 83.5
Esan, Nigeria 0.286 71
Finland 0.385 101
British, GB 0.381 100
Gujarati Indian, Tx 0.365
Gambian 0.291 62
Iberian, Spain 0.378 97
Indian Telegu, UK 0.362
Japan 0.366 105
Vietnam 0.360 99.4
Luhya, Kenya 0.291 74
Mende, Sierra Leone 0.283 64
Mexican in L.A. 0.376 88
Peruvian, Lima 0.373 85
Punjabi, Pakistan 0.366 84
Puerto Rican 0.369 83.5
Sri Lankan, UK 0.362 79
Toscani, Italy 0.376 99
Yoruba, Nigeria 0.285 71

Using the DAF from the GWAS on human stature, we note that derived alleles (col.  2) tend to be at lower frequencies among African than non-African populations, confirming the findings of a recent study (Henn et al., 2015) on different mutational load at common variants. The hypothesis that this phenomenon could mediate the association between IQ and polygenic scores is also confirmed by DAF’s positive correlation with population IQ (r=0.767).Note that the confounding effect would be present only when there are more derived positive than ancestral positive. If these are represented in equal proportions, the overrepresentation of derived alleles in some populations will be perfectly balanced by the underrepresentation of ancestral alleles and viceversa. However, in cases where there is a dramatic overrepresentation of derived alleles (such as the top significant hits in Rietveld et al., 2013), it is necessary to control for background DAF. Moreover, having a larger sample of SNPs (such as that from the height GWAS comprising 693 SNPs) will enable us to have a more accurate estimate of the background DAF than that we could gain from using a smaller subset of SNPs.

A DAF-calibrated polygenic score is then created by subtracting the DAF index from the average frequency of derived alleles with positive effect from GWAS SNPs. Table 2 reports standardized scores, in descending order (sorted by the mean value of the two scores).

Note that we could also apply the reverse procedure and calculate a background frequency of ancestral alleles (1-DAF). Then one could subtract that from the average frequency of ancestral alleles with positive effect. This is perhaps justified for traits such as height which were not subject to a dramatic increase during human evolution. However, since intelligence has been subject to a sharp increase and most intelligence-enhancing mutations are likely to be human-specific and not shared with our primate ancestors, by focusing on derived alleles one likely amplifies the signal of selection.

Table 2. Background “DAF-free” polygenic scores (P.S). Average is reported as Z scores and reported in descending order.

Population P.S, Rietveld et al., 2014 P.S, p<5*10-8 

(N=9)

P.S,p<5*10-7>=5*10-8 

(N=49)

Average
Toscani, Italy 1.671 1.620 1.496 1.596
Iberian, Spain 1.567 1.646 1.391 1.535
Finland 1.358 1.645 1.113 1.372
British, GB 0.886 1.446 1.397 1.243
Vietnam 0.481 0.798 1.679 0.986
Japan 1.667 -0.230 1.124 0.854
Utah Whites 0.239 1.319 0.908 0.822
Chinese, Bejing 0.462 0.536 0.736 0.578
Chinese, South 0.494 0.221 0.893 0.536
Chinese Dai -0.229 0.485 0.414 0.223
Gujarati Indian, Tx -0.267 -0.135 -0.159 -0.187
Mende, Sierra Leone 0.133 -0.276 -0.453 -0.199
Colombian -0.847 0.672 -0.433 -0.202
Yoruba, Nigeria 0.309 -0.456 -0.551 -0.233
Puerto Rican -1.178 0.683 -0.220 -0.239
US Blacks -0.245 -0.353 -0.600 -0.399
Gambian 0.233 -0.770 -0.709 -0.415
Afr.Car.Barbados 0.187 -0.931 -0.922 -0.555
Esan, Nigeria -0.626 -0.444 -0.746 -0.605
Punjabi, Pakistan -0.760 -0.928 -0.164 -0.618
Bengali Bangladesh 0.262 -0.646 -1.532 -0.639
Luhya, Kenya -0.947 -1.044 -0.356 -0.782
Indian Telegu, UK -0.389 -1.558 -0.702 -0.883
Sri Lankan, UK -0.230 -1.177 -1.293 -0.900
Mexican in L.A. -2.045 -0.602 -0.508 -1.052
Peruvian, Lima -2.187 -1.523 -1.804 -1.838

The correlation between this score and that obtained using the raw frequencies (total polygenic score= derived and ancestral alleles with positive effect) is r=0.889. These are reported in table 3.

The calibrated scores are correlated to population IQ: r=0.462, 0.628 and 0.752 for the Rietveld et al., 2014, the GWAS significant and the other hits (p<5*10-7>=5*10-8), respectively.

The correlations between the mean calibrated and uncalibrated score and IQ are r=0.68 and 0.790, respectively.

Table 3. Total polygenic scores (Ancestral and derived alleles with positive effect), reported in descending order.

Population Rietveld et al 2014; N=67 p<5*10-8; N=10 p<5*10-7>=5*10-8; N=49 Average
Iberian, Spain 0.468 0.566 0.569 0.534
Toscani, Italy 0.467 0.562 0.568 0.532
Finland 0.465 0.573 0.530 0.523
British, GB 0.458 0.548 0.560 0.522
Utah Whites 0.459 0.534 0.530 0.507
Vietnam 0.459 0.491 0.565 0.505
Chinese, Bejing 0.471 0.468 0.555 0.498
Chinese, South 0.466 0.448 0.543 0.485
Puerto Rican 0.449 0.483 0.520 0.484
Colombian 0.445 0.476 0.519 0.480
Chinese Dai 0.454 0.463 0.520 0.479
Japan 0.474 0.399 0.554 0.476
Gujarati Indian, Tx 0.449 0.403 0.493 0.448
Mexican in L.A. 0.431 0.370 0.515 0.439
Punjabi, Pakistan 0.453 0.357 0.490 0.433
US Blacks 0.451 0.360 0.468 0.426
Mende, Sierra Leone 0.458 0.355 0.462 0.425
Yoruba, Nigeria 0.458 0.340 0.468 0.422
Esan, Nigeria 0.455 0.341 0.461 0.419
Bengali Bangladesh 0.450 0.368 0.435 0.418
Gambian 0.456 0.325 0.456 0.412
Afr.Car.Barbados 0.459 0.317 0.460 0.412
Sri Lankan, UK 0.458 0.323 0.445 0.409
Peruvian, Lima 0.427 0.288 0.498 0.404
Luhya, Kenya 0.450 0.292 0.463 0.402
Indian Telegu, UK 0.451 0.293 0.457 0.400

We can apply the reverse procedure to determine if ancestral alleles contain signal above and beyond the background AAF (ancestral allele frequency) distribution. We can carry this out using the Rietveld et al., 2014, the Rietveld et al., 2013 hits with p<5*10-7>=5*10-8, but it is not possible to use the top 10 SNPs because they contain only 1 ancestral allele with positive effect. Table 9 reports the difference between AP for Rietveld et al., 2014 and 2013 and the background AAF (AP-AAF), and population IQ.

Table 4. Ancestral alleles with positive effect – AAF.

 

Population AP-AAF; Rietveld et al., 2014 AP-AAF; Rietveld et al., 2013 (p<5*10-7>=5*10-8) IQ
Afr.Car.Barbados -0.003 -0.079 83
US Blacks -0.025 -0.079 85
Bengali Bangladesh -0.074 -0.105 81
Chinese Dai -0.052 -0.025
Utah Whites -0.062 -0.030 99
Chinese, Bejing -0.022 0.030 105
Chinese, South -0.035 0.000 105
Colombian -0.075 0.012 83.5
Esan, Nigeria 0.007 -0.087 71
Finland -0.067 -0.039 101
British, GB -0.075 0.008 100
Gujarati Indian, Tx -0.069 -0.051
Gambian -0.009 -0.096 62
Iberian, Spain -0.058 0.026 97
Indian Telegu, UK -0.061 -0.096
Japan -0.034 0.012 105
Vietnam -0.051 0.008 99.4
Luhya, Kenya -0.005 -0.099 74
Mende, Sierra Leone 0.005 -0.098 64
Mexican in L.A. -0.097 0.011 88
Peruvian, Lima -0.104 0.038 85
Punjabi, Pakistan -0.052 -0.055 84
Puerto Rican -0.056 0.006 83.5
Sri Lankan, UK -0.043 -0.092 79
Toscani, Italy -0.061 0.019 99
Yoruba, Nigeria 0.000 -0.079 71

The correlation between AAP-AAF (Rietveld et al, 2014) and IQ is negative: r=-0.472. The correlation between AAP-AAF (Rietveld et al, 2013) and IQ is positive: r= 0.742.

Conclusions

Controlling for different population DAFs does not substantially alter the overall pattern, although there is a slight reduction in fit (r x population IQ drops from 0.79 to 0.68), which we do not know if it is just a fluke. The far from perfect correlation with population IQ is due to the top place occupied by Europeans instead of East Asians and a tendency for Latin Americans and South Asians (Indians, Bangladeshi) to score as low as sub-Saharan Africans. We also notice that ancestral positive alleles do not have as strong a correlation to population IQ (r= -0.472 and 0.742) as derived positive alleles (table 4). This is expected on evolutionary grounds, as selection on intelligence should have acted on human-specific mutations rather than on ancestral variants shared with non-human primates.

References:

Ensembl, 2015: http://www.1000genomes.org/faq/where-does-ancestral-allele-information-your-variants-come

Davies, G., Armstrong, N., Bis, J. C., et al. (2015). Genetic contributions to variation in general cognitive function: a meta-analysis of genome-wide association studies in the CHARGE consortium (N=53949).

Henn, B.M., Botigué, L.R., Peischl, S., Dupanloup,I.,  Lipatov,M., Maples,B.K., Martin, A.R., Musharoff, S., Cann, H., Snyder,M.P., Excoffier, L., Kidd, J.M.,  Bustamante, C.D. (2015). Distance from sub-Saharan Africa predicts mutational load in diverse human genomes. PNAS ; published ahead of print December 28, 2015, doi:10.1073/pnas.1510805112

Rietveld, C.A., Medland, S.E., Derringer, J., Yang, J., Esko, T., Martin, N.W., et al. (2013). GWAS of 126,559 individuals identifies genetic variants associated with educational attainment. Science, 340, 1467-1471. doi: http://doi.org/10.1126/science.1235488

Rietveld, C.A., Esko, T., Davies, G., Pers, T.H., Turley, P., Benyamin, B., et al. (2014). Common genetic variants associated with cognitive performance identified using the proxy-phenotype method. Proceedings of the National Academy of Sciences, USA, 111, 13790-13794. doi:10.1073/pnas.1404623111

Wood AR, Esko T, Yang J,et al.: Defining the role of common variation in the genomic and biological architecture of adult human height. Nat Genet. 2014; 46(11): 1173–86.