New Meta-Analysis of GWAS Highlights Missing Heritability Problem

Also debunks most of Sasha Gusev's claims about IQ not being like height

A new meta-analysis of GWAS and family-GWAS (FGWAS) just dropped yesterday.

Here’s the table with the main results:

Sasha Gusev was wrong

Recall that Sasha Gusev claimed 5 things: (read my response here)

1. IQ is much less heritable and more confounded than height

2. Genetic effects on IQ differ within families much more than for height

3. IQ estimates are much more biased by participation than height

4. The genetics of IQ is much more environmentally sensitive than height

5. Unlike height, no one knows what IQ is actually measuring

This meta-analysis provides data about 1 and 2. Sasha gave the following chart, claiming the within-family effects of IQ were much lower than the population effects:

And he also claimed that the height effects don’t differ. I pointed out his p-values were shit, and it was likely that the IQ effects did not differ.

Guess what didn’t replicate in the meta-analysis? The IQ effects being different:

Is IQ less heritable than height?

But you see above that the heritabilities for height and IQ are different. Does this mean that IQ is “more cultural”? No. The difference between GWAS heritability estimates for height and IQ can be explained by the purely random measurement error inherent in IQ tests.

In classic psychological test theory, IQ is modeled as follows:

\(IQ = g + \epsilon\)

IQ is the sum of underlying general intelligence and an error component. The error component is totally random and doesn’t correlate with anything, including SNPs.

So, given this model holds, if you know the correlation between SNPs and IQ, you can figure out the correlation between SNPs and g, if you know the magnitude of the error component relative to g.

This magnitude is captured by test reliability. We assume each person’s g doesn’t change. This means any difference in test scores over time is due to having different error components. This lets us estimate the variance of the error component.

\(r = \frac{Cov(IQ_{t}, IQ_{t+1})}{Var(IQ)} = \frac{Cov(g + \epsilon_{t}, g + \epsilon_{t+1})}{Var(IQ)} = \frac{Cov(g, g)}{Var(IQ)} = \frac{Var(g)}{Var(IQ)}\)

The reliability r is the how much variance g explains of IQ, similar to how heritability is how much variance genetics explains of phenotype.

So now say we want the correlation of SNPs with g instead of IQ:

\(Corr(g, SNPs) = \frac{Cov(g, SNPs)}{\sigma_g \sigma_{SNP}} = \frac{Cov(IQ, SNPs)}{\sqrt{r}\sigma_{IQ}\sigma_{SNP}} = \frac{Corr(IQ,SNP)}{\sqrt{r}}\)

So

\(h^{2}(g)_{SNP} = \frac{h^{2}(IQ)_{SNP}}{r}\)

Because the heritabilities are just the squared correlations.

This is known as correcting for attenuation.

It’s unclear what the average r was for the cognitive tests in this meta-analysis. But for the UK Biobank, it was a mere r=.55.

So I’ll give a number of possible r values. As you can see, the 95% CIs overlap with the height h^2. Consequently, there’s no evidence that general intelligence is less heritable than height in FGWAS.

Where did all the heritability go?

Sasha Gusev et al. like to claim that the heritability vanished in GWAS because of “cultural” factors, like the Equal Environments Assumption (EEA) being violated.

They take the low GWAS heritabilities of IQ as evidence that twin designs were flawed and IQ is “just a test” and is “determined by culture.”

But by that logic, height is just a mostly random measurement and is mostly determined by culture. Perhaps the EEA is violated and people bigotedly feed identical twins more similar diets than fraternal twins. Maybe height is determined by stereotype threat and the kinds of books your parents read to you as a child.

Meta-analysis of height h^2 in twin studies. h^2 =~ 75%

Because they’re missing 40+% of heritable variance in height GWAS. Where did the variance go?

By Occam’s razor, the IQ and height variance are missing in the same place. And because height is missing along with IQ, it’s probably not missing because of “culture.”

Where did the variance go? As far as I know, nobody knows for sure. However, they’re missing about half of the variance. This reminds me of another molecular study that was off from quantitative methods by a factor of 2. I hypothesized that the rest of the variance was hiding in the noncoding region of the DNA.

The coding region of the DNA is highly variable and small, about 2% of the genome. Most GWAS SNPs at this point are in this region. The non-coding region is 98% of DNA and varies far less. Most extremely rare variants will therefore likely be in this region. Just based on the size of the two regions, if each region has half of the variance, it will take 50^2¹ times the power to detect the average SNP in the non-coding region as the coding region.

So we will need sample sizes in the tens of millions, potentially the hundreds of millions.

Another further out possibility is extranuclear genetics, including the possibility of non-DNA or RNA inheritance. Did you know your whole nuclear genome is just 800 megabytes in size? Do you feel like 800 megabytes? Maybe this is a meaningless question, since you’re not likely to be more than 1.6 GB in size informationally, given he have half the expected heritability.

Given all the height heritability that’s missing, it’s hard to think of another explanation beyond them just missing alleles. Can anyone knowledgeable think of something else?

1. SE =~ 1/sqrt(n). To detect an effect t, 1.96SE < t. So sqrt(n) < 1.96/t → sqrt(min_n) = 1.96*t^-1. If t is multiplied by 1/50 then sqrt(min_n) is multiplied by 50, so min_n is multiplied by 50^2.