An environmentarian called Sasha Gusev has recently written a critique of classical twin studies, claiming that their design is biased and cannot tell us about the heritability of traits. One major point he makes is that the classical twin design (CTD) does not correctly measure the contribution of “cultural transmission” to the variance of a trait, thereby leading to inflated estimates of heritability.

How could this be, when the CTD measures the variance due to shared environment (c^2)? Sasha’s post gives a lot of FUD around “culture mimicking genetic inheritance.” But this has nothing to do with the twin design — rather, it references the idea that mother and father phenotypes directly influences kids equally, just like their genotypes. This is only a problem when trying to separate parental phenotypic transmission from genotypic transmission in data sets without monozygotic and dizygotic twins.

The real criticism comes down to the equal environments assumption.

In Sasha’s own equation, when we apply Falconer’s formula ( h^2 = 2(rmz - rdz)), we get

The Ar_a term means the heritability is actually underestimated when assortative mating is positive. Assortative mating is for IQ is about 0.33, and the CTD usually finds h^2 = .66. Adjusting for assortative mating then gives h^2 = 1. However, this is the phenotypic correlation between spouses. If we assume the genotypic correlation is 66% of .33, we get h^2 = .835, in line with what identical twins reared apart studies find (these are not biased by assortative mating).

So the heritability of IQ is probably about .83, and it’s unclear what the remaining term means or how to measure the bias it causes.

Sasha’s references don’t shine any light on this. In one case he claims

[Rao, Morton, Lalouel, Lew (1982)

Genome Res] applied path models with generalizations of assortative mating, including assortment on non-genetic components of the phenotype (aka social homogamy, wherein people tend to marry neighbors or co-workers who areenvironmentallysimilar). Here the models deviated more substantially: “Under the phenotypic homogamy model, genetic heritability is h2 = 0.31 and cultural heritability is b2 = 0.42. The social homogamy model nearly reverses these heritabilities in children (h2 = 0.44, b2 = 0.33), with greater cultural heritability in adults (b2 = 0.48).”.

What the study actually did was define a ridiculous 12 parameter model that wasn’t the best fit to the data.

Here, the lowest ch^2 is the best fit, and anything without a * is not a statistically unlikely fit. So the same data supports the heritability being .43 or .54, and these models have less parameters as well, making them more parsimonious.

Basically, environmentarians make models that look like this, but can’t follow basic frequentism.

This is obviously just dishonesty.

Since we’re getting nowhere with Sasha’s post, let’s use our own reason. Let’s imagine shared environment as the result of a sampling process of information within the home. If this sampling process is total, or not influenced by genetics, then we’re back to the old concept of shared environment — identical and fraternal twins have equally similar shared environments, so the variance components cancel out in Falconer’s equation.

For identical twins to have *more similar *shared environment components, the sampling process from the shared environment must be incomplete (meaning only a subset of the sharedenvironmentenes are obtained by each child) and correlated with genotype.

Therefore, the ultimate cause of the bias would be genetics, so it would still give a good broad sense estimate of the heritability.

We can also estimate how much the heritability estimates are biased.

Here, m is how much shared environment variance MZ twins have as a fraction of population shared environment variance, and likewise for d and DZ twins. This means 0 < m,d < 1 and m <= d while m’ >= d’.

We get the following bias for heritability: (equation source)

Here, C_A is the increase in similarity in MZs over DZs due to gene driven violation of the EEA.

Here, C_E is basically the increase in shared environmental variance due to MZs now having more variation due to not perfectly sharing shared environmental variance.

c^2 is basically what shared environment variance would be under the EEA.

You can see that

It is a category error to consider C_A the same as C_E or c^2. Clearly, the different components of C are different. C_A is rightfully a part of broad sense heritability.

Now for how large these components actually are:

Here’s a visualization, the red is how much h^2 is added to by C_A, the green is how much the c^2 estimate is of C, x is MZ similarity, and y is DZ similarity.

Here’s a visualization restricted to the similarities being between 1/2 and 1.

If you just kind of go in the middle of the plausibility region, you get something like MZ similarity being 0.90 while DZ is .80. If C is 20%, then h^2 would be inflated by .04 and the estimate for c^2 would be about 16%.

I conclude that this criticism isn’t very important and probably doesn’t bias heritability upward more than not accounting for assortative mating biases it downward. The real heritability for IQ is likely still greater than 60%.

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