[rbehrends]

Heritability has a very specific meaning in quantitative genetics [1], which in many ways is not what your intuition would suggest [2]. It is this usage that the article talks about that.

That said, there are plenty of critiques of this definition of heritability, and not just because it is different from what a layperson would expect it to mean.

For example, the way it is used also usually has a big problem in that the standard formula assumes that Cov(G, E) = 0 (or at least is negligible), whereas in practice that is not actually true [3, 4].

This definition of heritability is also mathematically flawed in that it assumes (without evidence) that P = G + E, or at least can be reasonably approximated this way. Given that human development is the result of a feedback loop involving genetic and environmental factors, one would expect a model closer to something like a Markov chain. Proposed justifications of a simple additive model as an approximation (e.g. via the central limit theorem for highly polygenic traits) have to my knowledge never been tested.

More recent genome-wide association studies [5] have actually shown a considerable gap between heritability estimates from genotype data and heritability estimates from twin studies, known as the "missing heritability problem".

[1] https://en.wikipedia.org/wiki/Heritability

[2] https://en.wikipedia.org/wiki/Genetic_variance

[3] https://en.wikipedia.org/wiki/Gene%E2%80%93environment_inter...

[4] https://en.wikipedia.org/wiki/Gene%E2%80%93environment_corre...

[5] https://en.wikipedia.org/wiki/Genome-wide_association_study

[codethief]

OP has another post on the definition of heritability, which I really liked: https://dynomight.net/heritable/ . I'm a layman, though, so since you seem knowledgeable, I would love to hear your thoughts on that article!

For instance, OP's definition H = Var[G] / Var[P] seems to bypass the issues you mentioned:

> For example, the way it is used also usually has a big problem in that the standard formula assumes that Cov(G, E) = 0 (or at least is negligible), whereas in practice that is not actually true [3, 4].

> This definition of heritability is also mathematically flawed in that it assumes (without evidence) that P = G + E, or at least can be reasonably approximated this way.

[rbehrends]

> For instance, OP's definition H = Var[G] / Var[P] seems to bypass the issues you mentioned:

No, this is exactly the definition I am talking about. The problem is that while theoretically you could work with Var(G)/Var(P) even if Cov(G, E) ≠ 0, studies are not designed to capture that.

In fact, the standard ACE model [1] used in twin studies explicitly assumes among other things that there is no gene-environment correlation. This means that it gets silently added to one or more of the ACE components; not because of any ill intentions, but simply because if you included covariance, the resulting system of equations would be underdetermined and could not be solved [2].

But to make matters worse, gene-environment correlation/interaction itself is disproportionately absorbed by the A and C components rather than E. All this can lead to inflated heritability estimates.

And to clarify, I am not making any pronunciations about how much relevance or magnitude that effect has; for all I know, this could in the end be a minor effect. My point here is that there is a lot of mathematical handwaving going on with very limited testability of the modeling.

[1] https://en.wikipedia.org/wiki/ACE_model

[2] If you want to be precise, you need to actually distinguish between gene-environment correlation and interaction and use P = G + E + (G x E), but that makes the system even more underdetermined, because now we have both Cov(G, E) and Var(G x E) to worry about.

[IshKebab]

> Heritability has a very specific meaning in quantitative genetics [1]

Literally the first paragraph of that page is

> Heritability is a statistic used in the fields of breeding and genetics that estimates the degree of variation in a phenotypic trait in a population that is due to genetic variation between individuals in that population. The concept of heritability can be expressed in the form of the following question: "What is the proportion of the variation in a given trait within a population that is not explained by the environment or random chance?"

That matches what I assumed it meant, and it seems like OP and the post are arguing that that is some kind of surprising interpretation.

> OK, but check this out: Say I redefine “hair color” to mean “hair color except ignoring epigenetic and embryonic stuff and pretending that no one ever goes gray or dyes their hair et cetera”. Now, hair color is 100% heritable. Amazing, right?

Uhm, no. That is exactly what I (and I think most people) would expect the answer to be.

[rbehrends]

> That matches what I assumed it meant, and it seems like OP and the post are arguing that that is some kind of surprising interpretation.

The unintuitive part is that in quantitative genetics, heritability is defined in terms of variance in traits at the population level, not as the passing of traits from parents to offspring (that would be heredity [1]). Of course, I may have misinterpreted what you said in your OP when you cited the wiktionary definition of "[g]enetically transmissible from parent to offspring", and if so, I apologize, but at the time it seemed to me that you were talking about heredity.

> Uhm, no. That is exactly what I (and I think most people) would expect the answer to be.

What the article is talking about is that if you fix Var(E) = 0, then Var(P) = Var(G) in the standard heritability model, i.e. all phenotypic variance is explained entirely by genotypic variance (because in that model, Var(P) = Var(G) + Var(E)).

Fun fact (even if only tangentially unrelated): In Western countries, wearing glasses is a highly heritable trait, because wearing glasses is a strong proxy variable for refractive error [2], such as nearsightedness, which is highly heritable. It is often brought up as another example of how the quantitative genetics definition does not match conventional use of the word.

[1] https://en.wikipedia.org/wiki/Heredity

[2] https://en.wikipedia.org/wiki/Refractive_error