Comment by codethief
6 hours ago
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.
> 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.