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.