Last equation of the maths. The author writes change in phenotype = h2 * change in genetic score. I think it should be h * change in genetic score. 

Replying to Reviewer 1

Dear reviewer 2, I think you raise some interesting points. I would like to ask a question, just to satisfy my own curiosity. It doesn't really matter if we reach common grounds. I want to make sure I understand this paragraph of yours here:

I would strongly suggest removing the mathematical modelling. I've spent more time thinking about the model and I'm not convinced it is good model, and I think there may be at least one mathematical mistake. The effect on the phenotype should be h, not h2, times the change in the genetic score. h is the correlation or effect of the genetic score on the phenotype. You might have thought h2 is correct because you are familiar with the breeder's equation. The reason why the breeder's equation uses h2 is because it involves the effect of selecting the parent's phenotype on the genetic score and then the effect of genetic score on the child's phenotype. Here the correlation between phenotype and genetic score occurs twice! 

I had to read this multiple times, as I'm still not sure what you're pointing at. My interpretation of the formula underlying the paternal age correlation model (which I think this is what you are referring to? let me know if I'm wrong), is that the scaling factor h² is meant to accommodate the proportion (ie, not correlation) of the genetic variance attributable to new mutations relative to total genetic variance, due to mutational pressure creating genetic variance, and in this case h² translates genetic variance into its contribution to phenotypic variance (ie, h² links Var(G) to Var(P)). So, this genetic contribution from new mutations is being converted into phenotypic variancec, hence why h². (It might help that the author clarifies this issue too, if I misinterpret or misread something.)

On the other hand I agree with reviewer 2 about the simplifying assumption of that model, about allele effects and random mutation, etc. This is the curse of such models though. Like in twin studies, where critics often point out about GxE related-biases, but at the same time there is no definite conclusion on its magnitude of effect, direction of effect, let alone its specific mechanism. Yet twin studies are still very useful, despite the fact its limitations are worth keeping in mind.