Suppose <assortative mating> raises the dizygotic genetic correlation from $1/2$ to $\rho>1/2$. Then
$$
r_{\rm DZ}=\frac{\rho V_A+V_C}{V_Y},
$$
so the formula returns
$$
2(r_{\rm MZ}-r_{\rm DZ})
=2(1-\rho)\frac{V_A}{V_Y}
<h^2.
$$
Thus using the nominal one-half genetic correlation produces downward bias in estimated heritability, assuming the other ACE assumptions remain valid.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 221 / 2 / iii / Solution

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Assortative mating is nonrandom mating in which partners are more or less similar than random pairs for a trait or correlated characteristic. Positive assortment can increase genetic similarity among siblings.


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