So, the trait "wizard" is conferred by a recessive locus with alleles W and M. What is the breeding value of Harry Potter?
Let "wizard" be scored as 1 and "Muggle" as 0.
The different genotypes have a value, in a classical "Falconerian" setting, of
WW WM MM
a d -a
0.5 -0.5 -0.5
so that $a=0.5$, $d=-0.5.$ The substitution effect of W is $\alpha=a+(q-p)d$ , the question is, what is the allelic frequency of W?
If the number of wizards is 1% of the population, then $p^2=0.01$ and $\alpha=0.5+(0.9-0.1)(-0.5)=0.1$.
The breeding value of Harry Potter is $2 \alpha= 0.2$.
The allelic frequency can actually be worked out from here: "According to Rowling, the average Hogwarts annual intake for Muggle-borns is 25%" we can work out the frequency of the allele p.
The bulk of these Muggle-borns come from couples WM x WM, of which there is a frequency $4 p^2 q^2$. These couples produce a wizard WW out of every 4 kids, so the frequency of WW born from Muggle-borns is $p^2 q^2.$ The wizard couples WW x WW are $p^4$ of the population, and every kid is wizard WW too. So they represent p^4 . Then we have that
$$\frac{p^2 q^2}{p^2 q^2 + p^4} =\frac{1}{4}$$
This gives a quadratic equation but it has not solutions in the range $0<p<1$. This is because, if being wizard is rare, by far most wizards come from "Muggle" couples. If the pure wizards are 1% of the population and $p=0.1$, then wizards from Muggle couples WM x WM are 80-fold more than from Wizard WW x WW couples. Should we conclude that most wizards do not go to Rowlands?
