Consider a model for the mutation-selection balance at an X-linked locus. Let normal females and males have fitness 1, carrier females fitness tx, and affected males fitness ty. Also, let the mutation rate from the normal allele A2 to the disease allele A1 be µ in both sexes.

It is possible to write and solve two equations for the equilibrium frequencies p∞x and p∞y of carrier females and affected males.

(a) Derive the two approximate equations p∞x ≈ 2µ + p∞x 1

2 tx + p∞yty p∞y ≈ µ + p∞x 1

2 tx

(b) Solve the two equations in (a).

(c) When tx = 1, show that the fraction of affected males representing new mutations is 1 3 (1 − ty). This fraction does not depend on the mutation rate.

(d) If tx = 1 and ty = 0, then prove that p∞x ≈ 4µ and p∞y ≈ 3µ.