Oh, I’m very sorry: I completely misunderstood what you were doing, and failed to read your last paragraph as an application of the calculation you’d just done.
Just to say it again in a different way for the benefit of anyone else who misunderstood in the same way as I did, the point is this:
In equilibrium, the rate at which a mutation enters the population has to equal the rate at which it leaves. If it’s rare and recessive, the main way it leaves will be by homozygotes being less fit. So, taking the simplest possible approximations everywhere: if the mutation rate is m and the prevalence of this thing in (the genes of) the population is f, then every new generation will gain a fraction m and lose a fraction f^2 from dead/infertile homozygotes, so we should have m=f^2. So, e.g., if m=10^-8 then we will eventually get f=10^-4.
All of this needs adjusting if having the thing heterozygously makes a difference to fitness, or if having it homozygously doesn’t reduce your fitness to zero, and that adjustment is what the more complicated formula in skeptical_lurker’s earlier comment is for.
Oh, I’m very sorry: I completely misunderstood what you were doing, and failed to read your last paragraph as an application of the calculation you’d just done.
Just to say it again in a different way for the benefit of anyone else who misunderstood in the same way as I did, the point is this:
In equilibrium, the rate at which a mutation enters the population has to equal the rate at which it leaves. If it’s rare and recessive, the main way it leaves will be by homozygotes being less fit. So, taking the simplest possible approximations everywhere: if the mutation rate is m and the prevalence of this thing in (the genes of) the population is f, then every new generation will gain a fraction m and lose a fraction f^2 from dead/infertile homozygotes, so we should have m=f^2. So, e.g., if m=10^-8 then we will eventually get f=10^-4.
All of this needs adjusting if having the thing heterozygously makes a difference to fitness, or if having it homozygously doesn’t reduce your fitness to zero, and that adjustment is what the more complicated formula in skeptical_lurker’s earlier comment is for.