Mutation) In an attempt to reduce levels of methicillin resistance in Staphylococcus aureus, methicillin use is completely halted. Let us assume that in the absence of methicillin, neither the resistant allele (A), nor the sensitive allele (a) is selected against. New sensitive alleles arise with frequency 1 x 10-5, and the back mutation rate (i.e., sensitive → resistant) is 4 x 10-8.
a. What is the equilibrium frequency of the resistant allele in the absence of methicillin? (Note: Although we have been deriving population genetic models to explain evolution in diploids, this particular model is appropriately used for haploid bacteria, where p = f(A) and q = f(a), just like in diploids.)
b. How does your answer explain why antibiotic resistance evolves so fast?