How Well Can We Infer Selection Benefits and Mutation Rates from Allele Frequencies?

Experimentalists observe allele frequency distributions and try to infer mutation rates and selection coefficients. How easy is this? We calculate limits to their ability in the context of the Wright-Fisher model by first finding the maximal amount of information that can be acquired using allele frequencies about the mutation rate and selection coefficient- at least 2 bits per allele- and then by finding how the organisms would have shaped their mutation rates and selection coefficients so as to maximize the information transfer.