Abstract
An intriguing fact long defying explanation is the observation of a universal exponential distribution of beneficial mutations in fitness effect for different microorganisms. Here we use a general and straightforward analytic model to demonstrate that, regardless of the inherent distribution of mutation fitness effect across genomic sites, an observed exponential distribution of fitness effects emerges naturally, as a consequence of the evolutionary process. Using this result, we develop a technique to measure the mutation fitness effects for specific genomic sites from a single-time sequence set and apply it to influenza A H1N1 hemagglutinin protein. Our results demonstrate the difference between the distribution of fitness effects experimentally observed for naturally occurring mutations and the inherent distribution obtained in directed-mutagenesis experiments. The technique will enable researchers to measure fitness effects of mutations across the genome from a single DNA sample, which is important for predicting the evolution of a population.