The evolutionary origin of the universal distribution of mutation fitness effect

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 in the long term, as a consequence of the evolutionary process. This result follows from the exponential statistics of the frequency of the less-fit alleles f predicted to evolve, in the long term, for both polymorphic and monomorphic sites. The exponential distribution disappears when the system arrives at the steady state, when it is replaced with the classical mutation-selection result, f = /s. Based on these findings, we develop a technique to measure selection coefficients for specific genomic sites from two single-time sequence sets. Our results demonstrate the striking difference between the distribution of fitness effects observed experimentally, for naturally occurring mutations, and the "inherent" distribution obtained in a directed-mutagenesis experiment, which can have any shape depending on organism. Based on these results, we develop a new method to measure fitness effects of mutations for each variable residue based on DNA sequences isolated from an adapting population at two time points. This new method is not sensitive to linkage effects and does not require one-site model assumptions.