Abstract
An intriguing fact long defying explanation is the observation of a universal exponential distribution of beneficial mutations in fitness effect for different microorganisms. To explain this effect, we use a population model including mutation, directional selection, linkage, and genetic drift. The multiple-mutation regime of adaptation at large population sizes (traveling wave regime) is considered. We demonstrate analytically and by simulation that, regardless of the inherent distribution of mutation fitness effect across genomic sites, an exponential distribution of fitness effects emerges in the long term. This result follows from the exponential statistics of the frequency of the less-fit alleles, f, that we predict to evolve, in the long term, for both polymorphic and monomorphic sites. We map the logarithmic slope of the distribution onto the previously derived fixation probability and demonstrate that it increases linearly in time. Our results demonstrate a 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 the organism. Based on these results, we develop a new method to measure the fitness effect of mutations for each variable residue using DNA sequences sampled from adapting populations. This new method is not sensitive to linkage effects and does not require the one-site model assumptions.
Highlights
Evolutionary dynamics of a population of nucleic acid sequences is controlled by several acting forces, including random mutation, natural selection, genetic drift, and linkage opposed by recombination
The spectrum of beneficial mutations in their fitness effect observed in an adaptation experiment has often an exponential form
Regardless of the inherent distribution of the fitness effect across genomic sites, an observable exponential distribution emerges in the long term, as a consequence of the evolutionary process
Summary
Evolutionary dynamics of a population of nucleic acid sequences is controlled by several acting forces, including random mutation, natural selection, genetic drift, and linkage opposed by recombination. The existing models with directional selection and adaptation in a multisite population demonstrate that only those beneficial mutations that are established in a population, as opposed to those becoming extinct, contribute to the average speed of adaptation in the long term. The advantage of each favorable mutation is measured by the relative change it causes in genome fitness (average progeny number). The knowledge of fitness effects for different mutations is essential for predicting the evolutionary trajectory of a population, for example, during the development of resistance of a pathogen to treatment or the immune response. A great effort has been invested in their estimation
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