Adaptation reshapes the distribution of fitness effects
Abstract
The process of adaptation has been of interest since the XIX century, when Darwin first proposed the idea of natural selection. Since then, there has been a myriad of theoretical and empirical works that have expanded the field. From the many evolutionary insights these works have produced, a foundational idea is that spontaneous mutations in the genome of organisms can produce changes to their reproductive success that might confer an advantage for the mutant organisms with respect to their peers. Therefore, mutations drive adaptive evolution by virtue of their heritable effects on fitness. Empirical measures of the distribution of these fitness effects of new mutations (the DFE) have been increasingly successful, and have recently highlighted the fact that the DFE changes during adaptation. Here, we analyze these dynamic changes to the DFE during a simplified adaptive process: an adaptive walk across a well-studied fitness landscape. First, we derive analytical approximations for the fitness distributions of both available and previously fixed alleles, and use these to derive expressions for the DFE at each step of the adaptive walk. We then confirm these predictions with independent simulations that relax several simplifying assumptions made in the analysis. Along with these quantitative predictions, we find that as de novo mutations accumulate, the DFE is reshaped in two important qualitative ways: the fraction of deleterious mutations increases (a shift to the left), and the variance of the distribution decreases. Our analysis makes the surprising prediction that, at least in additive fitness landscapes, adaptation may be more limited by the availability of low-fitness alleles to be replaced, rather than by the availability of beneficial mutations.