Dynamics of the distribution of fitness effects during adaptation

Empirical measures of the distribution of 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 an additive fitness landscape. First, we derive analytical approximations for the underlying fitness distributions of alleles present in the genotype and available through mutation 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. As expected, our analysis predicts that as adaptation proceeds, the DFE is reshaped dynamically throughout the walk by a decrease in the beneficial fraction of mutations (a shift to the left). Surprisingly, different mechanisms drive this change depending on the number of alleles available per site: for a small number of available alleles, we observe a depletion of high-fitness alleles available through mutation as expected, however for a large number of alleles we observe that adaptation may be more limited by the availability of low-fitness alleles to be replaced, rather than by the availability of high-fitness alleles to replace them.