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Evolutionary dynamics and patterns of molecular evolution are stronglyinfluenced by selection on linked regions of the genome, but our quantitativeunderstanding of these effects remains incomplete. Recent work has focused onpredicting the distribution of fitness within an evolving population, and thisforms the basis for several methods that leverage the fitness distribution topredict the patterns of genetic diversity when selection is strong. However, inweakly selected populations random fluctuations due to genetic drift are moresevere, and neither the distribution of fitness nor the sequence diversitywithin the population are well understood. Here, we briefly review themotivations behind the fitness-distribution picture, and summarize the generalapproaches that have been used to analyze this distribution in thestrong-selection regime. We then extend these approaches to the case of weakselection, by outlining a perturbative treatment of selection at a large numberof linked sites. This allows us to quantify the stochastic behavior of thefitness distribution and yields exact analytical predictions for the sequencediversity and substitution rate in the limit that selection is weak.

Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution