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Compared to a neutral model, purifying selection distorts the structure ofgenealogies and hence alters the patterns of sampled genetic variation.Although these distortions may be common in nature, our understanding of how weexpect purifying selection to affect patterns of molecular variation remainsincomplete. Genealogical approaches such as coalescent theory have provendifficult to generalize to situations involving selection at many linked sites,unless selection pressures are extremely strong. Here, we introduce aneffective coalescent theory (a "fitness-class coalescent") to describe thestructure of genealogies in the presence of purifying selection at many linkedsites. We use this effective theory to calculate several simple statisticsdescribing the expected patterns of variation in sequence data, both at thesites under selection and at linked neutral sites. Our analysis combines ourearlier description of the allele frequency spectrum in the presence ofpurifying selection (Desai et al. 2010) with the structured coalescent approachof Nordborg (1997), to trace the ancestry of individuals through thedistribution of fitnesses within the population. Alternatively, we can deriveour results using an extension of the coalescent approach of Hudson and Kaplan(1994). We find that purifying selection leads to patterns of genetic variationthat are related but not identical to a neutrally evolving population in whichpopulation size has varied in a specific way in the past.

The Structure of Genealogies in the Presence of Purifying Selection: A "Fitness-Class Coalescent"