Abstract
Purifying selection can substantially alter patterns of molecular evolution. Its main effect is to reduce overall levels of genetic variation, leading to a reduced effective population size. However, it also distorts genealogies relative to neutral expectations. A structured coalescent method has been used to describe this effect, and forms the basis for numerical methods and simulations. In this study, we extend this approach by making the additional approximation that lineages may be treated independently, which is valid only in the strong selection regime. We show that in this regime, the distortions due to purifying selection can be described by a time-dependent effective population size and mutation rate, confirming earlier intuition. We calculate simple analytical expressions for these functions, N(e)(t) and U(e)(t). These results allow us to describe the structure of genealogies in a population under strong purifying selection as equivalent to a purely neutral population with varying population size and mutation rate, thereby enabling the use of neutral methods of inference and estimation for populations in the strong selection regime.
Highlights
Over thirty years ago the first analysis of genetic variation at the nucleotide level was performed (Kreitman 1983)
With this data comes the fundamental question, which is central to population genetics: What exactly can we discern about the history of a population from this data? As our ability to generate massive amounts of experimental data has grown tremendously over the years, so too has our understanding of population genetics from a theoretical perspective
After computing coalescence probabilities with both approaches, we show how these probabilities can be used to analyze the structures of genealogies, and we calculate various statistics describing genetic variation in these populations, which we compare to numerical simulations
Summary
Over thirty years ago the first analysis of genetic variation at the nucleotide level was performed (Kreitman 1983). Evidence from sequence data points to the general importance of these selective forces among many linked variants in microbial and viral populations, and on short distance scales in the genomes of sexual organisms (Hahn 2008; Comeron et al 2008; Seger et al 2010) In these situations, existing theory does not fully explain patterns of molecular evolution (Hahn 2008). This simple and intuitive approximation — background selection reduces Ne — has been widely used to interpret patterns of molecular evolution in sequence data We refer to it as the effective population size (EPS) approximation, and it successfully captures the dominant effect of strong purifying selection on the structure of genealogies: to decrease coalescence times without distorting genealogical structure
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