The accumulation of beneficial mutations on competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the frequencies of observed mutations, randomizes the fixation times of successful mutations, and leaves distinct signatures on patterns of genetic variation. Here, we show how this form of "genetic draft" affects the forward-time dynamics of site frequencies in rapidly adapting asexual populations. We calculate the probability that mutations at individual sites shift in frequency over a characteristic timescale, extending Gillespie's original model of draft to the case where many strongly selected beneficial mutations segregate simultaneously. We then derive the sojourn time of mutant alleles, the expected fixation time of successful mutants, and the site frequency spectrum of beneficial and neutral mutations. Finally, we show how this form of draft affects inferences in the McDonald-Kreitman test and how it relates to recent observations that some aspects of genetic diversity are described by the Bolthausen-Sznitman coalescent in the limit of very rapid adaptation.T HE effects of linkage between beneficial mutations in altering evolutionary dynamics and the structures of genealogies in adapting populations has been recognized for nearly a century, particularly in the context of the evolutionary advantage of sex (Muller 1932). In both asexually reproducing organisms and in regions of low recombination in sexual organisms, the chance congregation of beneficial mutations on competing genetic backgrounds skews evolutionary dynamics. Because of this "clonal interference" effect, the success of a mutation depends not only on its fitness effect, but also on the quality of the genetic background in which it occurs and the fortune of the mutant's progeny in amassing more beneficial mutations (Smith and Haigh 1974;Gerrish and Lenski 1998;Gillespie 2000Gillespie , 2001Kim and Orr 2005).Recent work in experimental evolution has confirmed that clonal interference is widespread in large adapting laboratory microbial and viral populations (de Visser et al. 1999;Miralles et al. 1999;de Visser and Rozen 2006;Kao and Sherlock 2008;Lang et al. 2011Lang et al. , 2013. Several recent studies also suggest that classic "hard" selective sweeps may be rare in Drosophila (Sella et al. 2009;Karasov et al. 2010) and humans (Pritchard et al. 2010;Hernandez et al. 2011), implying that models that better account for linkage between sites need to be explored. As a result, in recent years there has been an influx of theoretical work describing the effects of clonal interference on the evolution of large populations (see Park et al. 2010
for a recent review).This work has provided a good understanding of evolutionary dynamics in the regime of rare interference, where the number of strongly beneficial mutations segregating in a population is rarely more than two (Gerrish and Lenski 1998;Gillespie 2000Gillespie ...