  The accumulation of beneficial mutations on many 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. 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.
Finally, we describe how our method can be extended to model evolution on
fitness landscapes that include some forms of epistasis, such as landscapes
that are partitioned into two or more incompatible evolutionary trajectories.
