  Positive selection distorts the structure of genealogies and hence alters
patterns of genetic variation within a population. Most analyses of these
distortions focus on the signatures of hitchhiking due to hard or soft
selective sweeps at a single genetic locus. However, in linked regions of
rapidly adapting genomes, multiple beneficial mutations at different loci can
segregate simultaneously within the population, an effect known as clonal
interference. This leads to a subtle interplay between hitchhiking and
interference effects, which leads to a unique signature of rapid adaptation on
genetic variation both at the selected sites and at linked neutral loci. Here,
we introduce an effective coalescent theory (a "fitness-class coalescent") that
describes how positive selection at many perfectly linked sites alters the
structure of genealogies. We use this theory to calculate several simple
statistics describing genetic variation within a rapidly adapting population,
and to implement efficient backwards-time coalescent simulations which can be
used to predict how clonal interference alters the expected patterns of
molecular evolution.
