  In the absence of selection, the structure of allelic diversity is described
by the elegant sampling formula of Ewens. This formula has helped shape our
expectations of empirical patterns of molecular variation. Along with
coalescent theory, it provides statistical techniques for rejecting the null
model of neutrality. However, we still do not fully understand the statistics
of the allelic diversity we expect to see in the presence of natural selection.
Earlier work has described the effects of strongly deleterious mutations linked
to many neutral sites, and allelic variation in models where offspring fitness
is unrelated to parental fitness, but it has proven difficult to understand
allelic diversity in the presence of purifying selection at many linked sites.
Here, we study the population genetics of infinitely many perfectly linked
sites, some neutral and some deleterious. Our approach is based on studying the
lineage structure within each class of individuals of similar fitness in the
deleterious mutation-selection balance. Analogous to the Ewens sampling
formula, we derive expressions for the likelihoods of any configuration of
allelic types in a sample. We find that for moderate and weak selection
pressures the patterns of allelic diversity cannot be described by a neutral
model for any choice of the effective population size, indicating that there is
power to detect selection from patterns of sampled allelic diversity.
