  We consider the Moran model of population genetics with two types, mutation,
and selection, and investigate the line of descent of a randomly-sampled
individual from a contemporary population. We trace this ancestral line back
into the distant past, far beyond the most recent common ancestor of the
population (thus connecting population genetics to phylogeny), and analyse the
mutation process along this line.
  To this end, we use the pruned lookdown ancestral selection graph, which
consists of a set of potential ancestors of the sampled individual at any given
time. Relative to the neutral case (that is, without selection), we obtain a
general bias towards the beneficial type, an increase in the beneficial
mutation rate, and a decrease in the deleterious mutation rate. This sheds new
light on previous analytical results. We discuss our findings in the light of a
well-known observation at the interface of phylogeny and population genetics,
namely, the difference in the mutation rates (or, more precisely, mutation
fluxes) estimated via phylogenetic methods relative to those observed in
pedigree studies.
