When
beneficial mutations are rare, they accumulate by a series of
selective sweeps. But when they are common, many
beneficial mutations will occur before any can fix, so there will be many different
mutant lineages in the population concurrently. In an asexual population, these different
mutant lineages interfere and not all can fix simultaneously. In addition, further
beneficial mutations can accumulate in
mutant lineages while these are still a
minority of the population. In this article, we analyze the dynamics of such multiple
mutations and the interplay between multiple
mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between
selection, which destroys variation, and
beneficial mutations, which create more. The behavior depends in a subtle way on the
population parameters: the
population size, the
beneficial mutation rate, and the distribution of the fitness increments of the potential
beneficial mutations. The
mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both
population size and
mutation rate and sets the rate at which the population accumulates
beneficial mutations, which thus also grows only logarithmically with
population size and
mutation rate. These results imply that mutator
phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.
