  The vast majority of mutations are deleterious, and are eliminated by
purifying selection. Yet in finite asexual populations, purifying selection
cannot completely prevent the accumulation of deleterious mutations due to
Muller's ratchet: once lost by stochastic drift, the most-fit class of
genotypes is lost forever. If deleterious mutations are weakly selected,
Muller's ratchet turns into a mutational "meltdown" leading to a rapid
degradation of population fitness. Evidently, the long term stability of an
asexual population requires an influx of beneficial mutations that continuously
compensate for the accumulation of the weakly deleterious ones. Here we propose
that the stable evolutionary state of a population in a static environment is a
dynamic mutation-selection balance, where accumulation of deleterious mutations
is on average offset by the influx of beneficial mutations. We argue that this
state exists for any population size N and mutation rate $U$. Assuming that
beneficial and deleterious mutations have the same fitness effect s, we
calculate the fraction of beneficial mutations, \epsilon, that maintains the
balanced state. We find that a surprisingly low \epsilon suffices to maintain
stability, even in small populations in the face of high mutation rates and
weak selection. This may explain the maintenance of mitochondria and other
asexual genomes, and has implications for the expected statistics of genetic
diversity in these populations.
