The quasispecies adapts on the fitness landscape. It
will move from regions of lower fitness to regions of
higher fitness. It will climb up mountain slopes and
edges to reach local peaks. There will be transitions from
lower peaks to higher peaks. For deterministic dynamics,
there is only one globally stable equilibrium,
which is given by the eigenvector associated with the
largest eigenvalue of the linear operator wij=aiqij. The
largest eigenvalue corresponds to the highest average
fitness, f, at equilibrium.
A crucial phenomenon of quasispecies dynamics is the
error threshold. For many reasonable fitness landscapes
the mutation rate, u, has to be less than 1/n, for the
equilibrium quasispecies distribution to be localized in a
particular region of sequence space. Localization is
required for the ability of the quasispecies to adapt to
peaks in the fitness landscape. Localization and adaptation
are required for evolution. In contrast, if u>1/n,
then for most fitness landscapes, the quasispecies will
be delocalized, which means that all sequences will be
roughly equally frequent. In this case, any finite
population will wander endlessly in sequence space.
The new idea that we introduce in the present paper is
that individual genomes are not only associated with a
specific fitness value, but also with a specific mutation
rate. We imagine that large parts of the genome encode
for enzymes involved in DNA replication or error
correction. For example, more than 30 genes encode for
DNA replication and error correction in the T4 phage
whose total genome contains 300 genes. In the
eukaryotic genome, hundreds or thousands of genes