  Consider a mathematical model of evolutionary adaptation of fitness landscape
and mutation matrix as a reaction to population changes. As a basis, we use an
open quasispecies model, which is modified to include explicit death flow. We
assume that evolutionary parameters of mutation and selection processes vary in
a way to maximize the mean fitness of the system. From this standpoint,
Fisher's theorem of natural selection is being rethought and discussed. Another
assumption is that system dynamics has two significant timescales. According to
our central hypothesis, major evolutionary transitions happen in the
steady-state of the corresponding dynamical system, so the evolutionary time is
much slower than the one of internal dynamics. For the specific cases of
quasispecies systems, we show how our premises form the fitness landscape
adaptation process.
