  Many complex systems in mathematical biology and other areas can be described
by the replicator equation. We show that solutions of a wide class of
replicator equations minimize the production of information under
time-dependent constraints, which, in their turn, can be computed explicitly at
every instant due to the system dynamics. Therefore, the Kullback principle of
minimum discrimination information, as well as the maximum entropy principle,
for systems governed by the replicator equations can be derived from the system
dynamics rather than postulated. Applications to the Malthusian inhomogeneous
models, global demography, and the Eigen quasispecies equation are given.
