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

Replicator equations and the principle of minimal production of information