Replicators System and Models of Natural Evolution

Replicator systems represented the mathematical models for description of the evolutionary process for macromolecules, bacteria, viruses and cells. These models were proposed by M. Eigen in 1971. Now replicator models composed the basis of contemporary theory of mathematical biology. Two basic model of replicator system is considered: the model of quasicpecies and the model of hypercycling replication. The quasicpecies model described the process of replication and mutation of species and based on some aspects of probability theory. From mathematical point of view this model represented by system of nonlinear ODE of high dimension. Therefore it is natural to pass to continue description in this case. Nevertheless we have not unit approach to that problem. Hypercycling replication model present the object having unique mathematical properties which satisfied to main tirade of Darwin evolution theory: Heredity-Variability-Natural Selection. The example of evolution of hypercycling system is presented.