Mathematical model of evolutionary adaptation of replicator systems

Adaptation to changing external conditions is the basis of the evolutionary process. The paper considers a mathematical model of the evolutionary adaptation of replicator systems that describe the quantitative and qualitative characteristics of a community of biological organisms. The dynamics of these systems is determined by the solutions of systems of nonlinear ODES of sufficiently large dimension. The main hypothesis of the proposed model is the assumption that the time of evolutionary adaptation of the fitness landscape (a set of parameters that determine the dynamics of the system) is many times slower than the time of active dynamics of the system (fast time of active dynamics, slow adaptation time). Another important postulate of this theory is based on the statement of the fundamental theorem on natural selection by R. Fischer that any biological system in the process of evolution tends to increase the value of average fitness. Examples of the evolutionary adaptation of specific systems are given. It is proved that as a result of the process of evolutionary adaptation, systems become resistant (resistant) to parasitic macromolecules and microorganisms, from the effects of which they died before the moment of evolutionary change. The problems of evolutionary adaptation of the fitness landscape with changes in mortality rates of species are considered. It is shown that with the targeted destruction of the so-called main species, other species gain an advantage in evolutionary development during therapy. These results make it possible to predict the reaction of systems to changes in mortality rates and have practical application in the problem of therapy of malignant cells and pathogenic bacteria.