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.
Two classical approaches to replicator systems are considered: quasispecies and hypercycle models. We expand the adaptive landscape metaphor by S. Wright and Fisher's fundamental theorem of natural selection, combining it with Kimura's maximal principals to the case of dynamical fitness landscape. We assume that the parameters of the replicator system depend continuously on the evolutionary time, which distinguish from the internal system dynamics time. We suppose that evolutionary time is much slower that ordinary time of the system. Each step of the process of the fitness landscape adaptation place occurs in a steady-state. This process is equivalent to maximization the mean fitness of the system. From mathematical point of view, it is reduced to a series mathematical programming problems or to a first eigenvalue maximization problem. New properties of the adapted systems are discussed.
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