Evolutionary Adaptation of the Permanent Replicator System

Bratus, Alexander S.; Drozhzhin, Sergei; Yakushkina, Tatiana

doi:10.1007/978-3-030-46306-9_1

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Open Crow-kimura System With Competition1

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2021

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“…Our key assumption of the proposed mathematical model is the following: the adaption process (as a reaction to direct treatment or elimination of particular types) happens in the slower evolutionary timescale and can not be described by the internal replicator dynamics. As in the previous studies [6,7,8], we introduce the iteration process to describe fitness landscape changes in evolutionary scale.…”

Section: Open Crow-kimura System With Competitionmentioning

confidence: 99%

Fitness landscape adaptation in open replicator systems with competition: application to cancer therapy

Samokhin¹,

Yakushkina²,

Markin³

et al. 2021

Preprint

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This study focuses on open quasispecies systems with competition and death flow, described by modified Eigen and Crow-Kimura models. We examine the evolutionary adaptation process as a reaction to changes in rates. One of the fundamental assumptions, which forms the basis of our mathematical model, is the existence of two different timescales: internal dynamics time and evolutionary time. The latter is much slower and exhibits significant adaptation events. These conditions allow us to represent the whole evolutionary process through a series of steady-state equations, where all the elements continuously depend on the evolutionary parameter. The process can be seen as a formalization of Fisher's fundamental theorem of natural selection, with mean fitness adaptation. Such models can describe

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Section: Open Crow-kimura System With Competitionmentioning

confidence: 99%