On the evolution of hypercycles

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

doi:10.1016/j.mbs.2018.09.001

Cited by 14 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that an equivalent statement holds for the Crow-Kimura setting of the system (6). We provide the discussing for the Theorem 2.1 in terms of system (3) , however, implying the same proof takes place for (6).…”

Section: Open Crow-kimura System With Competitionmentioning

confidence: 75%

“…2.2 Similar derivations are valid for the Crow-Kimura model setting (6). Instead of the system (9), in this case we have the following:…”

Section: Open Crow-kimura System With Competitionmentioning

confidence: 82%

“…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%

See 2 more Smart Citations

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

Samokhin¹,

Yakushkina²,

Markin³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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

show abstract

Section: Open Crow-kimura System With Competitionmentioning

confidence: 75%

“…2.2 Similar derivations are valid for the Crow-Kimura model setting (6). Instead of the system (9), in this case we have the following:…”

Section: Open Crow-kimura System With Competitionmentioning

confidence: 82%

Section: Open Crow-kimura System With Competitionmentioning

confidence: 99%

See 1 more Smart Citation

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

Samokhin¹,

Yakushkina²,

Markin³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, for practical applications, it is reasonable to consider the impact of changing environment and, thus, dynamical fitness landscapes. There are several ways to include these variations in the fitness landscape, e.g., considering random evolutionary parameters [2,3] or some optimization process over these parameters [4,5] In this paper, we discuss the underlying concept of the recent studies [4,5], which propose a new method of fitness landscape adaptation and describe it in the form of the optimization problem. One of the first researchers, who suggested using the extreme principle for Darwinian evolution, was R. Fisher.…”

Section: Replicator Systemsmentioning

confidence: 99%

“…, h m h      A and calculating a new equilibrium ˆ() th  u at each step, we reduce the maximization problem to a sequence of linear programming problems (detailed analysis is presented in [4]).…”

Section:    mentioning

confidence: 99%

Mathematical Models of Evolution for Replicator Systems: Fitness Landscape Adaptation

Bratus¹,

Yakushkina²,

Drozhzhin³

et al. 2018

Proceedings of the International Conference "Mathematical Biology and Bioinformatics"

View full text Add to dashboard Cite

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.

show abstract