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Modeling Evolution on Nearly Neutral Network Fitness Landscapes
Journal of the Physical Society of Japan. 2017. Vol. 86. P. 084801-1–084801-6.
Yakushkina T., Saakian D.
To describe virus evolution, it is necessary to define a fitness landscape. In this article, we consider the microscopic models with the advanced version of neutral network fitness landscapes. In this problem setting, we suppose a fitness difference between one-point mutation neighbors to be small. We construct a modification of the Wright–Fisher model, which is related to ordinary infinite population models with nearly neutral network fitness landscape at the large population limit. From the microscopic models in the realistic sequence space, we derive two versions of nearly neutral network models: with sinks and without sinks. We claim that the suggested model describes the evolutionary dynamics of RNA viruses better than the traditional Wright–Fisher model with few sequences.
Samokhin I., Yakushkina T., Bratus A., Chinese Journal of Physics 2021 P. 1–27
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 ...
Added: February 4, 2022
Drozhzhin S., Yakushkina T., Bratus A., Journal of Mathematical Biology 2021 Vol. 82 No. 3 Article 15
In this paper, we discuss fitness landscape evolution of permanent replicator systems applying the hypothesis that the specific time of evolutionary adaptation of system parameters is much slower than the time of internal evolutionary dynamics. In other words, we suppose that the extremal principle of Darwinian evolution based on Fisher’s fundamental theorem of natural selection ...
Added: February 26, 2021
Saakian D., Yakushkina T., Journal of the Physical Society of Japan 2020 Vol. 89 Article 044801
The mutator gene model is one of the fundamental models of modern evolutionary dynamics. Usually, one considers a transition between two evolutionary regimes: the wild-type and mutator type. In this study, we introduce a hierarchy of three types with the transitions between them, considering an extra allele for the mutator gene. We examine both the ...
Added: May 14, 2020
Yakushkina T., Saakian D., Chinese Journal of Physics 2019 Vol. 57 P. 309–313
We consider the two-habitat quasispecies model, which describes evolutionary process with migration on the basis of the Eigen model. In the first habitat there is only one genotype, and here is an influx of the replicators from the first habitat to the second one with the rate h. We solve exactly the case of a single-peak ...
Added: February 18, 2020
Saakian D., Chinese Journal of Physics 2019
We consider the two-habitat quasispecies model, which describes evolutionary process with migration on the basis of the Eigen model. In the first habitat there is only one genotype, and here is an influx of the replicators from the first habitat to the second one with the rate h. We solve exactly the case of a single-peak ...
Added: December 10, 2019
Saakian D., Vardanyan E., Yakushkina T., Physica A: Statistical Mechanics and its Applications 2020 Vol. 541 Article 123091
We investigate the evolutionary model with recombination and random switches in the fitness function due to change in a special gene. The dynamical behaviour of the fitness landscape induced by the specific mutations is closely related to the mutator phenomenon, which, together with recombination, plays an important role in modern evolutionary studies. It is of ...
Added: December 10, 2019
Bratus A., Drozhzhin S., / Series "Working papers by Cornell University". 2019.
In this paper, we discuss the fitness landscape evolution of permanent replicator systems using a hypothesis that the specific time of evolutionary adaptation of the system parameters is much slower than the time of internal evolutionary dynamics. In other words, we suppose that the extreme principle of Darwinian evolution based the Fisher's fundamental theorem of ...
Added: December 10, 2019
Saakian D., Yakushkina T., Koonin E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 99 P. 1–6
Evolution on changing fitness landscapes (seascapes) is an important problem in evolutionary biology. We
consider the Moran model of finite population evolution with selection in a randomly changing, dynamic
environment. In the model, each individual has one of the two alleles, wild type or mutant. We calculate the
fixation probability by making a proper ansatz for the logarithm ...
Added: March 18, 2019
Yakushkina T., Saakian D., Chinese Journal of Physics 2018 Vol. 56 No. 5 P. 2235–2240
In this study, we considered the model by Beckman and Loeb [Proc. Natl. Acad. Sci. U.S.A. 103 (2006) 14140] for the mutator phenomena. We construct an infinite population Crow-Kimura model with a mutator gene, directed mutations, a linear fitness function, and a finite genome length. We solved analytically the dynamics of the model using the ...
Added: October 25, 2018
Yakushkina T., Saakian D., Physica A: Statistical Mechanics and its Applications 2018 Vol. 507 P. 470–477
In this paper, the impact of lethal mutations on evolutionary dynamics of asexual populations is analyzed. We suggest distinguishing different definitions of lethality, which lead to different mathematical formalizations of the microscopic model. Most of the studies focus on polyphasic lethality, meaning that individuals carrying lethal mutations have no offspring but consume common resources. In ...
Added: June 22, 2018
Yakushkina T., Saakian D., Journal of the Physical Society of Japan 2017 Vol. 86 P. 084801-1–084801-6
To describe virus evolution, it is necessary to define a fitness landscape. In this article, we consider the microscopic models with the advanced version of neutral network fitness landscapes. In this problem setting, we suppose a fitness difference between one-point mutation neighbors to be small. We construct a modification of the Wright–Fisher model, which is ...
Added: July 19, 2017
Saakian D., Yakushkina T., Hu C., Scientific Reports 2016 Vol. 6
We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase ...
Added: September 16, 2016