Evolution models with lethal mutations on symmetric or random fitness landscapes

Kirakosyan, Zara; Saakian, David B.; Hu, Chin‐Kun

doi:10.1103/physreve.82.011904

Cited by 15 publications

(16 citation statements)

References 36 publications

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“…To summarize-recent studies and experiments [6,24,27,28,[30][31][32][33]38] show that evolutionary trajectories in realistic and correlated fitness landscapes may pass through fitness valleys due to epistatic interactions or through long-range connections due to multiple mutations in a single step. Also, lethal mutations would lead to infeasible paths.…”

Section: Various Paths Suggested By Experimental Evolutionmentioning

confidence: 99%

“…It is observed that many point mutations are responsible for the lethality of an individual [28,[33][34][35][36]. These lethal genotypes are not connected with other viable genotypes through an evolutionary path due to natural selection [4,5,37].…”

Section: Various Paths Suggested By Experimental Evolutionmentioning

confidence: 99%

“…Apart from well-known adaptive walks, three other possible evolutionary paths are: (a) Non-adaptive path passing through a valley "ab" → "Ab" → "AB" as studied in Poelwijk et al [8] and Wang et al [9], (b) multiple mutations in a single step as studied in Refs. [24,32], and, (c) infeasible path leading to the lethal mutation "aB" [33]. Topologically inspired walks on fitness landscapes with heterogeneous connectivities can successfully model (a), (b), and (c).…”

Section: Various Paths Suggested By Experimental Evolutionmentioning

confidence: 99%

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Topologically Inspired Walks on Randomly Connected Landscapes With Correlated Fitness

2018

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Strictly adaptive walks on uncorrelated and correlated fitness landscapes have been a subject of intense research. However, some experimental findings tend to advance the notion of non-adaptive evolution in terms of epistasis. To address such evolutionary paths, herein we introduce the concept of topologically inspired walks on connected and correlated landscapes with complex topologies. These walks are dictated solely by the topology of connections and are not explicitly dependent on the underlying fitness values. In the biologically significant regime of sparse randomness, we observe that such topologically inspired walks might carry a population to a local optimum even faster than strictly adaptive walks. This effect becomes more pronounced with increasing correlations in fitness. We observe interesting tradeoffs between topologically inspired walks governed by the minimum and maximum value of a set of given network metrics.

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Section: Various Paths Suggested By Experimental Evolutionmentioning

confidence: 99%

Section: Various Paths Suggested By Experimental Evolutionmentioning

confidence: 99%

Section: Various Paths Suggested By Experimental Evolutionmentioning

confidence: 99%

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Topologically Inspired Walks on Randomly Connected Landscapes With Correlated Fitness

2018

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“…Главное наше допущение -однопиковая функции приспособленности, применяемая биологами как грубое приближение к реальности [Gupta, Dixit, 2015]. Но те же математические результаты остаются корректными для случайной функции приспособленности [Kirakosyan, Saakian, Hu, 2010], которая довольно распространена в моделях вирусологии [Sanjuan, Moya, Elena, 2004]. Результат М. Казарян, Т. С. Якушкина, Д. Б. Саакян (13), точечная -численным более ранней работы [Saakian, Hu, 2004] получил широкое применение к различным задачам эволюционной биологии.…”

Section: заключениеunclassified

Exact evolutionary dynamics on multi dimensional fitness landscape

Ghazaryan¹,

Yakushkina²,

Saakian³

2015

CRM

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Получено 20 мая 2015 г., после доработки 11 ноября 2015 г.В данной работе рассматривается одна из самых значимых моделей популяционной генетики -модель Кроу-Кимуры. В последнее десятилетие были исследованы модели с ландшафтами приспособленности малой размерности. Цель статьи состоит в анализе модели Кроу-Кимуры c многомерным ландшафтом приспособленности в рамках формализма Гамильтона-Якоби. Для случая однопикового ландшафта приспособленности выводятся точные аналитические выражения, которые подтверждаются численно.Ключевые слова: модель Кроу-Кимуры, модели эволюции, многомерный ландшафт приспособленности Abstract. -Crow-Kimura model is one of the famous models of population genetics. Last decade models with low-dimensional fitness landscape have been investigated. We consider the Crow-Kimura model of evolutionary dynamics on multi-dimensional fitness landscape with a single peak. We deduce exact solution for the dynamics, confirmed well by the numerics.

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“…In smooth fitness landscapes, the steady-state distributions of the Crow-Kimura and Eigen models can be mapped to each other. In the large genome limit, the Crow-Kimura model is equivalent to a discrete-time Eigen model 33 and is very close to branching processes. Moreover, the Wright-Fisher model 34 35 for large populations can be mapped to a discrete-time Eigen model 33 .…”

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confidence: 99%

The rich phase structure of a mutator model

Saakian

Yakushkina

2016

Sci Rep

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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 and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.

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Evolution models with lethal mutations on symmetric or random fitness landscapes

Cited by 15 publications

References 36 publications

Topologically Inspired Walks on Randomly Connected Landscapes With Correlated Fitness

Topologically Inspired Walks on Randomly Connected Landscapes With Correlated Fitness

Exact evolutionary dynamics on multi dimensional fitness landscape

The rich phase structure of a mutator model

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