Eigen Model with Correlated Multiple Mutations and Solution of Error Catastrophe Paradox in the Origin of Life

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

doi:10.1143/jpsj.81.114801

Cited by 8 publications

(4 citation statements)

References 41 publications

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“…40) Statistical physics has been applied to understand relaxation, folding, and aggregation of proteins, 41,42) biological evolution [43][44][45] and the origin of life 46,47) from the molecular level. Following this trend, the two-chain model of Fig.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Evolutionary Games with Randomly Changing Payoff Matrices

et al. 2015

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Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism. The Master Equation and Its Solution via Hamilton-Jacobi EquationLet us consider the model with constant matrices: A ¼ fa ij g, B ¼ fb ij g, i; j ¼ 1; 2; . . . ; m. The total population size is N; variable X represents the number of players in the first population category. As shown in Fig. 1, the whole system can exist in two versions: the upper chain with matrix A and the lower chain with matrix B, and there are transitions between the two chains.Here we have the probability conservation condition at any moment of time τ:where PðX; Þ is the probability that the system is in state A and there are X players with the first strategy, and QðX; Þ is the probability that the system is in state B with X players with the first strategy.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Evolutionary Games with Randomly Changing Payoff Matrices

et al. 2015

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“…Applications of the methods of statistical physics to the study of the molecular models of biological evolution [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the origin of life [1,18] have attracted much attention in recent decades. In this paper, we use the methods of statistical physics to study punctuated equilibria [19][20][21]: a well-known phenomenon of biological evolution during long geological time scales, related to the the life tree [22].…”

Section: Introductionmentioning

confidence: 99%

Punctuated equilibrium and shock waves in molecular models of biological evolution

Saakian

Ghazaryan

2014

Phys. Rev. E

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We consider the dynamics in infinite population evolution models with a general symmetric fitness landscape. We find shock waves, i.e., discontinuous transitions in the mean fitness, in evolution dynamics even with smooth fitness landscapes, which means that the search for the optimal evolution trajectory is more complicated. These shock waves appear in the case of positive epistasis and can be used to represent punctuated equilibria in biological evolution during long geological time scales. We find exact analytical solutions for discontinuous dynamics at the large-genome-length limit and derive optimal mutation rates for a fixed fitness landscape to send the population from the initial configuration to some final configuration in the fastest way.

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“…Applications of statistical physics to molecular models of biological evolution [1][2][3][4][5][6][7][8] and the origin of life [2,9,10] have attracted much attention in recent years. A still unsolved and interesting problem in evolution theory is the origin of sex.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary advantage via common action of recombination and neutrality

Saakian

2013

Phys. Rev. E

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We investigate evolution models with recombination and neutrality. We consider the Crow-Kimura (parallel) mutation-selection model with the neutral fitness landscape, in which there is a central peak with high fitness A, and some of 1-point mutants have the same high fitness A, while the fitness of other sequences is 0. We find that the effect of recombination and neutrality depends on the concrete version of both neutrality and recombination. We consider three versions of neutrality: (a) all the nearest neighbor sequences of the peak sequence have the same high fitness A; (b) all the l-point mutations in a piece of genome of length l≥1 are neutral; (c) the neutral sequences are randomly distributed among the nearest neighbors of the peak sequences. We also consider three versions of recombination: (I) the simple horizontal gene transfer (HGT) of one nucleotide; (II) the exchange of a piece of genome of length l, HGT-l; (III) two-point crossover recombination (2CR). For the case of (a), the 2CR gives a rather strong contribution to the mean fitness, much stronger than that of HGT for a large genome length L. For the random distribution of neutral sequences there is a critical degree of neutrality ν(c), and for μ<μ(c) and (μ(c)-μ) is not large, the 2CR suppresses the mean fitness while HGT increases it; for ν much larger than ν(c), the 2CR and HGT-l increase the mean fitness larger than that of the HGT. We also consider the recombination in the case of smooth fitness landscapes. The recombination gives some advantage in the evolutionary dynamics, where recombination distinguishes clearly the mean-field-like evolutionary factors from the fluctuation-like ones. By contrast, mutations affect the mean-field-like and fluctuation-like factors similarly. Consequently, recombination can accelerate the non-mean-field (fluctuation) type dynamics without considerably affecting the mean-field-like factors.

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Eigen Model with Correlated Multiple Mutations and Solution of Error Catastrophe Paradox in the Origin of Life

Cited by 8 publications

References 41 publications

Evolutionary Games with Randomly Changing Payoff Matrices

Evolutionary Games with Randomly Changing Payoff Matrices

Punctuated equilibrium and shock waves in molecular models of biological evolution

Evolutionary advantage via common action of recombination and neutrality

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