Error threshold in finite populations

Alves, Domingos; Fontanari, José F.

doi:10.1103/physreve.57.7008

Cited by 84 publications

(81 citation statements)

References 23 publications

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“…(15) into Eq. (16). Moreover, since y(t) differs from x(t) only by a scalar factor, we can restore the original variables via…”

Section: Static Landscapesmentioning

confidence: 99%

“…Eigen's quasispecies model [1] has been the basis of a vivid branch of molecular evolution theory ever since it has been put forward almost 30 years ago [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Its two main statements are the formation of a quasispecies consisting of several molecular species with well defined concentrations, and the existence of an error threshold above which all information is lost because of accumulating erroneous mutations.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic fitness landscapes in molecular evolution

2001

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We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates of the molecules. In general, therefore, molecular evolution takes place in a dynamic rather than a static fitness landscape. We incorporate dynamic replication and decay rates into the standard quasispecies theory of molecular evolution, and show that for periodic time-dependencies, a system of evolving molecules enters a limit cycle for t → ∞. For fast periodic changes, we show that molecules adapt to the timeaveraged fitness landscape, whereas for slow changes they track the variations in the landscape arbitrarily closely. We derive a general approximation method that allows us to calculate the attractor of time-periodic landscapes, and demonstrate using several examples that the results of the approximation and the limiting cases of very slow and very fast changes are in perfect agreement. We also discuss landscapes with arbitrary time dependencies, and show that very fast changes again lead to a system that adapts to the time-averaged landscape. Finally, we analyze the dynamics of a finite population of molecules in a dynamic landscape, and discuss its relation to the infinite population limit.

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“…(15) into Eq. (16). Moreover, since y(t) differs from x(t) only by a scalar factor, we can restore the original variables via…”

Section: Static Landscapesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic fitness landscapes in molecular evolution

2001

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“…All normalized ( l y l = 1) solutions to (8) are also fixed points to the rate equations, since summing over k gives the relation λ = ( l A l y l ) 2 = c. There may however exist solutions to equation (8) which cannot be normalized to a vector of concentrations, since all elements must be non-negative.…”

Section: Recombinationmentioning

confidence: 99%

“…The behavior of these systems has been extensively studied, see for instance [1,2,3,4,5]. Quasispecies have also been fruitfully studied using concepts and techniques from statistical physics, see, e.g., [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Quasispecies and recombination

Jacobi

Nordahl

2006

Theoretical Population Biology

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Recombination is introduced into Eigen's theory of quasispecies evolution. Comparing numerical simulations of the rate equations in the non-recombining and recombining cases show that recombination has a strong effect on the error threshold and, for a wide range of mutation rates, gives rise to two stable fixed points in the dynamics. This bi-stability results in the existence of two error thresholds. We prove that, under some assumptions on the fitness landscape but for general crossover probability, a fixed point localized about the sequence with superior fitness is globally stable for low mutation rates.

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“…When the concentration of a sequence (as predicted for an infinite population) approaches the inverse of the population size, that sequence will most certanily be lost through sampling fluctuations. In the case of the master sequence, this effect is responsible for the shift of the error catastrophe towards smaller error rates for finite populations in the ordinary quasispecies model [25][26][27][28]. Now, since the concentration of the master sequence can be made arbitrarily small with suitable maternal effects, it follows that the error threshold can be shifted.…”

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confidence: 99%

Maternal Effects in Molecular Evolution

Wilke¹

2002

Phys. Rev. Lett.

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We introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent's genotype. The model can be solved by means of a nonlinear mapping onto the standard quasispecies model. The dependency on the parental genotypes cancels from the mean fitness, but not from the individual sequence concentrations. For finite populations, the position of the error threshold is very sensitive to the influence from parent genotypes. In addition to biological applications, our model is important for understanding the dynamics of self-replicating computer programs.PACS numbers: 87.23.KgSimple models of asexual evolution, such as the quasispecies model, typically assume that the fitness of an organism is a function of only its genotype and the environment. This allows for the analysis of evolution in static [1][2][3][4][5][6][7] or variable [8][9][10] environments, many to one mappings from genotype to phenotype (neutrality) [11][12][13], and phenotypic plasticity [14]. These models disregard the potential influence of the mother (or parent, in general) on the organism's phenotype. This influence comes about because in addition to the genetic material, a wealth of proteins and other substances is transferred from mother to child. In the context of sexual reproduction, the influence of the mother on a child's phenotype is usually called a maternal effect. A classic example is that of the snail Partula suturalis [15], for which the directionality in the coiling of the shells is determined by the genotype of the mother of an organism, rather than the organism's own genotype. Maternal effects are not exclusive to sexually reproducing organisms, however, they can be observed in simple asexual organisms as well. In bacteria, for example, the fitness of a strain in a given environment may depend on the environment that was experienced by the strain's immediate ancestors [16,17].Here, our objective is to define and study a model of the evolution of asexual organisms that takes such maternal effects into account. We assume that the fitness of an organism is given by the product of two quantities a and b, where a depends solely on the genotype of the mother of the organism, and b depends solely on the organism's own genotype. Since we need to keep track of the abundances of all possible mother/child combinations, we need n 2 concentration variables if we distinguish n different genotypes in our model. In the following, we denote by x ij the concentration of organisms of genotype j descended from genotype i, and by q ji the probability that a genotype i mutates into genotype j. The time evolution of the x ij is then, in analogy to the quasispecies model,ẋ

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Error threshold in finite populations

Cited by 84 publications

References 23 publications

Dynamic fitness landscapes in molecular evolution

Dynamic fitness landscapes in molecular evolution

Quasispecies and recombination

Maternal Effects in Molecular Evolution

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