On the theory of selection of coupled macromolecular systems

Jones, B. L.; Enns, Richard H.; Rangnekar, S. S.

doi:10.1016/s0092-8240(76)80040-7

Cited by 57 publications

(34 citation statements)

References 3 publications

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“…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%

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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Section: Introductionmentioning

confidence: 99%

Dynamic fitness landscapes in molecular evolution

2001

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“…The second term ensures the total normalization of the population ( l x l = 1). These differential equations can be solved analytically [23,24]. Equation (2) can be made linear through a change of variables and we can then use standard techniques to find x k .…”

Section: Quasispeciesmentioning

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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“…As soluções no equilíbrio de seleção para essa equação podem ser encontradas, em termos dos auto-valores e auto-vetores da matriz de replicação W [30,31]. Se definirmos o vetor x = (x 1 , x 2 , ...x L ), cujas componentes representam a concentração de cada espécie molecular dentro de toda população, podemos escrever…”

Section: Modelagem Da Evolução Dos Patógenosunclassified

Técnicas de Modelagem de Processos Epidêmicos e Evolucionários

2006

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On the theory of selection of coupled macromolecular systems

Cited by 57 publications

References 3 publications

Dynamic fitness landscapes in molecular evolution

Dynamic fitness landscapes in molecular evolution

Quasispecies and recombination

Técnicas de Modelagem de Processos Epidêmicos e Evolucionários

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