Stationary mutant distributions and evolutionary optimization
Molecular evolution is modelled by erroneous replication of binary sequences. We show how the selection of two species of equal or almost equal selective value is influenced by its nearest neighbours in sequence space. In the case of perfect neutrality and sufficiently small error rates we find that the Hamming distance between the species determines selection. As the error rate increases the fitness parameters of neighbouring species become more and more important. In the case of almost neutral sequences we observe a critical replication accuracy at which a drastic change in the “quasispecies”, in the stationary mutant distribution occurs. Thus, in frequently mutating populations fitness turns out to be an ensemble property rather than an attribute of the individual.
In addition we investigate the time dependence of the mean excess production as a function of initial conditions. Although it is optimized under most conditions, cases can be found which are characterized by decrease or non-monotonous change in mean excess productions.
KeywordsSequence Space Excess Production Evolutionary Optimization Fitness Landscape Error Threshold
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- Domingo, E., P. Ahlquist and J. J. Holland (Eds.) In press.RNA-Genetics, Vols I and II. Baton Rouge: CRC-Press.Google Scholar
- — 1985. “Macromolecular Evolution: Dynamical Ordering in Sequence Space.”Ber. Bunsenges. phys. Chem.,89, 658–667.Google Scholar
- — and P. Schuster. 1979.The Hypercycle—a Principle of Natural Self-Organization. Berlin: Springer.Google Scholar
- Eigen, M., J. McCaskill and P. Schuster. In press. “Dynamics of Darwinian Molecular Systems.”J. phys. Chem. Google Scholar
- Ewens, W. J. 1979. “Mathematical Population Genetics.” InBiomathematics, Vol. 9. Berlin: Springer.Google Scholar
- Feinberg, M. 1977. “Mathematical Aspects of Mass Action Kinetics.” InChemical Reaction Theory: A Review, N. Amundsen and L. Lapidus (Eds), pp. 1–78. New Jersey: Prentice Hall.Google Scholar
- Jones, B. L. 1978 (Eds) “Some Principles Governing Selection in Self-Reproducing Macromolecular Systems.”J. math. Biol. 6, 169–75.Google Scholar
- Kato, T. 1966. “Perturbation Theory for Linear OperatorsGrundl. Math. Wiss. 132.Google Scholar
- Kimura, M. 1983.The Neutral Theory of Molecular Evolution, Cambridge University Press.Google Scholar
- — and K. Sigmund. 1985. “Dynamics of Evolutionary Optimization.”Ber. Bunsenges. phys. Chem.,89, 668–682.Google Scholar