Polynucleotide evolution and branching processes
The theory of multitype branching processes is applied to the kinetics of polynucleotide replication. The results obtained are compared with the solutions of the deterministic differential equations of conventional chemical kinetics.
KeywordsPolynucleotide Selection Equation Deterministic Equation Error Threshold Dominant Eigenvalue
Unable to display preview. Download preview PDF.
- Athreya, K. B. and P. E. Ney. 1972.Branching Processes. Berlin: Springer.Google Scholar
- Billingley, P. 1965.Ergodic Theory and Information. New York: J. Wiley.Google Scholar
- Ebeling, W. and R. Fesitel 1977. “Stochastic Theory of Molecular Replication Processes with Selection Character.”Ann. Phys. 34, 81–90.Google Scholar
- — and P. Schuster. 1979.The Hypercycle. A Principle of Natural Self-organisation. Berlin: Springer.Google Scholar
- Eigen, M., J. S. McCaskill and P. Schuster. 1984. “Physics of Evolutionary Optimization.” To be published.Google Scholar
- Gassner, B. and P. Schuster. 1982. “Model Studies on RNA Replication I. The Quasiequilibrium Assumption and the Analysis of a Simplified Mechanism.”Mh. Chem. 113, 237–263.Google Scholar
- Harris, T. E. 1963.The Theory of Branching Processes. Berlin: Springer.Google Scholar
- Jagers, P. 1975.Branching Processes with Biological Applications. London: Wiley.Google Scholar
- Karlin, S. 1974.A First Course in Stochastic Processes, 2nd edn. New York: Academic Press.Google Scholar
- Schuster, P. 1981. “Prebiotic Evolution.” InBiochemical Evolution, Ed. H. Gutfreund, pp. 15–87. Cambridge: Cambridge University Press.Google Scholar
- — 1983. “Selection and Evolution in Molecular Systems—A Combined Approach by Stochastic and Deterministic Chemical Kinetics.” InStochastic Processes Applied to Physics and Other Related Fields, Eds. B. Gomez, S. M. More, A. M. Rodriguez-Vargas and A. Rueda, pp. 134–59. Singapore: World Scientific.Google Scholar
- — and K. Sigmund. 1984a. “Random Selection and the Neutral Theory—Sources of Stochasticity in Replication.” InStochastic Phenomena and Chaotic Behaviour in Complex Systems, Ed. P. Schuster, pp. 186–207. Berlin: Springer.Google Scholar