Abstract
A stochastic theory of selection introduces the possibility of metastable distributions of macromolecular sequences, “metaspecies”, which succeed one another in a slowing optimization walk which may not reach the deterministic quasispecies in biological time. The stochastic theory is formulated using a hierarchy of conditional transition probabilities as a hierarchy of differential difference equations in which the non linearity of a constraint term is essential. An approximate closure of the hierarchy is discussed and it is shown that the mean provides a poor characterization. Expressions for the metastable lifetimes are given and conditions for metastable successions as opposed to non-optimizing drift are formulated. A single description of the complementary roles of adaptive and neutral selection in macromolecular evolution is achieved.
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Abramowitz, M., Stegun, I.A.: “Handbook of Mathematical Functions” New York, Dover, p. 504 (1965)
Bessho, C., Kuroda, N.: Bull. Math. Biol. 45, 143–149 (1983)
Biebricher, C.K., Eigen, M., Gardiner, W.C.: Biochemistry 22, 2544–2559 (1983)
Biebricher, C.K., Eigen, M., Luce, R.: J. Mol. Biol. 148, 369–410 (1981)
Courant, R., Hilbert, D.: “Methods of Mathematical Physics” Vol. II, New York, Wiley, Interscience, (1962)
Cox, D.R., Miller, H.D.: “The Theory of Stochastic Processes” Wiley, New York (1965)
Darvey, I.G., Ninham, B.W., Staff, P.J.: J. Chem. Phys. 45, 2145–2155 (1966)
Demetrius, L.: J. Theor. Biol. 103, 619–643 (1983)
Ebeling, W., Feistel, R.: Ann. Physik 34, 81–160 (1977) “Physik der Selbstorganisation und Evolution” Berlin, Akademie Verlag (1982)
Eigen, M.: Naturwissenschaften 58, 465–523 (1971)
Fisher, R.A.: “The Genetical Theory of Natural Selection” Oxford, Clarendon Press (1930)
Haldane, J.B.S.: Trans. Cambridge Philos. Soc. 23, 19–41 (1924)
Jones, B.L., Enns, R.H., Rangnekar, S.S.: Bull. Math. Biol. 38, 15–28 (1976)
Kimura, M.: editor “Molecular Evolution, Protein Polymorphism and the Neutral Theory” Berlin, Springer (1983)
Kimura, M., Crow, J.F.: Genetics 49, 725–738 (1964)
Kimura, M., Crow, J.F. “An Introduction to Population Genetics” New York, Harper and Row (1970)
McCaskill, J.S.: “A localization threshold for macromolecular quasispecies from continuously distributed replication rates”, submitted to J. Chem. Phys. (1983)
Mou, C.Y.: J. Chem. Phys. 68, 1385–1390 (1978)
Thompson, C.J., McBride, J.L.: Math. Biosci. 21, 127–142 (1974)
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McCaskill, J.S. A stochastic theory of macromolecular evolution. Biol. Cybern. 50, 63–73 (1984). https://doi.org/10.1007/BF00317940
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DOI: https://doi.org/10.1007/BF00317940