A stochastic theory of macromolecular evolution

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.

[1]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[2]  Manfred Eigen,et al.  Product analysis of RNA generated de novo by Qβ replicase , 1981 .

[3]  J. S. McCaskill,et al.  A localization threshold for macromolecular quasispecies from continuously distributed replication rates , 1984 .

[4]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[5]  James F. Crow,et al.  An introduction to population genetics. , 1950 .

[6]  L. Demetrius.  Selection and evolution in macromolecular systems. , 1983, Journal of theoretical biology.

[7]  M. Eigen.  Selforganization of matter and the evolution of biological macromolecules , 1971, Naturwissenschaften.

[8]  A note on a more general solution of Eigen's rate equation for selection , 1983 .

[9]  Barry W. Ninham,et al.  Stochastic Models for Second‐Order Chemical Reaction Kinetics. The Equilibrium State , 1966 .

[10]  J. Griffiths.  The Theory of Stochastic Processes , 1967 .

[11]  Richard H. Enns,et al.  On the theory of selection of coupled macromolecular systems , 1976 .

[12]  J. Crow,et al.  THE NUMBER OF ALLELES THAT CAN BE MAINTAINED IN A FINITE POPULATION. , 1964, Genetics.

[13]  C. Mou.  Stochastic theory of phase transition in multiple steady state chemical system: Nucleation , 1978 .

[14]  Manfred Eigen,et al.  Kinetics of ribonucleic acid replication. , 1983 .

[15]  Werner Ebeling,et al.  Physik der Selbstorganisation und Evolution , 1984 .

[16]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

[17]  J. Edwards.  Molecular Evolution, Protein Polymorphism and the Neutral Theory , 1984 .

[18]  Colin J. Thompson,et al.  On Eigen's theory of the self-organization of matter and the evolution of biological macromolecules , 1974 .

[19]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .