McCaskill, J. S. “A stochastic theory of macromolecular evolution.” Biological Cybernetics 50, no. 1 (1984): 63-73.
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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.