Bulletin of Mathematical Biology

, Volume 50, Issue 6, pp 635-660

Stationary mutant distributions and evolutionary optimization

  • Peter SchusterAffiliated withInstitut für theoretische Chemie und Strahlenchemie der Universität Wien
  • , Jörg SwetinaAffiliated withInstitut für theoretische Chemie und Strahlenchemie der Universität Wien

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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.