Journal of Mathematical Biology

, Volume 27, Issue 4, pp 463–483 | Cite as

First and second moments and the mean hamming distance in a stochastic replication-mutation model for biological macromolecules

  • J. Swetina


In this work first and second moments for a many species Moran model are calculated. The model describes by means of a time-continuous birth- and death process the evolution of an ensemble of N macromolecules out of n possible species. The molecules may replicate (correct or erroneous, in the latter case producing mutants) and may undergo elimination. Replication and elimination will be coupled in order to keep population size constant. In the case of arbitrary replication rates an expansion of the moments in powers of 1/N is found. For equal replication rates exact calculation of the moments is possible. In the case of a v-cube model (binary macromolecules) the second moments may be used to find a simple expression for the mean Hamming distance in the system. This quantity provides a measure for the localization of the ensemble.

Key words

Self-organization Stochastic evolution Localization 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. Swetina
    • 1
  1. 1.Institut für theoretische Chemie und Strahlenchemie der Universität WienWienAustria

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