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Journal of Biological Physics

, Volume 32, Issue 6, pp 563–572 | Cite as

Survival Chances of Mutants Starting With One Individual

  • Christoph Kuhn
Erratum
  • 107 Downloads

Abstract

A simple theoretical model of a Darwinian system (a periodic system with a multiplication phase and a selection phase) of entities (initial form of polymer strand, primary mutant and satellite mutants) is given. First case: one mutant is considered. One individual of the mutant appears in the multiplication phase of the first generation. The probabilities to find N individuals of the mutant \(W^{{\text{S}}}_{{\text{n}}} {\left( N \right)}\) after the multiplication phase M of the n-th generation (with probability δ of an error in the replication, where all possible errors are fatal errors) and \(W^{{\text{S}}}_{{\text{n}}} {\left( N \right)}\) after the following selection phase S (with probability β that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction \(W^{{\text{S}}}_{\infty } {\left( 0 \right)}\) are obtained. Second case: two mutants are considered (primary mutant and new form). One individual of the primary mutant appears in the multiplication phase of the first generation. The probabilities to find N p individuals of the primary mutant and N m individuals of the new form \(W^{{\text{M}}}_{{\text{n}}} {\left( {N_{{\text{p}}} ,\;N_{{\text{m}}} } \right)}\) after the multiplication phase M of the n-th generation (probability ɛ of an error in the replication of the primary mutant giving the new form) and \(W^{{\text{S}}}_{{\text{n}}} {\left( {N_{{\text{p}}} ,\;N_{{\text{m}}} } \right)}\) after the following selection phase S (probabilities β p and β m that one individual each of the primary mutant and of the new form survives) are given iteratively. Again the evolutionary tree is evaluated. Averages from the distributions are obtained.

Keywords

Darwinian system Multiplication Error in replication Selection Initial form Primary mutant Satellite mutants Bernoulli polynomial Probability distribution Evolutionary tree Complementary and anti-parallel replication Plus-strand Minus-strand Translation apparatus Origin of life 

References

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Institut für Molekularbiologie und Biophysik, Gruppe Biophysik, ETH-HönggerbergZürichSwitzerland

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