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 mutants WnM(N) 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 WnS(N) 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∞S(0) 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 Np primary mutants and Nm of the new form WnM(Np, Nm) after the multiplication phase M of the n-th generation (probability ε of an error in the replication of the primary mutant giving the new form) and WnS(Np, Nm) after the following selection phase S (probabilities βp and βm 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.
Key words: 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
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Footnotes
An erratum to this article is available at http://dx.doi.org/10.1007/s10867-007-9036-1.
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