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 
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 
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 
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 individuals of the primary mutant and Nm individuals of the new form 
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 
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.
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
Footnotes
The online version of the original article can be found at 10.1007/s10867-005-6061-9.
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