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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. [ABSTRACT FROM AUTHOR]

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 W n M( 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 W n S( 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 N p primary mutants and N m of the new form W n M( N p, N m) 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 W n S( N p, N m) 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. [ABSTRACT FROM AUTHOR]