Survival Chances of Mutants Starting With One Individual.

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]