Survival chances of mutants starting with one individual.

UNLABELLED

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(n)(S)(N) after the multiplication phase M of the n-th generation (with probability delta 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 beta that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction W(infinity)(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) individuals of the primary mutant and N(m) individuals of the new form W(n)(M)(N(p), N(m)) after the multiplication phase M of the n-th generation (probability varepsilon 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 beta(p) and beta(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.