Abstract
This paper develops a two-gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by yields a viable organism with first-order growth rate constant if it is equal to some target “master” sequence The second gene, denoted by yields an organism capable of genetic repair if it is equal to some target “master” sequence This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on the product of sequence length and per base pair replication error probability, and the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of the three possible “phases.” In the first phase, the population is localized about the viability and repairing master sequences. As exceeds the fraction of deleterious mutations, the population undergoes a “repair” catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when exceeds while above the repair catastrophe, the distribution undergoes the error catastrophe when exceeds where denotes the fraction of deleterious mutations.
- Received 9 June 2003
DOI:https://doi.org/10.1103/PhysRevE.69.011902
©2004 American Physical Society