## 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 [Formula presented] yields a viable organism with first-order growth rate constant [Formula presented] if it is equal to some target “master” sequence [Formula presented] The second gene, denoted by [Formula presented] yields an organism capable of genetic repair if it is equal to some target “master” sequence [Formula presented] This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on [Formula presented] the product of sequence length and per base pair replication error probability, and [Formula presented] 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 [Formula presented] 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 [Formula presented] exceeds [Formula presented] while above the repair catastrophe, the distribution undergoes the error catastrophe when [Formula presented] exceeds [Formula presented] where [Formula presented] denotes the fraction of deleterious mutations.

Original language | English |
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Pages (from-to) | 11 |

Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 69 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2004 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics