Equilibrium Distribution of Mutators in the Single Fitness Peak Model

Abstract

This paper develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak (SFP) model, which has been used in Eigen's quasispecies equations in order to understand various aspects of evolutionary dynamics. As with the quasispecies model, our model for mutator-nonmutator equilibrium undergoes a phase transition in the limit of infinite sequence length. This "repair catastrophe" occurs at a critical repair error probability of ${\epsilon }_r=L_{via}/L$, where $L_{via}$ denotes the length of the genome controlling viability, while $L$ denotes the overall length of the genome. The repair catastrophe therefore occurs when the repair error probability exceeds the fraction of deleterious mutations. Our model also gives a quantitative estimate for the equilibrium fraction of mutators in {\it Escherichia coli}.

arXiv comment4 pages, 2 figures (included as separate PS files)

References in corpus (2)

• Error Thresholds on Dynamic Fittness-Landscapes
• Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes

Cited by in corpus (8)

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• Semiconservative Replication in the Quasispecies Model
• The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model
• The Effect of Mutators on Adaptability in Time-Varying Fitness Landscapes
• Asexual and sexual replication in sporulating organisms
• Nonlinear deterministic equations in biological evolution
• Semiconservative quasispecies equations for polysomic genomes: The general case
• The effect of the SOS response on the mean fitness of unicellular populations: A quasispecies approach