Exact phase diagram of quasispecies model with mutation rate modifier

TL;DR

This paper derives the exact phase diagram for a quasispecies model with a mutation rate modifier, identifying a phase transition between mixed and pure mutator populations and calculating critical parameters.

Contribution

It provides an exact analytical solution for the phase transition and mutator fraction in a quasispecies model with mutation rate modifiers, extending prior approximate methods.

Findings

Identifies a critical mutation rate transition point $f_c$.

Calculates the mutator fraction $Q$ exactly in the mixed phase.

Findings agree with microbial population observations.

Abstract

We consider an infinite asexual population with a mutator allele which can elevate mutation rates. With probability $f$, a transition from nonmutator to mutator state occurs but the reverse transition is forbidden. We find that at $f=0$, the population is in the state with minimum mutation rate and at $f=f_c$, a phase transition occurs between a mixed phase with both nonmutators and mutators and a pure mutator phase. We calculate the critical probability $f_c$ and the total mutator fraction $Q$ in the mixed phase exactly. Our predictions for $Q$ are in agreement with those seen in microbial populations in static environments.