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Stochastic multistability of clonal-like states in the Eigen model: A fidelity catastrophe

Emanuele Crosato1,2,3,*, Richard E. Spinney1,2,*, and Richard G. Morris1,2,4,†

  • 1School of Physics, UNSW, Sydney, New South Wales 2052, Australia
  • 2EMBL Australia Node in Single Molecule Science, School of Biomedical Sciences, UNSW, Sydney, New South Wales 2052, Australia
  • 3Living Systems Institute and Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QD, United Kingdom
  • 4ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems, UNSW Node, Sydney, New South Wales 2052, Australia

  • *These authors contributed equally to this work.
  • †Contact author: r.g.morris@unsw.edu.au
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Phys. Rev. Research 8, 033325 – Published 16 September, 2026

DOI: https://doi.org/10.1103/dltj-jrj6

Abstract

The Eigen model is a prototypical toy model of evolution that is synonymous with the so-called error catastrophe: When mutation rates are sufficiently high, the genetic variant with the largest replication rate does not occupy the largest fraction of the total population because it acts as a source for the other variants. Here, we show that, in the stochastic version of the Eigen model, there is also a fidelity catastrophe. This arises due to the state-dependence of fluctuations and occurs when rates of mutation fall beneath a certain threshold, which we calculate. The result is a type of noise-induced multistability in which the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants—potentially ∼4L, with L≫1 the length of the genome—is significantly larger than the population size, there is only a vanishingly small interval of mutation rates for which the Eigen model is neither in the fidelity- nor error-catastrophe regimes.

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Phys. Rev. Research 8, 033325– Published 16 September, 2026
  • Received 20 August 2025
  • Accepted 3 August 2026
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