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Main Authors: Crosato, Emanuele, Spinney, Richard E., Morris, Richard G.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2508.12871
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author Crosato, Emanuele
Spinney, Richard E.
Morris, Richard G.
author_facet Crosato, Emanuele
Spinney, Richard E.
Morris, Richard G.
contents 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 whereupon the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants -- typically $\sim4^L$, with $L\gg 1$ 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, seemingly subverting traditional expectations for evolutionary systems.
format Preprint
id arxiv_https___arxiv_org_abs_2508_12871
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stochastic Multistability of Clonallike States in the Eigen Model: a Fidelity Catastrophe
Crosato, Emanuele
Spinney, Richard E.
Morris, Richard G.
Populations and Evolution
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 whereupon the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants -- typically $\sim4^L$, with $L\gg 1$ 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, seemingly subverting traditional expectations for evolutionary systems.
title Stochastic Multistability of Clonallike States in the Eigen Model: a Fidelity Catastrophe
topic Populations and Evolution
url https://arxiv.org/abs/2508.12871