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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.12871 |
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| _version_ | 1866911109995298816 |
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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 |