The tournament ratchet's clicktime process, and metastability in a Moran model
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| Format: | Preprint |
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2025
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| author | Igelbrink, Jan Lukas Smadi, Charline Wakolbinger, Anton |
| author_facet | Igelbrink, Jan Lukas Smadi, Charline Wakolbinger, Anton |
| contents | Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. In the classical variant, an individual's selective advantage is proportional to the difference between the population average and the individual's mutation load, whereas in the ratchet with {\em tournament selection} only the signs of the differences of the individual mutation loads matter. In a parameter regime which leads to slow clicking (i.e. to a loss of the currently fittest class at a rate $\ll 1/N$) we prove that the rescaled process of click times of the tournament ratchet converges as $N\to \infty$ to a Poisson process. Central ingredients in the proof are a thorough analysis of the metastable behaviour of a two-type Moran model with selection and deleterious mutation (which describes the size of the fittest class up to its extinction time) and a lower estimate on the size of the new fittest class at a clicktime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_24779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The tournament ratchet's clicktime process, and metastability in a Moran model Igelbrink, Jan Lukas Smadi, Charline Wakolbinger, Anton Probability Populations and Evolution Primary 92D15, secondary 60K35, 60J80, 60J27, 60F17 Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. In the classical variant, an individual's selective advantage is proportional to the difference between the population average and the individual's mutation load, whereas in the ratchet with {\em tournament selection} only the signs of the differences of the individual mutation loads matter. In a parameter regime which leads to slow clicking (i.e. to a loss of the currently fittest class at a rate $\ll 1/N$) we prove that the rescaled process of click times of the tournament ratchet converges as $N\to \infty$ to a Poisson process. Central ingredients in the proof are a thorough analysis of the metastable behaviour of a two-type Moran model with selection and deleterious mutation (which describes the size of the fittest class up to its extinction time) and a lower estimate on the size of the new fittest class at a clicktime. |
| title | The tournament ratchet's clicktime process, and metastability in a Moran model |
| topic | Probability Populations and Evolution Primary 92D15, secondary 60K35, 60J80, 60J27, 60F17 |
| url | https://arxiv.org/abs/2512.24779 |