Can deleterious mutations surf deterministic population waves? A functional law of large numbers for a spatial model of Muller's ratchet
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918375847886848 |
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| author | Madeira, João Luiz de Oliveira Ortgiese, Marcel Penington, Sarah |
| author_facet | Madeira, João Luiz de Oliveira Ortgiese, Marcel Penington, Sarah |
| contents | The spatial Muller's ratchet is a model introduced by Foutel-Rodier and Etheridge to study the impact of cooperation and competition on the fitness of an expanding asexual population. The model is an interacting particle system consisting of particles performing symmetric random walks that reproduce and die with rates that depend on the local number of particles. For each particle, we keep track of the number of deleterious mutations that it carries, and after each birth event, with some positive probability, the offspring particle can acquire an additional mutation that gives it a lower reproduction rate than its parent. We show that under an appropriate scaling, the process converges weakly to the solution of an infinite system of partial differential equations (PDEs), confirming non-rigorous computations of Foutel-Rodier and Etheridge. In the PDE limit, when the reaction term of the system of PDEs is monostable, we establish bounds on the ratio between the density of particles with a given number of mutations and the density of particles without mutations. If the reaction term satisfies a Fisher-KPP condition, we can also rigorously determine the spreading speed of the population into an empty habitat. Finally, by considering the PDE limit of a form of tracer dynamics, we answer the question of whether deleterious mutations can surf population waves in this setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06478 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Can deleterious mutations surf deterministic population waves? A functional law of large numbers for a spatial model of Muller's ratchet Madeira, João Luiz de Oliveira Ortgiese, Marcel Penington, Sarah Probability Analysis of PDEs Populations and Evolution The spatial Muller's ratchet is a model introduced by Foutel-Rodier and Etheridge to study the impact of cooperation and competition on the fitness of an expanding asexual population. The model is an interacting particle system consisting of particles performing symmetric random walks that reproduce and die with rates that depend on the local number of particles. For each particle, we keep track of the number of deleterious mutations that it carries, and after each birth event, with some positive probability, the offspring particle can acquire an additional mutation that gives it a lower reproduction rate than its parent. We show that under an appropriate scaling, the process converges weakly to the solution of an infinite system of partial differential equations (PDEs), confirming non-rigorous computations of Foutel-Rodier and Etheridge. In the PDE limit, when the reaction term of the system of PDEs is monostable, we establish bounds on the ratio between the density of particles with a given number of mutations and the density of particles without mutations. If the reaction term satisfies a Fisher-KPP condition, we can also rigorously determine the spreading speed of the population into an empty habitat. Finally, by considering the PDE limit of a form of tracer dynamics, we answer the question of whether deleterious mutations can surf population waves in this setting. |
| title | Can deleterious mutations surf deterministic population waves? A functional law of large numbers for a spatial model of Muller's ratchet |
| topic | Probability Analysis of PDEs Populations and Evolution |
| url | https://arxiv.org/abs/2603.06478 |