Branching with selection and mutation II: Mutant fitness of Gumbel type
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915163436744704 |
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| author | Park, Su-Chan Krug, Joachim Mörters, Peter |
| author_facet | Park, Su-Chan Krug, Joachim Mörters, Peter |
| contents | We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_14774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branching with selection and mutation II: Mutant fitness of Gumbel type Park, Su-Chan Krug, Joachim Mörters, Peter Probability Statistical Mechanics Biological Physics 60J80, 60J85, 92D25 We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave. |
| title | Branching with selection and mutation II: Mutant fitness of Gumbel type |
| topic | Probability Statistical Mechanics Biological Physics 60J80, 60J85, 92D25 |
| url | https://arxiv.org/abs/2502.14774 |