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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.07762 |
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| _version_ | 1866909536838746112 |
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| author | Schertzer, Emmanuel Wences, Alejandro H. |
| author_facet | Schertzer, Emmanuel Wences, Alejandro H. |
| contents | We consider an extension of the noisy $N$-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical structure into two regimes, which we respectively call the semi-pulled and the fully-pulled regimes. In the fully-pulled regime, the genealogy converges to a discrete time Poisson-Dirichlet coalescent. In the semi-pulled regime, the genealogy converges to the Bolthausen-Sznitman coalescent. We discuss some interesting biological consequences of this result. In particular, our model predicts a non-monotone relation between the selection strength and the effective population size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07762 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Genealogical transition in the noisy $N$-Branching Random Walk. How stronger selection may promote genetic diversity Schertzer, Emmanuel Wences, Alejandro H. Populations and Evolution 60J80 (Primary), 60K35 (Secondary) We consider an extension of the noisy $N$-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical structure into two regimes, which we respectively call the semi-pulled and the fully-pulled regimes. In the fully-pulled regime, the genealogy converges to a discrete time Poisson-Dirichlet coalescent. In the semi-pulled regime, the genealogy converges to the Bolthausen-Sznitman coalescent. We discuss some interesting biological consequences of this result. In particular, our model predicts a non-monotone relation between the selection strength and the effective population size. |
| title | Genealogical transition in the noisy $N$-Branching Random Walk. How stronger selection may promote genetic diversity |
| topic | Populations and Evolution 60J80 (Primary), 60K35 (Secondary) |
| url | https://arxiv.org/abs/2301.07762 |