Fixation and stationary times for the $Λ$-Wright-Fisher process
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914043230420992 |
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| author | Blancas, Airam Casanova, Adrián González Hummel, Sebastian Palau, Sandra |
| author_facet | Blancas, Airam Casanova, Adrián González Hummel, Sebastian Palau, Sandra |
| contents | We study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large offspring variance. Using a lookdown construction, we characterize the distribution of fixation times and the order of allele extinctions in the absence of mutations, and identify a strong stationary time in the presence of mutations. Our results include explicit expressions for the mean fixation and stationary times for the Wright-Fisher diffusion, and mean fixation times in the Beta-coalescent case. A key component of our approach is the analysis of the fixation line introduced by Hénard in (Ann. Appl. Probab., 25:3007-3032, 2015). We extend this process to incorporate mutation, providing a unified framework for studying both fixation and equilibrium behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09218 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fixation and stationary times for the $Λ$-Wright-Fisher process Blancas, Airam Casanova, Adrián González Hummel, Sebastian Palau, Sandra Probability 92D15, 60J25, 60J27, 60J90, 60J95 We study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large offspring variance. Using a lookdown construction, we characterize the distribution of fixation times and the order of allele extinctions in the absence of mutations, and identify a strong stationary time in the presence of mutations. Our results include explicit expressions for the mean fixation and stationary times for the Wright-Fisher diffusion, and mean fixation times in the Beta-coalescent case. A key component of our approach is the analysis of the fixation line introduced by Hénard in (Ann. Appl. Probab., 25:3007-3032, 2015). We extend this process to incorporate mutation, providing a unified framework for studying both fixation and equilibrium behavior. |
| title | Fixation and stationary times for the $Λ$-Wright-Fisher process |
| topic | Probability 92D15, 60J25, 60J27, 60J90, 60J95 |
| url | https://arxiv.org/abs/2308.09218 |