$Λ$-Seed-Bank-Wright-Fisher process conditioned on fixation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908675642228736 |
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| author | Fittipaldi, María Clara Casanova, Adrián González Trejo, Julio Ernesto Nava |
| author_facet | Fittipaldi, María Clara Casanova, Adrián González Trejo, Julio Ernesto Nava |
| contents | We investigate the $Λ$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this process on the eventual fixation of a specified genetic type. The resulting process is again a $Λ$-Wright-Fisher process with a seed bank, but now features coordinated mutations driven by a random switching environment. Our analysis relies on two key techniques: the lookdown construction and sampling duality. These tools provide a pathwise construction of the conditioned process while preserving a means to recover the conditioned population genealogy. The resulting genealogy corresponds to a structured $Λ$-coalescent with coordinated mutations determined by the switching environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20483 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $Λ$-Seed-Bank-Wright-Fisher process conditioned on fixation Fittipaldi, María Clara Casanova, Adrián González Trejo, Julio Ernesto Nava Probability 60J25, 60J90, 60J95, 60J70 We investigate the $Λ$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this process on the eventual fixation of a specified genetic type. The resulting process is again a $Λ$-Wright-Fisher process with a seed bank, but now features coordinated mutations driven by a random switching environment. Our analysis relies on two key techniques: the lookdown construction and sampling duality. These tools provide a pathwise construction of the conditioned process while preserving a means to recover the conditioned population genealogy. The resulting genealogy corresponds to a structured $Λ$-coalescent with coordinated mutations determined by the switching environment. |
| title | $Λ$-Seed-Bank-Wright-Fisher process conditioned on fixation |
| topic | Probability 60J25, 60J90, 60J95, 60J70 |
| url | https://arxiv.org/abs/2511.20483 |