Multi-type $Ξ$-coalescents from structured population models with bottlenecks
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912331023253504 |
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| author | Pra, Marta Dai Etheridge, Alison Koskela, Jere Wilke-Berenguer, Maite |
| author_facet | Pra, Marta Dai Etheridge, Alison Koskela, Jere Wilke-Berenguer, Maite |
| contents | We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the (non-Markovian) allele-frequency process converges to a Markovian diffusion process with jumps in a suitable relaxation of the Skorokhod J1 topology. Backward in time we find that genealogies of samples of individuals are described by multi-type $Ξ$-coalescents presenting multiple simultaneous mergers with simultaneous migrations. These coalescents are also moment-duals of the limiting jump diffusions. We then show through a numerical study that our model is flexible and can predict various shapes for the site frequency spectrum, consistent with real data, using a small number of interpretable parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11875 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-type $Ξ$-coalescents from structured population models with bottlenecks Pra, Marta Dai Etheridge, Alison Koskela, Jere Wilke-Berenguer, Maite Probability Populations and Evolution 60K35, 60J90, 60J70 We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the (non-Markovian) allele-frequency process converges to a Markovian diffusion process with jumps in a suitable relaxation of the Skorokhod J1 topology. Backward in time we find that genealogies of samples of individuals are described by multi-type $Ξ$-coalescents presenting multiple simultaneous mergers with simultaneous migrations. These coalescents are also moment-duals of the limiting jump diffusions. We then show through a numerical study that our model is flexible and can predict various shapes for the site frequency spectrum, consistent with real data, using a small number of interpretable parameters. |
| title | Multi-type $Ξ$-coalescents from structured population models with bottlenecks |
| topic | Probability Populations and Evolution 60K35, 60J90, 60J70 |
| url | https://arxiv.org/abs/2504.11875 |