Exchangeable coalescents beyond the Cannings class
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909172133527552 |
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| author | Siri-Jégousse, Arno Wences, Alejandro H. |
| author_facet | Siri-Jégousse, Arno Wences, Alejandro H. |
| contents | We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings' models, and replace it by a less restrictive condition of non-heritability of reproductive success. We provide a general criterion for the weak convergence of their genealogies to $Ξ$-coalescents, and apply it to a simple parametrization of our scenario (which, under mild conditions, we also prove to essentially include the general case). We provide examples for such populations, including models with highly-asymmetric offspring distributions and populations undergoing random but recurrent bottlenecks. Finally we study the limit genealogy of a new exponential model which, as previously shown for related models and in spite of its built in (fitness) inheritance mechanism, can be brought into our setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02154 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exchangeable coalescents beyond the Cannings class Siri-Jégousse, Arno Wences, Alejandro H. Probability Populations and Evolution 60F05 (Primary), 60G09, 60J05, 60J90, 92D15 (Secondary) We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings' models, and replace it by a less restrictive condition of non-heritability of reproductive success. We provide a general criterion for the weak convergence of their genealogies to $Ξ$-coalescents, and apply it to a simple parametrization of our scenario (which, under mild conditions, we also prove to essentially include the general case). We provide examples for such populations, including models with highly-asymmetric offspring distributions and populations undergoing random but recurrent bottlenecks. Finally we study the limit genealogy of a new exponential model which, as previously shown for related models and in spite of its built in (fitness) inheritance mechanism, can be brought into our setting. |
| title | Exchangeable coalescents beyond the Cannings class |
| topic | Probability Populations and Evolution 60F05 (Primary), 60G09, 60J05, 60J90, 92D15 (Secondary) |
| url | https://arxiv.org/abs/2212.02154 |