The peripatric coalescent

Abstract : We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size \varepsilon_NN, usually called peripheral isolates in ecology, where N\to\infty and \varepsilon_N\to 0 in such a way that \varepsilon_NN\to\infty. The main population periodically sends propagules to found new colonies (emigration), and each colony eventually merges with the main population (fusion). Our aim is to study the genealogical history of a finite number of lineages sampled at stationarity in such a metapopulation. We make assumptions on model parameters ensuring that the total outer population has size of the order of N and that each colony has a lifetime of the same order. We prove that under these assumptions, the scaling limit of the genealogical process of a finite sample is a censored coalescent where each lineage can be in one of two states: an inner lineage (belonging to the main population) or an outer lineage (belonging to some peripheral isolate). Lineages change state at constant rate and (only) inner lineages coalesce at constant rate per pair. This two-state censored coalescent is also shown to converge weakly, as the landscape dynamics accelerate, to a time-changed Kingman coalescent.
Type de document :
Pré-publication, Document de travail
17 pages,1 figure. 2013
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https://hal.archives-ouvertes.fr/hal-00801197
Contributeur : Amaury Lambert <>
Soumis le : vendredi 15 mars 2013 - 11:29:39
Dernière modification le : mardi 11 octobre 2016 - 15:16:56

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  • HAL Id : hal-00801197, version 1
  • ARXIV : 1303.3277

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UPMC | INSMI | PMA | PSL | USPC

Citation

Amaury Lambert, Chunhua Ma. The peripatric coalescent. 17 pages,1 figure. 2013. <hal-00801197>

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