June 2015 The coalescent in peripatric metapopulations
Amaury Lambert, Chunhua Ma
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J. Appl. Probab. 52(2): 538-557 (June 2015). DOI: 10.1239/jap/1437658614

Abstract

We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size ε N N, usually called peripheral isolates in ecology, where N → ∞ and ε N → 0 in such a way that ε N N → ∞. The main population, as well as the colonies, independently send propagules to found new colonies (emigration), and each colony independently, 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.

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Amaury Lambert. Chunhua Ma. "The coalescent in peripatric metapopulations." J. Appl. Probab. 52 (2) 538 - 557, June 2015. https://doi.org/10.1239/jap/1437658614

Information

Published: June 2015
First available in Project Euclid: 23 July 2015

zbMATH: 1325.60159
MathSciNet: MR3372091
Digital Object Identifier: 10.1239/jap/1437658614

Subjects:
Primary: 60K35
Secondary: 60G10 , 60J05 , 92D10 , 92D15

Keywords: Censored coalescent , metapopulation , peripatric speciation , peripheral isolate , Population genetics , weak convergence

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 2 • June 2015
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