The peripatric coalescent

TL;DR

This paper models the genealogical history of a metapopulation with a large main population and peripheral colonies, deriving a censored coalescent process that simplifies to a time-changed Kingman coalescent under rapid landscape dynamics.

Contribution

It introduces a novel two-state censored coalescent model for metapopulations with dynamic colonies, extending classical coalescent theory to structured populations with migration and merging.

Findings

The genealogical process converges to a two-state censored coalescent.

Lineages switch states at a constant rate, with only inner lineages coalescing.

Under fast landscape dynamics, the process converges to a time-changed Kingman 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 inner lineages (only) 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.