We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size epsilon N-N, usually called peripheral isolates in ecology, where N --\textgreater infinity and epsilon(N) --\textgreater 0 in such a way that epsilon N-N --\textgreater infinity. 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.

@article{lambert_coalescent_2015,

Author = {Lambert, Amaury and Ma, Chunhua},

Title = {The {Coalescent} in {Peripatric} {Metapopulations}},

Journal = {Journal of Applied Probability},

Volume = {52},

Number = {2},

Pages = {538--557},

Note = {WOS:000358811700015},

Keywords = {Censored coalescent, genealogical process,

metapopulation, peripatric speciation, peripheral

isolate, population genetics, populations, Weak

convergence},

abstract = {We consider a dynamic metapopulation involving one

large population of size N surrounded by colonies of

size epsilon N-N, usually called peripheral isolates in

ecology, where N --{\textgreater} infinity and

epsilon(N) --{\textgreater} 0 in such a way that

epsilon N-N --{\textgreater} infinity. 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.},

doi = {10.1239/jap/1437658614},

issn = {0021-9002},

language = {English},

month = jun,

year = 2015

}