2,314 research outputs found
Coalescent approximation for structured populations in a stationary random environment
We establish convergence to the Kingman coalescent for the genealogy of a
geographically - or otherwise - structured version of the Wright-Fisher
population model with fast migration. The new feature is that migration
probabilities may change in a random fashion. This brings a novel formula for
the coalescent effective population size (EPS). We call it a quenched EPS to
emphasize the key feature of our model - random environment. The quenched EPS
is compared with an annealed (mean-field) EPS which describes the case of
constant migration probabilities obtained by averaging the random migration
probabilities over possible environments
The coalescent effective size of age-structured populations
We establish convergence to the Kingman coalescent for a class of
age-structured population models with time-constant population size. Time is
discrete with unit called a year. Offspring numbers in a year may depend on
mother's age.Comment: Published at http://dx.doi.org/10.1214/105051605000000223 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
The peripatric coalescent
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.Comment: 17 pages,1 figur
A new model for evolution in a spatial continuum
We investigate a new model for populations evolving in a spatial continuum.
This model can be thought of as a spatial version of the Lambda-Fleming-Viot
process. It explicitly incorporates both small scale reproduction events and
large scale extinction-recolonisation events. The lineages ancestral to a
sample from a population evolving according to this model can be described in
terms of a spatial version of the Lambda-coalescent. Using a technique of
Evans(1997), we prove existence and uniqueness in law for the model. We then
investigate the asymptotic behaviour of the genealogy of a finite number of
individuals sampled uniformly at random (or more generally `far enough apart')
from a two-dimensional torus of side L as L tends to infinity. Under
appropriate conditions (and on a suitable timescale), we can obtain as limiting
genealogical processes a Kingman coalescent, a more general Lambda-coalescent
or a system of coalescing Brownian motions (with a non-local coalescence
mechanism).Comment: 63 pages, version accepted to Electron. J. Proba
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