• Corpus ID: 2169486

A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks

@article{Birkner2008AML,
  title={A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks},
  author={Matthias C. F. Birkner and Jochen Blath and Martin Moehle and Matthias Steinruecken and Johanna Tams},
  journal={arXiv: Probability},
  year={2008}
}
Letbe a finite measure on the unit interval. A �-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions (�-coalescent) in analogy to the duality known for the classical Fleming-Viot process and Kingman's coalescent, whereis the Dirac measure in 0. We explicitly construct a dual process of the coalescent with simultaneous multi- ple collisions (�-coalescent) with mutation, the �-Fleming-Viot process with muta- tion, and provide… 

Figures from this paper

Generalized Fleming-Viot processes with immigration via stochastic flows of partitions

The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key

Pathwise construction of tree-valued Fleming-Viot processes

In a random complete and separable metric space that we call the lookdown space, we encode the genealogical distances between all individuals ever alive in a lookdown model with simultaneous multiple

The spatial Lambda-Fleming–Viot process: An event-based construction and a lookdown representation

We construct a measure-valued equivalent to the spatialΛ-Fleming–Viot process (SLFV) introduced in (Banach Center Publ. 80 (2008) 121–144). In contrast with the construction carried out there, we fix

The spatial Lambda-Fleming-Viot process: an event-based construction and a lookdown representation

We construct a measure-valued equivalent to the spatial Lambda-Fleming-Viot process (SLFV) introduced in [Eth08]. In contrast with the construction carried out in [Eth08], we fix the realization of

Distinguished exchangeable coalescents and generalized Fleming-Viot processes with immigration

Coalescents with multiple collisions (also called Λ-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected

Tree-valued resampling dynamics Martingale problems and applications

The measure-valued Fleming–Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate

A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes

We give a de Finetti type representation for exchangeable random coalescent trees (formally described as semi-ultrametrics) in terms of sampling iid sequences from marked metric measure spaces. We

Some support properties for a class of ${\varLambda}$-Fleming–Viot processes

Using Donnelly and Kurtz's lookdown construction, we prove that the Lambda-Fleming-Viot process with underlying Brownian motion has a compact support at any fixed time provided that the associated

The symmetric coalescent and Wright–Fisher models with bottlenecks

We define a new class of $\Xi$-coalescents characterized by a possibly infinite measure over the non negative integers. We call them symmetric coalescents since they are the unique family of
...

References

SHOWING 1-10 OF 46 REFERENCES

A countable representation of the Fleming-Viot measure-valued diffusion

The Fleming-Viot measure-valued diffusion arises as the infinite population limit of various discrete genetic models with general type space. The paper gives a countable construction of the process

Stochastic flows associated to coalescent processes. III. Limit theorems

We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot

Fleming-Viot processes in population genetics

Fleming and Viot [Indiana Univ. Math. J., 28 (1979), pp. 817–843] introduced a class of probability-measure-valued diffusion processes that has attracted the interest of both pure and applied

CONVERGENCE TO THE COALESCENT WITH SIMULTANEOUS MULTIPLE MERGERS

The general coalescent process with simultaneous multiple mergers of ancestral lines was initially characterized by Mohle and Sagitov (2001) in terms of a sequence of measures defined on the

Stochastic flows associated to coalescent processes

Abstract. We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Möhle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models

Coalescents with multiple collisions

k−2 � 1 − xb−k � � dx� . Call this process a � -coalescent. Discrete measure-valued processes derived from the � -coalescent model a system of masses undergoing coalescent collisions. Kingman's

Jump-type Fleming-Viot processes

In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching

GRAPHICAL REPRESENTATION OF SOME DUALI- TY RELATIONS IN STOCHASTIC POPULATION MO- DELS

We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. [1]) and for the self-duality of Feller’s branching diffusion

The general coalescent with asynchronous mergers of ancestral lines

  • S. Sagitov
  • Mathematics
    Journal of Applied Probability
  • 1999
Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral