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2018 SuperBrownian motion and the spatial Lambda-Fleming-Viot process
Jonathan A. Chetwynd-Diggle, Alison M. Etheridge
Electron. J. Probab. 23: 1-36 (2018). DOI: 10.1214/18-EJP191

Abstract

It is well known that the dynamics of a subpopulation of individuals of a rare type in a Wright-Fisher diffusion can be approximated by a Feller branching process. Here we establish an analogue of that result for a spatially distributed population whose dynamics are described by a spatial Lambda-Fleming-Viot process (SLFV). The subpopulation of rare individuals is then approximated by a superBrownian motion. This result mirrors [10], where it is shown that when suitably rescaled, sparse voter models converge to superBrownian motion. We also prove the somewhat more surprising result, that by choosing the dynamics of the SLFV appropriately we can recover superBrownian motion with stable branching in an analogous way. This is a spatial analogue of (a special case of) results of [6], who show that the generalised Fleming-Viot process that is dual to the beta-coalescent, when suitably rescaled, converges to a continuous state branching process with stable branching mechanism.

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Jonathan A. Chetwynd-Diggle. Alison M. Etheridge. "SuperBrownian motion and the spatial Lambda-Fleming-Viot process." Electron. J. Probab. 23 1 - 36, 2018. https://doi.org/10.1214/18-EJP191

Information

Received: 29 May 2017; Accepted: 25 June 2018; Published: 2018
First available in Project Euclid: 26 July 2018

zbMATH: 06924683
MathSciNet: MR3835477
Digital Object Identifier: 10.1214/18-EJP191

Subjects:
Primary: 60F05 , 60G57 , 60J25 , 60J68 , 60J80
Secondary: 60G51 , 60G55 , 60J75 , 92D10f

Keywords: scaling limits , spatial Lambda-Fleming-Viot model , stable branching process , Superprocess

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