Author
Chetwynd-Diggle, J
Etheridge, A
Journal title
Electronic Journal of Probability
DOI
10.1214/18-EJP191
Volume
23
Last updated
2024-03-13T01:58:54.223+00:00
Page
71-
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.
Symplectic ID
859240
Favourite
Off
Publication type
Journal Article
Publication date
26 Jul 2018
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