Spatial Lamda-Fleming-Viot process and SuperBrownian motion in random environments - lookdown perspective

We investigate the behaviour of an establishing mutation which is subject to rapidly fluctuating selection under the Spatial Lambda-Fleming-Viot model and show that under a suitable scaling it converges to the SuperBrownian in a random environment. The scaling results for the behaviour of the rare allele are achieved via particle representations which belong to the family of `lookdown constructions'. To our knowledge this is the first instance of the application of the lookdown approach in which other techniques seem unavailable. Joint with Jonathan Chetwynd-Diggle.