Tuesday, June 21, 2022 - 16:30 in HIM, Bonn
Classic and new approaches to the study of Λ-Wright-Fisher processes with selection (II) (joint with Fernando Cordero)
A talk in the Junior trimester programme 'Stochastic Modelling in the Life Sciences: From evolution to medicine' series by
Sebastian Hummel from Berkeley, USA
| Abstract: |
The boundary behaviour of Wright-Fisher processes with selection can be analysed by methods that rely on duality ideas. In the first part, we focus on classical approaches that use the coalescent and the ancestral selection graph. Formally, this means that some sort of sampling duality is at play. We discuss what kind of results have been obtained based on this idea, but also what limitations this method has. The second part exhibits a new approach based on Siegmund duality.
More specifically, we explain how to derive the Siegmund dual to the Lambda-Wright-Fisher process. The dual process is then sandwiched at the boundary in between two transformed Lévy processes. In this way we relate the long-term behaviour of the dual process to fluctuation properties of the Lévy processes. This in turn allows us to characterise the boundary behaviour of the Lambda-Wright-Fisher process.
The talk takes place at the Hausdorff Research Institute for Mathematics in Bonn.
Within the CRC this talk is associated to the project(s): C1 |
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