15/04/2026, 17:00 — 18:00 Europe/Lisbon —
Online
Arno Siri-Jegousse, Universidad Nacional Autonoma de Mexico
Self similar populations and coalescents
The aim of this talk is to construct a measure-valued Markov process, representing an evolving population, such that its genealogies are given, in some convenient sense, by the Lambda-coalescents (Pitman 1999). Our starting point for this work is the celebrated duality between Fleming-Viot processes and coalescents (Perkins 1992. Bertoin and Le Gall 2003). Our motivation comes from several recent works establishing such connections when the evolving process has the branching property. We are able to extend this duality between two Markov additive processes, a forward one related to the Fleming-Viot process and a backward one related to the coalescent. After some transformation and time change of the forward process, we obtain a wide new class of measure-valued self-similar Markov processes, characterized by the self-similarity index and a Lévy triplet, that fulfills the desired conditions. This provides a change of paradigm in population genetics where the branching property is let aside. This is a joint work with Alejandro H. Wences.
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