Speaker
Description
Lambda-coalescents, or multiple merger coalescents, have been extensively studied since their introduction in 1999, and were interpreted as genealogies of populations with skewed offspring distribution. More recently, multitype versions of such coalescents have garnered attention. However, it turned out that generalising the characterisation of multiple merger coalescents in terms of a finite measure on [0,1] isn't quite as straightforward a task as one might guess. In particular, the notion of asynchronity of mergers, or transitions, needs to be carefully treated when characterising multitype multiple merger coalescents.
In this talk, we discuss how multitype multiple merger coalescents are related to continuous state branching processes via duality, and we provide a characterisation as a class of partially exchangeable Markov coalescent processes.
This is joint work with Adrián González Casanova (Arizona State University), Imanol Nunez Morales (CIMAT, Guanajuato) and José Luis Pérez (CIMAT, Guanajuato).
