Convergence of genealogies through spinal decomposition

Consider a branching process where each individual is endowed with a heritable type that influences its reproductive success. In this presentation I will outline a new approach to study the scaling limit of the genealogy and distribution of types of such branching processes, when looked at a large time horizon. It relies on two main building blocks: 1) viewing genealogies as random metric measure spaces in the Gromov-weak topology and 2) computing the Gromov-weak “moments” of the genealogy using a many-to-few formula. I will illustrate this approach on the simple example of multi-type Galton-Watson processes and discuss some more complex models that we have been considering.

This is based on a joint work with Emmanuel Schertzer, and another with Florin Boenkost and Emmanuel Schertzer.