Modèles stochastiques en dynamique des populations et génétique

Liste des Contributions

1. Introduction to stochastic models of phylogenies and genealogies

Prof. Viet Chi Tran (INRIA Lille)

07/05/2025 14:00

We will review various stochastic models describing the phylogenies and genealogies for evolving populations: coalescent processes, branching processes, historical processes and processes valued in marked measured metric spaces.

2. Genealogies in structured frequency-dependent branching processes

Mathilde André (IBENS, PSL, INSERM & Université de Vienne)

07/05/2025 15:30

Genealogies in structured frequency-dependent branching processes
Our work delves into the universality class of a very celebrated entity in population genetics : Kingman’s coalescent. This object serves as baseline models for panmictic, neutral populations. More generally, Λ−coalescents catalog the genealogies of constant–sized exchangeable populations models known as Cannings models. We...

3. A generalised spatial branching process with ancestral branching to model the growth of a filamentous fungus

Lena Kuwata (MAP5, Université Paris Cité)

07/05/2025 16:00

We introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is the solution to a stochastic differential equation with a drift term which depends on all the other trajectories. Each filament can branch either at its tip or along its length, that is to...

4. Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel

Jules Olayé (CMAP, École polytechnique)

07/05/2025 16:45

In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks individuals evolving within a continuous-time framework indexed by a binary tree, characterised by age and a multidimensional trait. Branching events occur with...