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.
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...
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...
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...
