Related papers: The coalescent point process of multi-type branchi…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends…
Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…
We study the genealogy of a solvable population model with $N$ particles on the real line which evolves according to a discrete-time branching process with selection. At each time step, every particle gives birth to children around $a$…
It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical…
Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…
Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…
Consider a population evolving as a critical continuous-time Galton-Watson (GW) tree. Conditional on the population surviving until a large time $T$, sample $k$ individuals uniformly at random (without replacement) from amongst those alive…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Using topological summaries of gene trees as a basis for species tree inference is a promising approach to obtain acceptable speed on genomic-scale datasets, and to avoid some undesirable modeling assumptions. Here we study the…
It is well-known that 0 is the absorbing state for a branching system. Each particle in the system lives a random long time and gives a random number of new particles at its death time. It stops when the system has no particle. This paper…
A particular continuous-time multitype branching process is considered, it is the continuous-time embedding of a discrete-time process which is very popular in theoretical computer science: the m-ary search tree (m is an integer). There is…
We investigate recurrence and transience of Branching Markov Chains (BMC) in discrete time. Branching Markov Chains are clouds of particles which move (according to an irreducible underlying Markov Chain) and produce offspring…
The simple Galton--Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of…
This paper is concerned with the characterizations of fixed points of the generating function of branching processes with countably infinitely many types. We assume each particle of type $i$ can only give offspring of type $j\geq i$, whose…