Related papers: On the Eve property for CSBP
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
We study the pathwise description of a (sub-)critical continuous-state branching process (CSBP) conditioned to be never extinct, as the solution to a stochastic differential equation driven by Brownian motion and Poisson point measures. The…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
This paper is concerned with Crump-Mode-Jagers branching processes, describing spread of an epidemic depending on the proportion of the population that is vaccinated. Births in the branching process are aborted independently with a…
In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
The dynamics of gene regulatory networks are often modeled with the assumption of cellular homogeneity. However, this assumption contradicts the plethora of experimental results in a variety of systems, which designates that cell…
Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…
Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random…
Population-size dependent branching processes (PSDBP) and controlled branching processes (CBP) are two classes of branching processes widely used to model biological populations that exhibit logistic growth. In this paper we develop…
We consider a population constituted by two types of individuals; each of them can produce offspring in two different islands (as a particular case the islands can be interpreted as active or dormant individuals). We model the evolution of…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the…
We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of…
Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective of this paper is to present a general population model which takes essential features…
A branching L\'evy process can be seen as the continuous-time version of a branching random walk. It describes a particle system on the real line in which particles move and reproduce independently in a Poissonian manner. Just as for L\'evy…