Related papers: Immortal Branching Processes
We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The drift, diffusive…
Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival…
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
Sexually reproducing populations with small number of individuals may go extinct by stochastic fluctuations in sex determination, causing all their members to become male or female in a generation. In this work we calculate the time to…
We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
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…
We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, we firstly determine the behavior of the successive hitting…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during…
Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
We study branching processes of independently splitting particles in the continuous time setting. If time is calibrated such that particles live on average one unit of time, the corresponding transition rates are fully determined by the…