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We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the…

Statistics Theory · Mathematics 2019-02-27 Marc Hoffmann , Aline Marguet

Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…

Probability · Mathematics 2023-04-05 Vincent Bansaye , Michele Salvi

A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…

Probability · Mathematics 2019-03-13 Jie Yen Fan , Kais Hamza , Peter Jagers , Fima C. Klebaner

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities…

Populations and Evolution · Quantitative Biology 2021-11-08 Reinaldo García-García , Arthur Genthon , David Lacoste

We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…

Dynamical Systems · Mathematics 2024-05-08 Blake McGrane-Corrigan , Oliver Mason , Rafael de Andrade Moral

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"…

Probability · Mathematics 2010-01-13 Steven N. Evans , Peter L. Ralph

Under the assumption that the initial population size of a Galton-Watson branching process increases to infinity, the paper studies asymptotic behavior of the population size before extinction. More specifically, we establish asymptotic…

Probability · Mathematics 2008-12-08 Vyacheslav M. Abramov

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…

Probability · Mathematics 2011-12-05 Nicolas Champagnat , Sylvie Méléard

We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…

Probability · Mathematics 2007-05-23 A. D. Barbour , A. Pugliese

We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…

Probability · Mathematics 2015-09-08 Helene Leman

We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this…

Populations and Evolution · Quantitative Biology 2020-02-10 Anna Kraut , Anton Bovier

We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…

Probability · Mathematics 2022-01-17 Benoît Henry , Sylvie Méléard , Viet Chi Tran

We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process, where the type of an individual includes its gamete mean…

Populations and Evolution · Quantitative Biology 2023-11-17 Athanasios Benetos , Olivier Coudray , Anne Gégout-Petit , Lionel Lenôtre , Simon Toupance , Denis Villemonais

This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…

Probability · Mathematics 2025-09-16 George P. Yanev

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…

Probability · Mathematics 2022-10-31 Yanyun Li , Junping Li

In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…

Functional Analysis · Mathematics 2014-03-24 Shangbin Cui , Meng Bai

This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…

Probability · Mathematics 2016-11-10 Nicolas Champagnat , Denis Villemonais

We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large…

Probability · Mathematics 2015-11-11 Mamadou Ba , Etienne Pardoux

We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $\mu$ of…

Probability · Mathematics 2007-05-23 Nicolas Champagnat

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…

Probability · Mathematics 2020-05-21 Romain Abraham , Jean-François Delmas , Hui He