Related papers: Lambda-Fleming-Viot processes arising in logistic …
We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…
Our results characterize the long-term behavior for a broad class of $\Lambda$-Wright--Fisher processes with frequency-dependent and environmental selection. In particular, we reveal a rich variety of parameter-dependent behaviors and…
We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence…
Coalescents with multiple collisions (also called Lambda-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with…
We consider an infinite-dimensional system of stochastic differential equations describing the evolution of type frequencies in a large population. The type of an individual is the number of deleterious mutations it carries, where fitness…
$\Lambda$-Wright--Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
We consider the problem of estimating the elapsed time since the most recent common ancestor of a finite random sample drawn from a population which has evolved through a Bienayme-Galton-Watson branching process. More specifically, we are…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which…
The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
The purpose of this paper is to extend the investigation of the Fleming-Viot process in discrete space started in a previous work to two specific examples. The first one corresponds to a random walk on the complete graph. Due to its…
We study the genealogies of samples of $k$ distinguished particles drawn from the population alive at some fixed time in a continuous-time multitype Bienaym\'e-Galton-Watson (MBGW) process under two different type dependent sampling…