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We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy…

Probability · Mathematics 2012-02-01 Julien Berestycki , Nathanael Berestycki , Vlada Limic

Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…

Probability · Mathematics 2007-05-23 P. Pfaffelhuber , A. Wakolbinger

The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…

Probability · Mathematics 2021-07-01 Jochen Blath , Marcel Ortgiese

When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads…

Probability · Mathematics 2023-03-14 María Emilia Caballero , Adrián González Casanova , José-Luis Pérez

We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…

Probability · Mathematics 2025-01-30 Sylvain Billiard , Charles Medous , Charline Smadi

Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk…

Probability · Mathematics 2013-09-06 Amarjit Budhiraja , Dominik Reinhold

We give a short overview on our work on ancestral lineages in spatial population models with local regulation. We explain how an ancestral lineage can be interpreted as a random walk in a dynamic random environment. Defining regeneration…

Probability · Mathematics 2021-07-22 Matthias Birkner , Nina Gantert

Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…

Probability · Mathematics 2018-06-05 Alison M. Etheridge , Thomas G. Kurtz

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…

Probability · Mathematics 2020-01-06 Dang H. Nguyen , Edouard Strickler

We consider a critical branching process $Y_{n}$ in an i.i.d. random environment, in which one immigrant arrives at each generation. Let $% \mathcal{A}_{i}(n)$ be the event that all individuals alive at time $n$ are offspring of the…

Probability · Mathematics 2022-08-17 Charline Smadi , Vladimir A. Vatutin

We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics. More specifically, we extend the…

Probability · Mathematics 2011-05-11 Matthias Birkner , Jochen Blath , Matthias Steinruecken

We study the multi-type Cannings population model. Each individual has a type belonging to a given at most countable type space $E$. The population is hence divided into $|E|$ subpopulations. The subpopulation sizes are assumed to be…

Probability · Mathematics 2025-04-16 Maximilian Flamm , Martin Möhle

We consider a one-dimensional dyadic branching Brownian motion on $\mathbb{R}$ with positive drift $\beta \in (0,1)$, branching rate $1/2$, reflected at $0$ and killed at a boundary $L > 0$. The killing boundary $L$ is chosen so that the…

Probability · Mathematics 2026-04-06 Florin Boenkost , Julie Tourniaire

We consider branching processes for structured populations: each individual is characterized by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may…

Probability · Mathematics 2025-03-06 Vincent Bansaye , Tresnia Berah , Bertrand Cloez

Because biological processes can make different loci have different evolutionary histories, species tree estimation requires multiple loci from across the genome. While many processes can result in discord between gene trees and species…

Quantitative Methods · Quantitative Biology 2018-03-13 Md. Shamsuzzoha Bayzid , Siavash Mirarab , Bastien Boussau , Tandy Warnow

Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…

Populations and Evolution · Quantitative Biology 2012-07-31 Peter Pfaffelhuber , Benedikt Vogt

The coalescent is a foundational model of latent genealogical trees under neutral evolution, but suffers from intractable sampling probabilities. Methods for approximating these sampling probabilities either introduce bias or fail to scale…

Statistics Theory · Mathematics 2026-02-19 Martina Favero , Jere Koskela

The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the $\Lambda$-coalescent. In particular we formulate the…

Probability · Mathematics 2014-12-19 Boubacar Bah , Etienne Pardoux

In this work we study the stochastic process of two-species coagulation. This process consists in the aggregation dynamics taking place in a ring. Particles and clusters of particles are set in this ring and they can move either clockwise…

Analysis of PDEs · Mathematics 2014-04-22 Carlos Escudero , Fabricio Macia , Raul Toral , Juan J. L. Velazquez

We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\{1,\ldots,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be…

Probability · Mathematics 2013-11-27 Cedric Bernardin , Fabio Lucio Toninelli