Related papers: Branching processes with competition and generaliz…
Inspired by the work of [Kempe, Kleinberg, Oren, Slivkins, EC13] we introduce and analyze a model on opinion formation; the update rule of our dynamics is a simplified version of that of Kempe et. al. We assume that the population is…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
The classical Ray-Knight theorems for Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origin, or at the first hitting time of a given position b by…
Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under…
We propose a type-dependent branching model with mutation and competition for modeling phylogenies of a virus population. The competition kernel depends for any two virus particles on the particles' types, the total mass of the population…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…
In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here,…
The birth/death process with mutation describes the evolution of a population, and displays rich dynamics including clustering and fluctuations. We discuss an analytical `field-theoretical' approach to the birth/death process, using a…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyse a version of such models…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
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…
A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…