Related papers: A $N$-branching random walk with random selection
This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…
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…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law,…
We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…
The career of an employee can be described (under certain circumstances) by a random walk, where the states of the random walk are determined by the level and position of an employee. At each decision moment the state of the employee is…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
We propose a purely probabilistic model to explain the evolution path of a population maximum fitness. We show that after $n$ births in the population there are about $\ln n$ upwards jumps. This is true for any mutation probability and any…
We consider discrete-time branching random walks with a radially symmetric distribution. Independently of each other individuals generate offspring whose relative locations are given by a copy of a radially symmetric point process…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, $Z$ say, is in the domain of attraction of a stable law with index…
We consider the evolution of a population of fixed size with no selection. The number of generations $G$ to reach the first common ancestor evolves in time. This evolution can be described by a simple Markov process which allows one to…
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…
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…