Related papers: How far from the edge need a population be to surv…
We introduce the following model for the evolution of a population. At every discrete time $j\geq 0$ exactly one individual is introduced in the population and is assigned a death probability $c_j$ sampled from $C$, a fixed probability…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
The probability of the survival of the population of individuals of both sexes of given mature age, procreation rate and structure stability has been searched in the numerical experiment. The populations with long period of reproduction and…
We consider a stochastic model for an evolving population. We show that in the presence of genotype extinctions the population dies out for a low mutation probability but may survive for a high mutation probability. This turns upside down…
We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…
We consider an interacting particle process on a graph which, from a macroscopic point of view, looks like $\Z^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch). There are two birth rates: an inter-patch one…
A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a…
Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by $Z_0$ and the size of the $n$th change by $C_n$, $n= 1, 2,…
Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
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,…
In this kind of model, the main characteristic that determines population viability in the long term is the stochastic growth rate (SGR) denoted $\lambda_S$. When $\lambda_S$ is larger than one, the population grows exponentially with…
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 derive a central limit theorem for a spatial $\Lambda$-Fleming-Viot model with fluctuating population size. At each reproduction, a proportion of the population dies and is replaced by a not necessarily equal mass of new individuals. The…
We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $\lambda>0$. With probability $p \in [0,1]$ an offspring is fertile…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…
Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective of this paper is to present a general population model which takes essential features…