Related papers: Phase diagram for a logistic system under bounded …
The extinction of a single species due to demographic stochasticity is analyzed. The discrete nature of the individual agents and the Poissonian noise related to the birth-death processes result in local extinction of a metastable…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
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…
We consider the extinction regime in the spatial stochastic logistic model in $\mathbb{R}^d$ (a.k.a. Bolker--Pacala--Dieckmann--Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space…
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…
Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…
We consider a birth-death process with the birth rates $i\lambda$ and death rates $i\mu +i(i-1)\theta$, where $i$ is the current state of the process. A positive competition rate $\theta$ is assumed to be small. In the supercritical case…
Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…
Let $T$ be the extinction moment of a critical branching process $Z=(Z_{n},n\geq 0) $ in a random environment specified by iid probability generating functions. We study the asymptotic behavior of the probability of extinction of the…
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a…
Dynamics among central sources (hubs) providing a resource and large number of components enjoying and contributing to this resource describes many real life situations. Modeling, controlling, and balancing this dynamics is a general…
The problem of conditioning a continuous-state branching process with quadratic competition (logistic CB process) on non-extinction is investigated. We first establish that non-extinction is equivalent to the total progeny of the population…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
We study a general class of birth-and-death processes with state space $\mathbb{N}$ that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is…
Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We…
Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three…