Related papers: Extinction threshold in spatial stochastic logisti…
In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
The survival of populations hinges on their ability to offset local extinctions through new colonizations. The dispersal area ($A$) plays a crucial role in this process, as it determines the probability of finding colonizable vacant sites.…
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an…
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…
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental…
We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates).…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
We approximate the Bolker-Pacala model of population dynamics with the logistic Markov chain and analyze the latter. We find the asymptotics of the degenerated hypergeometric function and use these to prove a local CLT and large deviations…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations…
Established populations often exhibit oscillations in their sizes. If a population is isolated, intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a…
We prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space-time noise, corresponding to the Bak-Tang-Wiesenfeld model for self-organized criticality. This solves a problem posed and…
We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \phi until…
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…
In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…