Related papers: Extinction phase transitions in a model of ecologi…
We investigate correlation time numerically in extremal self-organized critical models, namely, the Bak-Sneppen evolution and the Robin Hood dynamics. The (fitness) correlation time is the duration required for the extinction or mutation of…
We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead…
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…
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
Variability on external conditions has important consequences for the dynamics and the organization of biological systems. In many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental…
We construct and analyse a simple {\em reduced} model to study the effects of the interplay between a density undergoing an active-to-absorbing state phase transition (AAPT) and a fluctuating environment in the form of a broken symmetry…
We study a mechanistic mathematical model of extinction and coexistence in a generic hunter-prey ecosystem. The model represents typical scenarios of human invasion and environmental change, characteristic of the late Pleistocene,…
As a result of climate change, many populations have to modify their range to follow the suitable areas - their "climate envelope" - often risking extinction. During this migration process, they may face absolute boundaries to dispersal,…
A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…
We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
Populations are often subject to catastrophes that cause mass removal of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the results reported, it has been considered whether dispersion…
Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in…
We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the…
The requisites for the persistence of small colonies of self-replicating molecules living in a two-dimensional lattice are investigated analytically in the infinite diffusion or mean-field limit and through Monte Carlo simulations in the…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in…