Related papers: A random walk with catastrophes
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
Forest-fire and avalanche models support the notion that frequent catastrophes prevent the growth of very large populations and as such prevent rare large-scale catastrophes. We show that this notion is not universal. A new model class…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We introduce a model to study the impact of catastrophes on evolutionary paths. If we do not allow catastrophes the number of changes in the maximum fitness of a population grows logarithmically with respect to time. Allowing catastrophes…
The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…
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…
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…
We introduce the following discrete time model. Each natural number represents an ecological niche and is assigned a fitness in $(0,1)$. All the sites are updated simultaneously at every discrete time. At any given time the environment may…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…
We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…
In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…
In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function…
In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The intensification and increased frequency of weather extremes is emerging as one of the most important aspects of climate change. We use Monte Carlo simulation to understand and predict the consequences of variations in trends (i.e.,…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
We consider immigration processes with binomial catastrophes and random survival parameters. Two sources of randomness are analyzed. In the first model, the survival parameter is independently resampled at each catastrophe. In the second…
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…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…