Related papers: Population extinction in a time-modulated environm…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover…
Given that extinction in a bisexual population is certain, we study a way to approximate the time when this extinction occurs. Our study is based on standard tools from Extreme Value Theory, which in practice are very easy to implement. We…
The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…
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).…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
Isolated populations ultimately go extinct because of the intrinsic noise of elementary processes. In multi-population systems extinction of a population may occur via more than one route. We investigate this generic situation in a simple…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
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,…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
The present paper is devoted to the study of the long term dynamics of diffusion processes modelling a single species that experiences both demographic and environmental stochasticity. In our setting, the long term dynamics of the diffusion…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We study the effect of phase separating diffusive dynamics on the mean time to extinction in several reaction-diffusion models with slow reactions. We consider a continuum theory similar to model AB, and a simple model where individual…
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…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion…
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…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…