Related papers: Extinction in Lotka-Volterra model
This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…
We aim to clarify the relationship between interacting three-species models and the two-species Lotka-Volterra (LV) model. We utilize mean-field theory and Monte Carlo simulations on two-dimensional square lattices to explore the temporal…
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…
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…
The Allee effect describes a decline in population fitness at low densities, potentially leading to extinction. In predator-prey systems, an emergent Allee effect can arise due to interactions such as density-dependent maturation rates and…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of Math. Biol. `18) where we have characterized the persistence…
Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial…
A fundamental problem in evolutionary ecology research is to explain how different species coexist in natural ecosystems. This question is directly related with species trophic competition. However, competition theory, based on the…
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 consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…
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 employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state…
We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…
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…