Related papers: Allee dynamics: Growth, extinction and range expan…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
Using a reaction-diffusion model with free boundaries in one space dimension for a single population species with density $u(t,x)$ and population range $[g(t), h(t)]$, we demonstrate that the Allee effects can be eliminated if the species…
The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate…
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…
How diffusion impacts on ecological dynamics under the Allee effect and spatial constraints? That is the question we address. Employing a microscopic minimal model in a metapopulation (without imposing nonlinear birth and death rates) we…
We consider a nonlocal parabolic equation describing the dynamics of a population structured by a spatial position and a phenotypic trait, submitted to dispersion , mutations and growth. The growth term may be of the Fisher-KPP type but may…
In stochastic population dynamics, stochastic wandering can produce transition to an absorbing state. In particular, under Allee effects, low densities amplify the possibility of population collapse. We investigate this in an…
We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the…
We study the combined impact of a colored environmental noise and demographic noise on the extinction risk of a long-lived and well-mixed isolated stochastic population which exhibits the Allee effect. The environmental noise modulates the…
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic…
A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic…
A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. However, many species are…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
This paper proposes a non-phenomenological model of population growth that is based on the interactions between the individuals that compose the system. It is assumed that the individuals interact cooperatively and competitively. As a…
We model sex-structured population dynamics to analyze pairwise competition between groups differing both genetically and culturally. A sex-ratio allele is expressed in the heterogametic sex only, so that assumptions of Fisher's analysis do…
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…
A habitat that is moving due to environmental change may result in tipping to extinction if the rate at which it moves is too great. We use a scalar reaction-diffusion equation with a non-autonomous reaction term, representing a spatially…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…