Related papers: Population invasion with bistable dynamics and ada…
Endangered populations often experience limited growth ability at low densities, a phenomenon described by the Allee effect. In this thesis, we investigate a predator-prey model incorporating the Allee effect within a two-dimensional…
The use of predator-prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka-Volterra system towards more realistic descriptions of the processes of predation, reproduction…
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…
An Allee effect occurs when the per-capita growth rate increases at low densities. Here, we investigate the evolutionary stability of a partial migration population with migrant population experiencing Allee effects. Partial migration is a…
This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch…
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 dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and…
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…
The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine…
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…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a…
We propose a reaction--diffusion model of predator--prey interaction in which the predators occupy only a subset of the prey's territory, leaving a predator-free exclusion zone. Ecological examples include marine protected areas where it is…
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…
The component Allee effect (AE) is the positive correlation between an organism's fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE…
We study the evolution in discrete time of certain age-structured populations, such as adults and juveniles, with a Ricker fitness function. We determine conditions for the convergence of orbits to the origin (extinction) in the presence of…
The management of common-pool resources is a complex challenge due to the risk of overexploitation and the tragedy of the commons. A novel framework has been introduced to address this issue, focusing on the coevolutionary relationship…
We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche. This model consists of a system of coupled…
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…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…