Hierarchical Model with Allee Effect, Immigration, and Holling Type II Functional Response
In this paper, we discuss a hierarchical model, based on a Ricker competition model. The species considered are competing for resources and may be subject to an Allee effect due to mate limitation, anti-predator vigilance or aggression, cooperative predation or resource defense, or social thermoregulation. The species may be classified into a more dominant species and less dominant or ``wimpy" species or just as a predator and prey. The model under consideration also has components taking into account immigration in both species and a more structured Holling type II functional response. Local and global stability analyses are discussed and simulations are provided. We also consider demographic stochasticity on the species due to environmental fluctuations in the form of Wiener processes and we show that there are conditions under which a global solution exists, stationary distributions exists, and strong persistence in mean of the species is possible. We also use Wasserstein distance to show empirically that stochasticity can acts as bifurcation parameter.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Study on the Specialist Predator with the Allee Effect on the Prey
Predator-prey models in theoretical ecology have a long and complex history, spanning decades of research. Most of the models rely upon simple reproduction and mortality rates associated with different types of functiona…
Allee effect in models of interacting species
The search for more realistic models for interacting species has produced many adaptations of the original Lotka-Volterra equations, such as the inclusion of the Allee effect and the different Holling's types of function…
Deterministic and Stochastic Research of Cubic Population Model with Harvesting
A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function represe…
Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure
We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical populat…
Effects and biological consequences of the predator-mediated apparent competition I: ODE models
This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model wi…