Hierarchical Model with Allee Effect, Immigration, and Holling Type II Functional Response

TL;DR

This paper presents a hierarchical ecological model incorporating Allee effects, immigration, and Holling type II responses, analyzing stability, stochasticity, and bifurcations in species competition dynamics.

Contribution

It introduces a novel hierarchical model combining multiple ecological factors and provides stability and stochastic analysis with empirical bifurcation insights.

Findings

Conditions for global solutions and stationary distributions identified.

Stochasticity can induce bifurcations in species dynamics.

Strong persistence of species possible under certain environmental fluctuations.

Abstract

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.