Hierarchical competition models with the Allee effect III: multispecies

Area of Science:

• Mathematical Biology
• Theoretical Ecology
• Dynamical Systems

Background:

• The Allee effect, where population growth rate decreases at low densities, is crucial in ecology.
• Understanding species interactions and population dynamics is vital for conservation.
• Higher-dimensional systems present complex challenges for ecological modeling.

Purpose of the Study:

• To propose a generalized Allee effect for higher-dimensional triangular maps.
• To establish a global dynamics theory for these systems.
• To apply the theory to multi-species hierarchical models, specifically three-species Ricker competition.

Main Methods:

• Development of a novel theoretical framework for the Allee effect in higher dimensions.
• Application of global dynamics theory to analyze multi-species competition models.
• Detailed mathematical analysis of three-species Ricker competition models incorporating the Allee effect.

Main Results:

• A general notion of the Allee effect for higher-dimensional triangular maps is proposed.
• A global dynamics theory is established and applied to hierarchical models.
• Specific regions of extinction, exclusion, and coexistence were identified for three-species Ricker models.

Conclusions:

• The established theory provides a robust framework for analyzing complex ecological dynamics.
• The findings offer insights into the persistence and stability of multi-species systems under Allee effects.
• This work advances the understanding of population dynamics in hierarchical ecological models.