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Hierarchical competition models with the Allee effect III: multispecies.

S Elaydi1, E Kwessi1, G Livadiotis2

  • 1a Trinity University , San Antonio , TX , USA.

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This study introduces a new Allee effect concept for complex ecological models. It identifies conditions for species extinction, exclusion, and coexistence in hierarchical systems.

Keywords:
39A1192D25Allee effectcompetition modelsglobal dynamicsinvariant manifoldsomega limit settriangular maps

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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.