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Updated: Apr 16, 2026

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Competitive exclusion and coexistence in an n-species Ricker model.

Azmy S Ackleh1, Paul L Salceanu

  • 1a Department of Mathematics , University of Louisiana at Lafayette , Lafayette , LA 70504 , USA.

Journal of Biological Dynamics
|March 19, 2015
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Summary

This study identifies conditions for a single species to dominate in a competition model, driving others to extinction. It also explores complex coexistence dynamics in smaller species groups.

Keywords:
Ricker competition modelcompetitive exclusionpersistencepopulation dynamics

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Ecological models are crucial for understanding species interactions.
  • The Ricker model is a standard tool for studying population dynamics and competition.
  • Existing research provides insights into species competition but leaves room for further analysis.

Purpose of the Study:

  • To analyze a discrete-time Ricker competition model with 'n' species.
  • To establish conditions for the survival of one species and extinction of others.
  • To investigate coexistence scenarios for a three-species model.

Main Methods:

  • Analysis of a discrete-time Ricker competition model.
  • Derivation of sufficient conditions based on competition coefficients.
  • Mathematical investigation of species persistence and extinction.
  • Numerical simulations for illustrating dynamics.

Main Results:

  • Sufficient conditions determined for single-species survival and extinction of competitors.
  • Results extend and complement existing literature on competition models.
  • For three species, scenarios for robust uniform persistence (coexistence) were explored.
  • Numerical simulations revealed complex dynamics, with coexistence not implying convergence to equilibrium.

Conclusions:

  • Competition coefficients alone can determine the dominance and extinction of species.
  • Coexistence in multi-species Ricker models can exhibit intricate and non-convergent dynamics.
  • The study contributes to a deeper understanding of ecological competition and population stability.