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Competition and allelopathy with resource storage: two resources.

James P Grover1, Feng-Bin Wang2

  • 1Department of Biology and Program in Earth and Environmental Science, University of Texas at Arlington, P.O. Box 19498, Arlington, TX 76019, United States.

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Summary
This summary is machine-generated.

Allelopathy, the production of toxins between species, can destabilize simple ecological models. Introducing toxins can lead to unpredictable outcomes like harmful algal blooms, especially under high resource conditions.

Keywords:
CoexistenceDroop׳s modelGlobal stabilityHarmful algaeMultiple attractors

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Environmental Science

Background:

  • Chemostat models are used to study species competition for resources.
  • Allelopathy, the production of toxins by one species affecting another, is a key ecological interaction.
  • Previous models without toxins showed competitive exclusion or stable coexistence.

Purpose of the Study:

  • To investigate the impact of allelopathy on a mathematical model of two-species competition for two resources in a chemostat.
  • To analyze how toxins affect competitive outcomes, including coexistence and exclusion.
  • To explore the conditions leading to multiple attractors and unpredictable population dynamics.

Main Methods:

  • Mathematical modeling of interspecies competition with resource storage and toxin production.
  • Analysis of species invasibility into resident equilibria.
  • Numerical analysis of model behavior under varying resource supply levels and ratios.

Main Results:

  • Introducing interspecies toxins can destabilize stable coexistence, leading to bistability or multiple attractors.
  • Mutual invasibility is sufficient for globally stable coexistence but not always necessary for local stability.
  • High resource supplies can promote bistability and multiple attractors, complicating predictions.

Conclusions:

  • Allelopathy significantly alters competitive dynamics, potentially leading to complex and less predictable ecological outcomes.
  • The emergence of multiple attractors under high resource conditions has implications for understanding phenomena like harmful algal blooms.
  • Mathematical models incorporating allelopathy are crucial for predicting species interactions and ecosystem stability.