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Updated: Jan 31, 2026

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Three-species competition with non-deterministic outcomes.

Tim M A Depraetere1, Aisling J Daly1, Jan M Baetens1

  • 1KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure links 653, B-9000 Ghent, Belgium.

Chaos (Woodbury, N.Y.)
|January 3, 2019
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Summary

Non-transitive competition networks can maintain biodiversity, but deterministic models are limited. Introducing uncertainty in competition outcomes reveals that spatial dimensions critically influence species coexistence, with chaotic patterns in 1D and spiral waves in 2D preserving biodiversity.

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Area of Science:

  • Ecology
  • Theoretical Ecology
  • Biodiversity Research

Background:

  • Non-transitive competition networks are known to support high biodiversity.
  • Previous theoretical models assumed deterministic competition outcomes and identical species, limiting real-world applicability.

Purpose of the Study:

  • To investigate the robustness of the biodiversity-biodiversity link under non-transitive competition with uncertain outcomes.
  • To explore how spatial dimensions affect species coexistence in a three-species *in silico* ecosystem with probabilistic competition.

Main Methods:

  • Introduced a three-dimensional winning probability parameter space to model uncertain competition outcomes.
  • Simulated a three-species ecosystem across different spatial dimensions (well-mixed, 1D, 2D).
  • Analyzed the impact of varying degrees of uncertainty on species coexistence and biodiversity.

Main Results:

  • Well-mixed systems collapse to monoculture, similar to deterministic settings.
  • One-dimensional systems exhibit chaotic patterns that maintain biodiversity, with coexistence time following a power law related to uncertainty.
  • Two-dimensional systems show spiral waves that preserve biodiversity for moderate uncertainty; high uncertainty negatively impacts coexistence.

Conclusions:

  • Non-transitive competition can maintain species coexistence even when competition outcomes are uncertain.
  • The spatial dimension is crucial, with 1D and 2D systems showing potential for biodiversity maintenance under probabilistic competition.
  • In collapsing systems, a 'survival of the strongest' dynamic emerges, favoring species with higher competitive probabilities.