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Related Experiment Videos

Deterministic extinction by mixing in cyclically competing species.

Cilie W Feldager1, Namiko Mitarai1, Hiroki Ohta2

  • 1Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.

Physical Review. E
|April 19, 2017
PubMed
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Deterministic extinction is proven for cyclically competing species models with N≥3 at finite mixing rates. This study analyzes trajectories and bifurcations leading to species loss in ecological systems.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Cyclically competing species models analyze ecological dynamics.
  • The Lotka-Volterra equation is a foundational model in population dynamics.
  • Global mixing at finite rates introduces complex behaviors not seen in infinite mixing limits.

Purpose of the Study:

  • To investigate the deterministic extinction of species in a cyclically competing model.
  • To analyze the impact of finite mixing rates on species coexistence.
  • To explore the mathematical conditions leading to species extinction in ecological networks.

Main Methods:

  • Perturbation analysis from the infinite mixing rate limit.
  • Analytical investigation of deterministic extinction.

Related Experiment Videos

  • Numerical analysis of extinction trajectories and bifurcations for small species numbers.

    • Main Results:

    • Analytical evidence for deterministic extinction at finite mixing rates for N≥3 species.
    • Demonstration that extinction occurs at specific, large but finite mixing rates.
    • Numerical results reveal trajectories and global bifurcations associated with changing mixing rates.

    Conclusions:

    • Finite mixing rates can deterministically drive species extinction in competing systems.
    • The model exhibits complex dynamics, including bifurcations, as mixing rates vary.
    • Understanding these dynamics is crucial for predicting species persistence in ecological communities.