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When organisms require the same limited resources within an environment, they may have to compete for them. Competition is a net-negative interaction. Even if two competing individuals or populations do not interact directly, the overall fitness of both competitors is lowered as a result of not having full access to the limited resource.
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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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A fixed action pattern (FAP) is a specific, hard-wired sequence of behaviors that occurs in response to an external stimulus, called a sign stimulus. The behavior is “fixed” because it is essentially unchangeable—proceeding similarly across individuals of a species every time it occurs.
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Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational

A Cangiani1, E H Georgoulis1,2, A Yu Morozov1

  • 1Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|June 12, 2018
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Summary

Researchers discovered novel wave propagation and pattern formation in cyclic competition models. These findings enhance understanding of biological pattern formation and invasion theory.

Keywords:
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Area of Science:

  • Mathematical Biology
  • Computational Science

Background:

  • Reaction-diffusion models are crucial for studying pattern formation and wave propagation in biological and chemical systems.
  • Classical models like Lotka-Volterra with spatial dependence still hold undiscovered dynamical regimes.
  • Understanding these regimes is key to advancing fields like invasion theory and biological pattern formation.

Purpose of the Study:

  • To identify and characterize new types of wave propagation and pattern formation in a three-species cyclic competition model with spatial diffusion.
  • To explore dynamical patterns in both two and three spatial dimensions within this model.

Main Methods:

  • Utilized an automatic adaptive finite element method for numerical simulations.
  • Employed a novel a posteriori error estimate to ensure the reliability of the numerical method and error bounds.
  • Applied the framework to investigate complex spatio-temporal dynamics.

Main Results:

  • Discovered previously undocumented, highly regular spatial patterns and wave propagation behaviors.
  • These novel patterns differ significantly from those known in existing reaction-diffusion models.
  • Successfully demonstrated the exploration of these patterns in 2D and 3D spatial domains.

Conclusions:

  • The study reveals new dynamical regimes in classical reaction-diffusion models, specifically in cyclic competition.
  • The developed numerical framework enables efficient discovery and analysis of complex patterns.
  • These findings have significant implications for biological pattern formation and invasion theory research.