Characterization of spiraling patterns in spatial rock-paper-scissors games

Area of Science:

• Ecology
• Theoretical Biology
• Mathematical Biology

Background:

• Spatiotemporal arrangement of interacting populations is crucial for species diversity.
• Cyclic competition models, such as "rock-paper-scissors," are key to understanding ecological dynamics.

Purpose of the Study:

• Investigate spatiotemporal patterns in a three-species cyclic competition model in two dimensions.
• Characterize spiral wave formation and properties under varying conditions.

Main Methods:

• Utilized a generic metapopulation model with "rock-paper-scissors" interactions, including reproduction, mutation, and individual movement.
• Combined analytical techniques, including complex Ginzburg-Landau equation analysis, with numerical simulations.
• Performed a multiscale expansion around the model's Hopf bifurcation.

Main Results:

• Obtained the model's phase diagram near the Hopf bifurcation.
• Quantitatively characterized spiraling patterns in different phases.
• Identified conditions under which spatial "rock-paper-scissors" competition generates stable spiral waves.
• Determined the influence of nonlinear mobility on spiral wave dynamics.

Conclusions:

• Spatial cyclic competition can lead to stable spiral waves.
• Nonlinear mobility plays a significant role in modulating these ecological patterns.
• The study provides a quantitative understanding of pattern formation in ecological systems.