Interplay between partnership formation and competition in generalized May-Leonard games

TL;DR

This paper explores complex population dynamics in generalized May-Leonard models, revealing diverse patterns of partnership and competition, and analyzing their formation, stability, and fluctuations through mathematical and computational methods.

Contribution

It introduces a classification of dynamic behaviors in N-species May-Leonard models using adjacency matrix analysis and Fourier methods, highlighting novel partnership formations and pattern coarsening.

Findings

Partnership formations follow 'enemy of my enemy' principle.

Cyclic dominance leads to unique coarsening patterns.

Interface fluctuations depend on initial team configurations.

Abstract

In order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized May-Leonard models with $N$ species. These models have a very rich structure, characterized by different types of space-time patterns. Interesting partnership formations emerge following the maxim that "the enemy of my enemy is my friend." In specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation. We classify the different types of dynamics through the analysis of the square of the adjacency matrix. The dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a Fourier analysis. Finally, after having identified collaborating teams, we study interface fluctuations where we initially populate different parts of the system with different teams.