Pattern formations driven by cyclic interactions: a brief review of recent developments

TL;DR

This paper reviews recent mathematical modeling research on pattern formations caused by cyclic interactions, emphasizing their role in biodiversity maintenance and potential links to social evolution, highlighting future research directions.

Contribution

It provides a comprehensive overview of recent developments in modeling cyclic interactions and their implications for biodiversity and social systems.

Findings

Cyclic dominance models help explain biodiversity persistence.

Mathematical models reveal complex pattern formations.

Potential links between ecological and social cyclic interactions.

Abstract

Lotka's seminal work (A.J. Lotka A., Proc. Natl. Acad. Sci. U.S.A. 6 (1920) 410) "on certain rhythmic relations'' is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It is because non-transitive interactions have paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires deeper understanding of related dynamical processes. In this perspective article we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.