# Modeling the Evolution of Collective Synchrony

## TL;DR

This paper explores how animal groups balance the benefits and drawbacks of synchronized mating displays using a model that combines game theory and physics.

## Contribution

The study introduces a novel model combining the Kuramoto model and evolutionary game theory to explain the evolution of collective synchrony with cheaters.

## Key findings

- Stable coexistence of honest cooperators and cheaters is possible with a limit on the cheating fraction.
- Symmetric enforcement of policing early and late signalers is necessary for long-term synchrony.
- The model provides testable predictions for natural population dynamics.

## Abstract

Group synchrony in the animal kingdom is usually associated with mating. Being in sync is likely advantageous, as it may help in luring the opposite sex. Yet there are also disadvantages—such as the homogenization of the group—which make it harder for individuals to stand‐out. Here we address this trade‐off, bringing together the Kuramoto model with concepts from evolutionary game theory. We focus on the existence of self‐interested cheaters, which have been extensively studied in a variety of species. In our scenario, cheating individuals take part in the synchronous group display but position themselves (in terms of phase) slightly ahead of or behind the pack. This allows them to enjoy both the group benefit of advertisement and the individual benefit of being unique. But a group can only tolerate a limited number of such individuals while still achieving synchrony. We therefore incorporate a form of policing into our model: If an individual strays too far form the group's synchronous phase, they reveal themselves as dishonest and are punished. Our model offers testable predictions regarding natural population compositions, and will hopefully spur further investigation into not only how, but also why, natural systems synchronize.

We model synchronized mating displays as a Kuramoto‐style evolutionary game with honest cooperators and phase‐shifted cheaters. Cheaters exploit group advertisement while remaining distinctive, but excessive deviation triggers policing. Our analysis shows stable coexistence with an upper bound on the fraction cheating, and predicts that only symmetric enforcement of early and late signalers sustains long‐term synchrony in animal groups.