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.
Amichay et al. (Sun,) studied this question.