A novel framework for identifying sequential and temporal structure of mutual displays: an application to crane dances

Although elaborate mutual displays play an important role in sexual or social communication, few quantitative studies have analysed their structure. To understand the unique characteristics of the mutual displays of the red-crowned crane, Grus japonensis , we analysed the structure and sex differences of pair dances. Five measures of the dance performance (i.e. total number of elements, duration and three measures of diversity) were positively associated between partners, suggesting that their performance was mutually dependent. Despite the symmetrical features, we found sex differences in both duration (males danced longer than females) and transfer entropy (female behaviour was more likely to induce changes in males' subsequent behaviour than vice versa). Analyses of sequences showed that three behavioural elements played pivotal roles in transition, conversion and synchrony within a pair. A temporal analysis revealed that a behavioural element performed by an individual was determined by a partner's preceding one. These results suggest that the pair dance is highly structured, reinforcing the idea that this mutual signal plays an important role in this species.