Complexity of mutual communication in animals exemplified by paired dances in the red-crowned crane

Non-human animals commonly perform mutual communication in which two individuals simultaneously exchange information in an interaction that can comprise multiple components and multimodal signals. The forms of mutual communication vary widely, ranging from simple greeting ceremonies to complex paired dances including ultiple behavioural elements. Our understanding of mutual communication lags markedly because few systematic studies have examined this topic. In this review, we used the example of paired dances in red-crowned cranes (Grus japonensis) to examine two important aspects of mutual communication: structure and function. We reviewed the difficulty analysing the key characteristics of structure quantitatively (e.g. sequential pattern and complexity), and examined suitable analytic methods such as etermining the four levels of its characteristics. We proposed that a combination of current methods and new methods, such as the Shannon entropy index and temporal associations among behavioural elements, is necessary to quantify the complexity of mutual communication. Regarding the function of paired dances, we critically discuss the pair bond hypothesis, which suggests that a paired dance strengthens pair bonds in monogamous, long-living birds. Testing this classical hypothesis remains a challenge due to the difficulty of performing quantitative analyses of paired dances and the ambiguous concept of pair bonds. We hope that the questions and predictions raised in this paper will encourage future research on mutual communication in non-human animals.