Exploring statistical relations between coda sequences of Dominica sperm whale pairs

In recent years, there has been a growing interest in the study of marine mammal vocalisations, particularly to understand their behavioural implications and to explore novel linguistic potentials. Among marine mammals, sperm whales (Physeter macrocephalus) have been identified to possess a highly intricate and diverse vocal repertoire, using sequences of clicks known as codas. In this research, we explore temporal dependencies between the codas within longer bouts as a first step towards understanding their longer vocal exchanges. Our results from analysing simultaneously emitted coda sequences from sperm whale pairs demonstrate that the structure of the next coda produced by the second whale is predictable and influenced by a sequence of up to 10 preceding codas from the first whale. The predictive features include the coda duration, the first and second inter-click-interval, and the duration of the delay between the codas. We explore the level of dependencies between the coda sequences by mutual information analysis. The prediction level is compared for a hidden Markov model, a multi-layer Long-Short-Term Memory (LSTM) and transformers models. Our findings provide insight into the complexity of sperm whale vocalisation interactions.