Measuring acoustic complexity in continuously varying signals: how complex is a wolf howl?

Communicative complexity is a key behavioural and ecological indicator in the study of animal cognition. Much attention has been given to measures such as repertoire size and syntactic structure in both bird and mammal vocalizations, as large repertoires and complex call combinations may give an indication of the cognitive abilities both of the sender and receiver. However, many animals communicate using a continuous vocal signal that does not easily lend itself to be described by concepts such as ‘repertoire’. For example, dolphin whistles and wolf howls both have complex patterns of frequency modulation, so that no two howls or whistles are quite the same. Is there a sense in which some of these vocalizations may be more ‘complex’ than others? Can we arrive at a quantitative metric for complexity in a continuously varying signal? Such a metric would allow us to extend familiar analyses of communicative complexity to those species where vocal behaviour is not restricted to sequences of stereotyped syllables. We present four measures of complexity in continuous signals (Wiener Entropy, Autocorrelation, Inflection Point Count, and Parsons Entropy), and examine their relevance using example data from members of the genus Canis. We show that each metric can lead to different conclusions regarding which howls could be considered complex or not. Ultimately, complexity is poorly defined and researchers must compare metrics to ensure that they reflect the properties for which the hypothesis is being tested.