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

Abstract 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.

摘要 交际复杂性是动物认知研究中的一个关键行为和生态指标。在鸟类和哺乳动物的发声研究中，人们对曲目大小和句法结构等指标给予了很多关注，因为较大的曲目和复杂的叫声组合可能表明发声者和接收者的认知能力。然而，许多动物使用连续的声音信号进行交流，这种信号不容易用“曲目”等概念来描述。例如，海豚的哨声和狼的嗥叫都有复杂的调频模式，以至于没有两种嗥叫或哨声是完全相同的。在某种意义上，这些发声是否有些可能比其他的更“复杂”呢？我们能否得出一个用于连续变化信号复杂性的定量指标呢？这样一个指标将使我们能够将常见的交际复杂性分析扩展到那些发声行为不限于刻板音节序列的物种。我们提出了连续信号复杂性的四种测量方法（维纳熵、自相关、拐点计数和帕森斯熵），并使用犬属动物的示例数据检验了它们的相关性。我们表明，对于哪些嗥叫可被视为复杂的，每种指标都可能得出不同的结论。最终，复杂性的定义并不完善，研究人员必须比较各种指标，以确保它们反映出正在检验的假设所涉及的特性。