Spectrogram cross-correlation can be used to measure the complexity of bird vocalizations

Birdsong is an important signal in mate attraction and territorial defence. Quantifying the complexity of these songs can shed light on individual fitness, sexual selection and behaviour. Several techniques have been used to quantify song complexity and be broadly categorized into measures of sequential variations and measures of diversity. However, these methods are unable to account for important acoustic features like the frequency bandwidth and the variety in the spectro-temporal shape of notes which are an integral part of these vocal signals. This study proposes a new complexity method that considers intra-song note variability and calculates a weighted index for birdsongs using spectral cross-correlation. We first compared previously described methods to understand their advantages and limitations based on the factors that would affect the complexity of songs. We then developed a new method, Note Variability Index (NVI), which incorporates the spectral features of notes to quantify complexity. This method alleviates the need for manual classification of notes that can be error-prone. We used spectrogram cross-correlation to compare notes within a song and used the output values to quantify song complexity. To evaluate the efficacy of the new method, we generated synthetic songs to caricature extremes in song complexity and compared selected conventional complexity methods along with the NVI. We provide case-specific limitations of these methods. Additionally, to examine the efficacy of this new method in real-world scenarios, we used natural birdsongs from multiple species across the globe with varying song structures to compare conventional methods with NVI. To our knowledge, NVI is the only song complexity method that captures the variation of spectro-temporal shapes of the notes in songs where the conventional methods fail to distinguish between similar song structures with different note types. Furthermore, as NVI does not need a manual classification of notes, it can be easily implemented for any type of birdsong with existing sound analysis software; it is quick, avoids the possible subjectivity in note classification and can be automated for large datasets.