The acoustic complexity index (ACI): theoretical foundations, applied perspectives and semantics

The acoustic complexity index (ACI) is a commonly used metric in ecoacoustics, demonstrating reliability across diverse environments and ecological conditions. However, this index requires specific procedures to be applied correctly. Based on the Canberra metric, the ACI is an unsupervised metric formulated to extract information from fast Fourier transform (FFT) sonic matrices. The ACI measures contiguous differences in acoustic energy of each frequency bin along temporal steps (ACI tf ) and a temporal interval along the frequency bins (ACI ft ). Aggregating data after an FFT with a clumping procedure allows for better scaling of sonic signals before computing the ACI. A filter must be applied to reduce the effects of nonenvironmental signals produced by microphone electrical noise . Due to the singularity of the index for values of 0, ACI requires ad hoc procedures to exclude element pairs for which one of the elements is equal to 0 from the comparisons. The spectral and temporal sonic signatures are vectors obtained from the sequence of ACI tf and ACI ft values, respectively. The comparison between sonic signatures using the chord distance index returns spectral and temporal sonic dissimilarities, allowing the evaluation of sonic patterns at different temporal and spatial resolutions. Sonic variability, sonic evenness, and the effective number of frequency bins are further derivative metrics that help interpret sonic heterogeneity by distinguishing the temporal and spatial heterogeneity of sonoscapes. Moreover, this paper proposes changing the terminology of ‘acoustic complexity index' to ‘sonic heterogeneity index.'