Rhythm of the Deep: Two-tier acoustic organization of sperm-whale codas from click waveforms to second-order sequence dependence

Sperm-whale codas are conventionally characterized by click count and inter-click intervals (ICIs), leaving recurring differences in constituent click waveforms unresolved. This study tests whether acoustic organization is nested across two scales: within codas, where recurring click-waveform differences may complement ICI timing, and across codas, where recurring whole-coda forms may themselves carry sequence dependence. Candidate recurring click and whole-coda groupings were identified from 1,483 codas without prespecifying waveform categories, then evaluated with native-rate spectral/envelope measurements, exact nuisance matching, held-out timing contrasts, and sequence controls. At the first tier, recurring click-waveform groups differed in spectral slope, bandwidth, flatness, high/low-band energy, and envelope structure within matched date, social unit, individual, and sample-rate strata. Their composition added information about whole-coda grouping beyond timing, while timing remained informative when click composition was fixed. The richer description also carried held-out social-unit-associated information beyond timing. At the second tier, direct native-rate waveform summaries recovered the recurring whole-coda forms well above context-preserving nulls, whereas conventional timing did not; the forms also cross-cut published timing-defined coda types. The preceding two-coda context then added held-out predictive information beyond the immediately preceding coda, while a third preceding coda provided no reliable further gain. Together, these results support two-tier acoustic organization: recurring waveform differences and ICI timing jointly organize individual codas, and acoustically grounded whole-coda forms in turn show bounded second-order predictive dependence across sequences.