Contextual and Combinatorial Structure in Sperm Whale Vocalisations
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Abstract
Sperm whales (Physeter macrocephalus) are long-lived and highly social mammals that engage in complex group behaviours, including navigation, foraging, and child-rearing. During these behaviours, sperm whales communicate primarily using sequences of short bursts of clicks with varying inter-click intervals, known as codas. Past research has identified around 150 discrete coda types globally, with 21 in the Caribbean. A subset of these have been shown to encode information about caller and clan identity. However, almost everything else about the sperm whale communication system, including basic questions about its structure and information-carrying capacity, remains unknown. In this study, we show that codas exhibit contextual and combinatorial structure with key similarities to aspects of human language and other primate communication systems. First, we report previously undescribed variations in coda structure that are sensitive to the conversational context in which they occur. We call these rubato and ornamentation , by analogy to musical terminology. These variations are systematically controlled and imitated across individual whales. Second, we show that coda types are not defined by arbitrary sequences of inter-click intervals, but instead form a combinatorial coding system in which rubato and ornamentation combine with two categorical, context-independent features that we call rhythm and tempo to give rise to a large inventory of distinguishable codas. In a dataset of 8,719 codas from the sperm whales of the Eastern Caribbean clan, this ‘sperm whale phonetic alphabet’ makes it possible to systematically explain observed variability in coda structure. Sperm whale vocalisations are more expressive and structured than previously believed, and are built from a repertoire comprising nearly an order of magnitude more distinguishable codas. These results show contextsensitive and combinatorial vocalisation systems extend beyond humans, and can appear in an organism with a divergent evolutionary lineage and vocal apparatus.
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Second, we evaluated whether sequences of codas reflect longer-term trends. To do so, we collected coda triples of the same discrete coda type, and measured the correlation between tempo drift across adjacent pairs. We found a significant positive correlation, compared to a null hypothesis that drift between adjacent pairs is uncorrelated (test: Spearman’s rank-order correlation (two-sided), r(2586) = 0.57, p = 2e−220, 95% CI= [0.54, 0.60], n = 2588). Thus, rubato is distributed across sequences of multiple codas.Finally, we evaluated whether rubato is perceived and controlled by measuring whales’ ability to match their interlocutors’ coda durations when chorusing. We measured the average absolute difference in duration between (1) pairs of overlapping codas from different whales, and (2) pairs of non-overlapping codas of the same …
Second, we evaluated whether sequences of codas reflect longer-term trends. To do so, we collected coda triples of the same discrete coda type, and measured the correlation between tempo drift across adjacent pairs. We found a significant positive correlation, compared to a null hypothesis that drift between adjacent pairs is uncorrelated (test: Spearman’s rank-order correlation (two-sided), r(2586) = 0.57, p = 2e−220, 95% CI= [0.54, 0.60], n = 2588). Thus, rubato is distributed across sequences of multiple codas.Finally, we evaluated whether rubato is perceived and controlled by measuring whales’ ability to match their interlocutors’ coda durations when chorusing. We measured the average absolute difference in duration between (1) pairs of overlapping codas from different whales, and (2) pairs of non-overlapping codas of the same discrete coda type. Durations are significantly more closely matched for overlapping codas (0.099s on average) than would be expected under a null hypothesis that chorusing whales match only discrete coda type (which would give a drift of 0.129s on average) (test: permutation test (one-sided), p = 0.0001, n = 908; see Supplementary Section 6).
I wonder if calculating the autocorrelation of coda durations might be a nice complementary measure here. Autocorrelation could give you a sense of the time scale over which the rubatos decay and, seemingly, might also provide a sense for the timescale of longer-term trends.
Similarly, I wonder if cross-correlation might be useful for comparing the information quantity shared with interlocutors? The correlation value would be interesting, in addition to any patterns of temporal lag between codas. It might be a comprehensive metric for comparing the similarities of codas over time (as opposed to just looking at overlapping codas).
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