Extreme Rhythm Keeping in Long‐Range Slow Click Communication of Sperm Whales

ABSTRACT

Male sperm whales produce loud, low‐frequency clicks at low repetition rates. By combining measurements of source properties with sound propagation modeling, we show that sperm whale slow clicks with source levels > 200 dB re 1 µPa (peak−peak) are the loudest communication signal of any mammal, and that such loud, low‐frequency clicks in deep ocean waters have an estimated active space of up to 70 km. We show that these slow clicks are highly rhythmic at rates of 0.1−0.3 Hz, which is an order of magnitude slower than other rhythmic communication signals among mammals and birds. Thus, slow clicks may allow for timing information to be maintained over extreme distances, and we, therefore, propose that sperm whale slow click production is a low entropy, long‐range communication signal that may offer honest advertisement through rhythm‐keeping to distant receivers. We speculate that the production of such loud, rhythmic clicks at extremely slow rates may be achieved by the sperm whales using extrinsic echo information from the environment to maintain extreme isochrony.

In this study, we show that male sperm whales produce low‐frequency slow clicks at low repetition rates with extreme source levels > 200 dB re 1 µPa (pp), making them the loudest mammalian communication signal, with an estimated active space of ∼70 km. Slow clicks are highly rhythmic at rates of 0.1−0.3 Hz, which is an order of magnitude slower than other rhythmic communication signals among mammals and birds.

1. Introduction

Rhythmicity, the temporal structuring of signals in time, plays a critical role in animal communication across diverse taxa [1, 2]. From the synchronized chorusing of frogs and insects to the elaborate vocal or percussion sequences of birds and primates, rhythmic patterns enable individuals to convey information, coordinate behavior, and optimize signal transmission in noisy environments [3]. This temporal organization of communication signals often reflects evolutionary adaptations in response to ecological and social drivers, including the need for mate attraction, territory defense, and group cohesion [4, 5]. Rhythmic communication may be innate or learned and is modulated and entrained in different species by intrinsic neural oscillators, biomechanical resonators, and extrinsic circadian or ultradian biological rhythms [5]. Furthermore, it can be modulated and entrained via learned and volitional motor patterns [6]. Recent advances in bioacoustics, neuroethology, and computational modeling have begun to elucidate the neural and biomechanical underpinnings of rhythmic signaling, revealing fundamental parallels between human musicality and nonhuman rhythmic behaviors [1, 2]. Comparative studies highlight both convergence and divergence in rhythmic capabilities, suggesting that rhythmicity has evolved independently under similar selective pressures [7, 8, 9, 10]. Moreover, interspecific and intraspecific variation in rhythmicity provides a valuable framework for investigating the cognitive, auditory, and sensory mechanisms and vocal‐motor control involved in temporal pattern recognition and production. Understanding rhythmicity in animal communication not only informs us about the convergent evolution of complex signaling systems among various taxa, including birds and mammals, but also offers insight into the functional underpinnings of rhythm perception and production in humans.

Rhythmicity in communication signals also plays a role in cetacean (whales, dolphins, and porpoises) communication [11]. The rhythmic structure of their vocalizations is hypothesized to enhance signal transmission across vast oceanic distances, facilitate individual or group recognition, and encode behavioral or contextual information [12, 13, 14, 15, 16]. Cetaceans are large‐brained, marine predators with a suite of unique sensory adaptations to hunt, navigate, and communicate in water. As visual cues are available only over short distances in low‐light and murky waters, cetaceans critically rely on sound, which propagates much farther underwater than light. Toothed whales (odontocetes) produce sounds for active sensing to hunt and navigate via echolocation as well as for communication [17]. Echolocation in toothed whales takes place by emission of powerful and directional clicks and subsequent auditory analysis of returning echoes milliseconds later [17]. Communication in many odontocete species also involves emission of tonal whistles that may carry identity information about the transmitter to mediate behavioral transitions and social coordination [18, 19, 20, 21]. Toothed whales produce clicks by the right pair of the so‐called phonic lips situated in a unique sound‐producing nasal complex around the blowhole [22]. In contrast, tonal communication sounds are, for those species that produce them [23], produced by a left pair of phonic lips in the same nasal sound production system, allowing many toothed whales to control the operation of two sound sources simultaneously to echolocate and communicate in tandem [22]. Range estimation with echolocation requires time keeping of the delay between outgoing clicks and returning echoes, and toothed whales have, therefore, evolved an acute auditory time resolution that, in turn, may allow them to also tap into detailed timing patterns of communication signals. Besides producing clicks for echolocation, many species of toothed whales also communicate with clicks by emitting them in stereotyped repetition rate patterns called burst pulses or rasps [24, 25]. Some species, such as cephalorhynchus dolphins and porpoises, seemingly do not whistle, but produce clicks and burst pulse patterns for communication using one or both phonic lip pairs [26, 27, 28]. Specifically, several small species of toothed whales, such as porpoises, use the same stereotyped, high‐frequency clicks both to echolocate prey and to communicate, using short, context‐dependent bursts of clicks with repetition rates of up to >1000 clicks per second [29, 30].

In the largest of the toothed whales, the sperm whale (Physeter macrocephalus), the sound‐producing nasal complex has evolved to be of extreme proportions, making up 1/3 of the body length in mature males and reaching a mass of more than 5 tons [31] (Figure 1A). Sperm whales thereby have the largest sound production system in the animal kingdom, made up of a complex system of a single, right large pair of phonic lips acoustically connected to the water via large containers of spermaceti oil bounded by air sacs [32, 33, 34]. Despite their complex social structure and large brains, sperm whales use their giant nose to produce a surprisingly limited vocal repertoire of mainly four click types used for both echolocation and communication: multipulsed usual clicks, buzzes, codas, and slow clicks [35, 36]. The usual clicks are produced at the highest known source levels (SLs) of any animal, up to 240 dB re 1 µPa peak−peak (pp) at 1 m in a narrow 10‐degree beam and at slow repetition rates of 1–3 Hz (Figure 1B) [36]. These powerful clicks centered at a frequency of 10–20 kHz are used for long‐range echolocation of deep‐sea prey, allowing sperm whales to locate and track prey several hundreds of meters ahead of them [37]. When sperm whales are within some 10 m of their prey, they transition to a buzz made up of much weaker, but higher frequency, clicks produced at repetition rates of around 50 Hz to enable acute tracking of their prey for capture (Figure 1B) [38]. Acoustic communication in sperm whales is mainly mediated by codas [39]; medium‐frequency clicks with frequencies around 3–4 kHz that are emitted in approximately 1‐s long, stereotyped rhythmic patterns of 3–11 clicks (Figure 1C). Codas are mainly exchanged among members of female social groups when socializing at the surface and during the descent and ascent of deep dives [40]. Growing evidence suggests that both the number of clicks in each coda and their exact timing may be vehicles of rhythmic information transfer of behavioral state and perhaps both individual and cultural affiliation [41, 42, 43]. Coda clicks have moderate SLs around 170 dB re 1 µPa (pp) at 1 m, leading to a median estimated active space of coda communication of <4 km [44]. Thus, sperm whale coda communication serves to mediate social cohesion and behavioral transitions within social groups or between closely spaced social groups [44]. This raises an interesting conundrum of how sperm whales find conspecifics and interact over the vast ranges in the deep‐water basins of the world's oceans they call home.

FIGURE 1.

Click types of sperm whales. (A) An overview of the sound production system of a sperm whale. A, blowhole; B, phonic lips; C (dark blue), distal air sac; D (dark blue), right naris; E (light blue), left naris; F (dark blue), frontal air sac; G, junk; H, brain; I, rostrum; J, mandible. Illustrations by Astrid S. Uebel. (B) Usual clicks with longer inter‐click intervals (ICIs) and buzz clicks with shorter ICI produced within an echolocation sequence. (C) Series of coda clicks. (D) Slow click train.

The intriguing, but less studied, fourth click type of sperm whales may provide the answer to that question. So‐called slow clicks are known to be produced only by male sperm whales, which display a marked sexual dimorphism both in overall size and in the relative proportions of their sound‐producing nose [45]. Adult male sperm whales are found in higher latitudes than females, and they return to lower latitudes to breed [46]. The males produce slow clicks both at higher and lower latitudes, and near the surface as well as at depths [36, 47, 48, 49, 50]. The limited data available suggest that they are medium‐frequency clicks around 3 kHz produced at very low repetition rates of 0.1−0.3 Hz, and with estimated SLs of 175–190 dB re 1 µPa (RMS) at 1 m [36].

Such properties of low‐frequency emphasis with low absorption and apparently high SLs lend themselves to long‐range detection, prompting us here to hypothesize that sperm whale slow clicks have the attributes to serve in slow rhythmic long‐range signaling. Here, we test that hypothesis by combining high‐quality source property measurements with sound propagation modeling and rhythmic analysis of slow click recordings.

2. Materials and Methods

2.1. Source Parameter Estimation of Slow Clicks

Recordings to estimate SLs of slow clicks were made off the Seychelles (S9°32’, E46°43’). Here, a single physically mature male sperm whale was encountered in the proximity of a social unit of approximately 10 female and young sperm whales. All slow clicks had an inter‐pulse interval (IPI) of 7.2 ms, consistent with a 15 m animal using the equation from Growcott et al. [51]. As only males grow to that length in sperm whales, we could unambiguously assign the clicks to the single male. Acoustic recordings were made with a single hydrophone (B&K 8101, sensitivity −184 dB re 1 V/ µPa, flat frequency response from 0.015 to 70 kHz) suspended from the vessel R/V Odyssey at a depth of 4 m from the surface. At all times, the hydrophone was positioned between the whale and the vessel. The hydrophone was connected to one channel of a DAT stereo‐recorder (Sony TCD‐D3) with a flat frequency response between 0.1 and 22 kHz at a sampling rate of 48 kHz. Throughout most of the 30‐min‐long recording, the DAT chain had a fixed gain (Cliplevel = 181 dB re 1 µPa), except for a period of 3 min where it was changed to avoid clipping (Cliplevel = 201 dB re 1 µPa). The distance to the male sperm whale was measured by an observer via a laser range finder, and distance estimates, as well as general comments on the behavior of the animals, were simultaneously annotated on the second channel of the DAT recorder. The recording chain was calibrated for both gain settings prior to and after recordings in the field using a Brüel and Kjær 4223 pistonphone and an on‐site tone generator (100 mV, 3 kHz sinus signal).

All slow clicks were recorded at a distance to the male of a maximum of 200 m and manually extracted from the recording in Adobe Audition version 3.0. The clicks had IPIs of 7.2 ms. Only slow clicks produced near the surface with a signal‐to‐noise ratio (SNR) of at least 10 dB were included for further analysis, defined as the ratio between the root‐mean‐square (RMS) level of the click 0.2 ms before to 0.8 ms after the highest peak and the RMS level of the noise in a 3 ms window 30 ms before the highest peak (following the procedure of Bøttcher et al. [52]).

All source parameters were quantified based on the procedure described by Madsen and Wahlberg [53] in MATLAB version 2024a (www.mathworks.com). The clicks were extracted from the raw recordings in a 60 ms symmetrical window centered around the peak amplitude of the click. The waveform was high‐pass filtered (500 Hz, 4‐pole Butterworth filter), and prior to quantification of click duration and amplitude, it was interpolated by a factor of 10. The click duration was quantified as the −10 dB endpoint of the amplitude (Hilbert) envelope, known as the D duration [54] (Figure 2A,C). Received levels were then quantified as the peak−peak amplitude, RMS amplitude, and the energy flux density (EFD) level. The RMS received level was computed over the D duration, and the EFD level was calculated by adding 10*log₁₀ (duration, in seconds) to the RMS level. To emphasize that we did not know the recording aspect to the acoustic axis, apparent source levels (ASLs, sensu Møhl et al. [31]) were then quantified using the measured distance to the whale at the time of the click by assuming spherical spreading and neglecting absorption owing to the short ranges and relatively low frequency of the clicks. The power spectrum for each click was computed using a 512‐point FFT (interpolated to 5120 for a nominal frequency resolution of ∼94 Hz). This spectrum was used to quantify the centroid frequency and the RMS bandwidth.

FIGURE 2.

(A) Spectrogram of a slow click recorded at a distance of 200 m (spectrogram: 128‐point hamming window, 95% overlap, FFT size 1024 points [zero padded], sample rate 48 kHz, frequency resolution 0.375 kHz, time resolution 0.13 ms). (B) Power spectrum of the slow click from (A), where the red line represents the centroid frequency and the red dotted line the RMS bandwidth. (C) Waveform plot of the slow click from (A), with apparent source level (ASL) on the y‐axis in kPa. The red line represents the D‐duration of the signal, and the arrows indicate the peak−peak amplitude of the signal. (D−G) Histograms showing the distribution of ASL (peak−peak), energy flux density (EFD), centroid frequency, and RMS bandwidth of all slow clicks, N = 65.

2.2. Propagation Model for Slow Clicks

To estimate the distance at which conspecifics can detect slow clicks, that is, the active space [55] of slow clicks and thereby understand how different SLs and depths affect conspecific detection range, sound propagation was modeled using the Bellhop ray tracing program [56], accessed from a Python notebook via the ARLpy library module. As the slow clicks are short pulses, the ray tracing program was used to estimate arrival time, relative amplitude, and phase of the arriving clicks, plus departure and arrival angle of each sound wave trajectory. To remain more generic, the propagation model was controlled by simplified environmental parameters using a constant salinity of 35 ppm and an exponential decaying temperature profile. Surface and bottom interfaces were assumed to be flat with a typical basalt bottom composition. For the simulation, source and receiver depth were either at 50–100 m or at 620 m, representing the center of the sound channel, that is, the SOFAR channel at which depth the focusing effect of a lower sound speed causes near‐horizontal sound transmission and thus efficient long‐range sound transmission [57]. This choice was based on the assumption that the whales would either be close to the surface or at depth, actively using the sound channel for maximizing active space.

The modeled click arrivals were convolved with the waveform of a synthetic off‐axis slow click and accumulated to generate a received time series (Figure 3A). For this, a synthetic on‐axis slow click, that is, the click waveform as produced directly in front of the whale on the acoustic axis, was constructed based on recorded slow clicks from a male sperm whale (Table 1). The generic pulse amplitude function for the synthetic on‐axis clicks was chosen such that the amplitude starts at zero and, after reaching a maximum, falls off exponentially, and the off‐axis waveform was obtained by convolving the synthetic on‐axis click with a circular piston model.

FIGURE 3.

(A) and (B) show the time series and spectrum of sperm whale slow clicks. In gray are the recorded clicks from the Seychelles field data, in solid black the modeled synthetic click, and the dashed line describes the (analytic) amplitude of the modeled click. (C) The off‐axis attenuation of the slow click beam pattern based on a flat piston model (sound source aperture) with a piston diameter of 1.1 m. The solid line represents the broadband beam pattern of the slow click, while the dashed line is the monochromatic piston response. Note that this model predicts that at an off‐axis angle of 20°, the apparent source level is reduced by 15 dB relative to the on‐axis source level. (D) shows the temperature (dotted red line) and sound speed profiles (solid blue line) as a function of depth. (E) The two‐dimensional sound transmission eigenrays based on the Bellhop transmission modeling, assuming a sound source located at 620 m depth and a receiver at 50 m. (F) and (G) depict the maximal RL of simulated time series at two different water depths; 3500 and 1100 m, respectively. The dashed black line presents spherical spreading with attenuation. The colored solid lines represent the depth of the transmitter (tx) and the receiver of the signal (rx).

TABLE 1.

Recording information.

Recording site	Latitude (decimal degrees)	Longitude (decimal degrees)	Hydrophone depth (m)	Year	Recording system	Sampling rate (kHz)
Seychelles	−9.32	46.43	4	2002	Hydrophone B&K 8101	48
Sri Lanka	6.6	82.05	Towed 100 m from the stern	2003	Two‐hydrophone array	48
Norway	69.4167	15.75	0−1581	2005	DTAG 2	96
Scotland	58.0918	−8.913433	168	2020−2021	RTSYS Sylence LP‐440 recorder with Co.l.mar GP1516M‐LP hydrophone	64
Scotland	57.09847	−8.968883	128	2020−2021		64
Scotland	56.53263	−8.856400	133	2020−2021		64

It was further assumed that the off‐axis angle is solely due to the pitch of the whale's head, that is, the transmitting whale is swimming in the direction of the receiving whale. Each pitch angle resulted in an off‐axis angle, and from all pitch angles, the off‐axis click that generated the loudest received level was selected. For detection threshold estimation, we assumed an ambient spectral noise level of 40 dB re 1 µPa²/Hz, an auditory integration bandwidth corresponding to the 1.5 kHz bandwidth of the click, a sperm whale hearing threshold below ambient noise, and a 10 dB SNR for conservatively high detection threshold of 82 dB re 1 µPa (RMS).

2.3. Rhythmic Properties of Slow Clicks

Sperm whale slow clicks were detected in acoustic recordings from different geographic regions, depths, and recording systems. Specifically, a larger data set collected both by passive acoustic recorders and onboard suction cup tags deployed on male sperm whales were included in the rhythmic analysis (Table 1). For recording details of static acoustic mooring deployments off Scotland, see Ref. [58]; for methods on the tagging of male sperm whales in Norway, see Ref. [48]; and for data collected in Sri Lanka, see Ref. [59]. For the rhythm analysis, each sound file was aurally and visually checked for slow clicks. Rough onset time of each slow click was initially manually marked in a spectrogram in MATLAB version 2024a. Recordings with low SNR (<6 dB) and with multiple slow‐clicking males were excluded from the analysis. Then, each click's precise onset time was calculated in waveform view as the maximum 6 dB increase of the 10‐times interpolated envelope of the first 10 ms of each signal. This analysis was conducted with an automated, custom MATLAB script. Subsequently, slow click inter‐click intervals (ICIs) were determined as the time difference between the onsets of two successive clicks. All slow click onsets were located for each sound file, and each recording was treated as an independent recording ID. We proceeded with the division of each recording into slow click bouts/series. Separate bouts were identified through visual inspection of the probability density plot of the ICI and through the extraction of the quantile at which 90% of the data were included. Based on these, we determined the start of a new bout whenever an interval exceeded 21 s. To avoid potential seafloor or surface reflections, only slow click trains with ICIs > 2 s were retained for further analysis.

2.3.1. Inter‐Click Intervals (ICI_k) and Tempo

ICI (hereafter also referred to as ICI_k) distribution of all slow clicks was calculated, and the local maxima were identified in the density distribution, and the corresponding tempo (in Hz) was calculated as the inverse of each peak location (1/ICI_k).

2.3.2. Rhythmic Ratios (r_k) Calculation

Rhythmic ratios describe local relationships between temporal intervals [60]. Following earlier studies (e.g., Refs. [60, 61, 62, 63]), we calculated these ratios as ICI_k/(ICI_k+ICI_k+1), where ICI_k and ICI_k+1 represent two adjacent intervals in a time series, that is, successive ICI. In addition, we generated a uniform distribution of 1000 values between 0 and 100 using the runif() function in R (stats package), corresponding to random ICI_k as the reference distribution, calculated their rhythmic ratios, and plotted these as a reference random distribution on the empirical r_k distribution [64].

2.3.3. Test Peaks Around Small‐Integer Ratios

Following the methodology introduced by Roeske and colleagues [60], we divided the density distribution of the r_k into different bins corresponding to the area close (on‐integer) or far (off‐integer) from the reference small integer (1:3, 1:2, 1:1, 2:1, 3:1). The off‐integer bin boundaries were located at [0.222, 0.235] and [0.267, 0.286] for the off‐1:3 integer, at [0.286, 0.308] and [0.364, 0.4] for the off‐1:2 integer, at [0.400, 0.444] and symmetrically on the right side of the distribution for the off‐ 2:1 and 3:1 integer. The on‐integer bin boundaries were located at [0.235, 0.25] and [0.25, 0.267] for the on‐1:3 small integer, at [0.308, 0.333] and [0.333, 0.364] for the on‐1:2 integer, at [0.444, 0.5] and [0.5, 0.556] for the on‐1:1 integer and symmetrically on the right side of the distribution for the on‐2:1 and 3:1 integer. We counted, for each recording, the number of r_k instances falling into the off‐ versus on‐small integer sectors of the curve.

To test the significance of the peak around the small integers, we used a generalized linear mixed model (GLMM; glmmTMB R package [65]). The count of r_k was specified as the response variable, and a negative binomial distribution was fitted (specified in the family argument of the model, nbinom2), suitable for modeling a count variable. We used the bin (factor variable with two levels: off, on), in interaction with the specific small integer (factor variable with five levels: 1:3, 1:2, 1:1, 2:1, 3:1) as fixed factors. An offset to the GLMM was added to account for the varying bin widths of the probability density distribution, effectively weighing the r_k counts by the bin width. The recording ID, a factor coinciding with the individual identity of the slow click‐producing sperm whale, was used as random intercepts. We tested the significance of the full model comparing it with a null model, the latter including only the offset and the random factors, with a likelihood ratio test (ANOVA with Chisq argument) [66]. p‐Values for predictors were obtained using the R summary() function. The residual distributions were checked through the simulateResiduals() function of the DHARMa package. We also checked for zero‐inflation (check_zeroinflation()) and overdispersion (check_overdispersion()) using the R package performance [67]. We performed post‐hoc pairwise comparisons through emmeans and produced an effect plot of the predicted counts through the sjPlot R package [68].

3. Results

3.1. Source Parameters of Slow Clicks

A total of 65 slow clicks associated with reliable measures of range were detected and extracted throughout the 30‐min‐long recording made off the Seychelles. During this time, the 15‐ to 16‐m‐long male sperm whale was always in the proximity (<1000 m) of a female unit producing codas. All slow clicks used for further analyses were produced at a maximum range of 200 m from the hydrophone, and all had the characteristic multipulsed nature of sperm whale clicks (Figure 2C). The recorded slow clicks were emitted at a median peak−peak ASL of 196, IQR [193−203] dB re 1 µPa (pp) at 1 m, and a median EFD of 157, IQR [155−161] dB re 1 µPa²·s. A few slow clicks had ASL's as high as 226 dB re 1 µPa (pp) at 1 m and an EFD of 182 (dB re 1 µPa²·s) (Figure 2D,E), which is likely close to or equal to SL measured on the acoustic axis. The analyzed slow clicks had a median centroid frequency of 4.3, IQR [3.5−5.6] kHz and a median RMS bandwidth of 1.7, IQR [1.4−2.3] kHz (Figure 2F,G).

3.2. Propagation Model

To estimate the active space of sperm whale slow clicks, a propagation model was run, and the model outputs were used in concert with average ambient sound levels to understand how different SLs and depths of slow click production will affect the ranges over which slow clicks can be heard by conspecifics. The initially created generic on‐axis synthetic slow click had a peak frequency of 3.5 kHz and a 50% bandwidth of 1.5 kHz (Figure 3A,B).

Modeling the sound intensity of the synthetic slow click pattern (Figure 3C) revealed a wider pattern than the expected pattern of usual echolocation clicks due to the lower frequency (3.5 kHz instead of 20 kHz). Furthermore, the propagation modeling revealed that the maximum received level (RL) of any of the multipath arrivals followed very closely a spherical spreading law when corrected for attenuation (Figure 3F,G). For the simulation geometry, the ray tracing model resulted in an acoustic communication range of around 70 km for the open ocean modeling environment applied here.

Furthermore, the ray modeling indicated that multipath arrivals that are typically associated with higher departure and arrival angles were close to straight paths; only rays at low vertical elevation angles (i.e., close to horizontal) were influenced by the sound speed profile. For this study, geometric ray analysis based on iso‐velocity sound‐speed profiles could also be adequate.

3.3. Rhythmic Properties of Slow Clicks

3.3.1. ICI_k (s) Distribution and Corresponding Repetition Rate (Hz)

To investigate the rhythmic properties of slow clicks, the ICIs were analyzed (Figure 4A). In total, the rhythmic data set comprised 1839 slow clicks from six different recording locations (Norway: two male sperm whales equipped with onboard suction cup tags, N = 209; Sri Lanka: N = 260; Scotland in three locations: N = 1272; Seychelles: N = 98) (Table 1), contributing 56 independent recordings and 1783 ICIs. Overall, the ICI distribution was right‐skewed, with a median located at 5.150 s, the third quartile at 7.139 s, and the maximum at 21.438 s (Figure S1). Individual density distributions of ICI_k were also investigated (Figure S2). The ICI distribution showed three local maxima between the minimum (0.095 s) and maximum (21.042 s): a peak at 3.196 s, a second peak at 4.723 s, and a third peak at 7.735 s, corresponding to 0.313, 0.212, and 0.129 Hz, respectively (Figure 4B).

FIGURE 4.

(A) A series of individual slow clicks. Blue horizontal lines indicate example inter‐click intervals, (ICI_k), extracted from each signal. (B) Probability density distribution of ICI_k values across the entire data set. Local maxima are indicated on the density curve. The corresponding tempo values (1/ICI_k) are shown alongside the curve. (C) Probability density functions of rhythmic ratios (ICI_k). The main (top) panel shows the overall probability density distribution of r_k values normalized to integrate to 1. The yellow curve represents the reference distribution derived from r_k values computed on a uniform random sampling of ICI_k, providing a null model for comparison. The two insets (bottom panels) present zoomed‐in views of the tails of the density distribution, specifically for r_k < 0.444 (right off‐boundary for the 1:2 small‐integer) and r_k > 0.556 (left off‐boundary for the 2:1 small‐integer). In these insets, the r_k values within each range are re‐extracted from the original distribution and renormalized so that their respective density functions integrate to 1, allowing clearer visualization and comparison of the relative distributions in these peripheral regions. (D) Scatterplot displaying the relationship between two adjacent intervals (ICI_k and ICI_k+1), on a sliding window within a bout. Dotted lines refer to the small‐integer relationships displayed in (C). (E) Effect plot showing predicted counts of r_k observations across small‐integer ratio bins (on‐ vs. off‐integer). Statistically significant pairwise comparisons are marked with blue asterisks (e.g., 1:2, 1:1, 2:1).

3.3.2. Rhythmic Ratios (r_k) Distribution

The distribution of rhythmic ratios (r_k) is displayed in Figure 4C. A prominent peak around isochrony (0.500) can be seen in the overall density distribution. Strikingly, the local maxima fell exactly at 0.501, indicating an almost perfect isochrony. The median of the distribution was also located at 0.501, while the mean was 0.502. The lower panels of Figure 4C are zoomed‐in presentations of the distribution density curve, highlighting the sections between the values 0−0.444 (right off‐boundary for the 1:2 small integer) and 0.556−1 (left off‐boundary for the 2:1 small integer). To represent the relative density of observations around those small integers, a local maximum was identified around 1:3 (0.250), at 0.249, and one around 1:2 (0.333), at 0.340. On the other hand, only one local maximum around 2:1 (0.666) was identified at 0.664. The density distributions of r_k per individual recording ID are shown in Figure S3. The relationship between adjacent intervals (ICI_k vs. ICI_k+1) is shown in Figure 4D; in line with rhythmic ratios distribution, it also displays the highest density of observations at the bisector line, corresponding to the 1:1 relationship, and around the 1:2 and 2:1 reference lines (observations falling in the vicinity of the small integers are marked in light blue in Figure 4D).

3.3.3. Peaks Significance Around Small Integers

The statistical model comparison confirmed a better data fit of the full compared to the null model (ANOVA: AICnull = 3969.743, AICfull = 3118.616, Chisq = 869.1272, p < 0.001). Overall, the count of rhythmic ratios of the full model varied across small integers (Table S1). Specifically, the observations falling within the off‐ and on‐isochrony bins were significantly more conspicuous than compared to all the other small integers. The interactions between small integer and type of bin were significant; thus, the pairwise comparisons for the interaction terms were checked (Table S1B). Results showed that the count of r_k falling within the 1:2, 1:1, and 2:1 on‐integer bins was significantly higher than for the off‐integer bins (Figure 4E). In other words, sperm whales tend to produce intervals that follow simple relationships as isochrony, where all intervals are the same, or with intervals double or half of the others.

4. Discussion

4.1. Slow Clicks Are Extremely Loud, Low‐Frequency Signals

Here, we tested the hypothesis that a unique click type, the so‐called slow clicks, exclusively produced by male sperm whales, has properties to serve slow rhythmic signaling over long distances. Previous research, using animal‐borne suction cup tags, has shown that slow clicks are not produced in a behavioral context consistent with foraging and echolocation [48]. While a communication function can conclusively be shown only via playback studies and/or detailed behavioral observations, source property data, propagation modeling, and rhythm analysis were used to test if slow clicks have the potential for serving a function in such long‐range communication [36]. In support of that hypothesis, we find in line with an earlier study [36] that slow clicks are produced with a mean ASL of more than 200 dB re 1 µPa (pp) and are thus emitted with the highest SLs of any communication signal in the animal kingdom: The peak−peak SLs are some 40 dB higher than delphinid whistles and burst pulses [69], and 10–20 dB higher than the loud, low‐frequency calls of blue and fin whales [70]. Importantly, the omnidirectional baleen whale calls are about 2 orders of magnitude longer in duration than sperm whale slow clicks. The calls of blue and fin whales, therefore, carry more energy than slow clicks when accounting for the slow click directionality inferred here. Such baleen whale calls with peak frequencies at 15–20 Hz, where there is essentially no absorption in seawater, may, under the right propagation conditions, have a potential active space of thousand kilometers (e.g., Ref. [71]). This is much larger than the maximum active space of up to 70 km obtained here modeled with the measured source properties of slow clicks. Nevertheless, this active space of slow clicks is 1–2 orders of magnitude larger than reported for other toothed whales, and importantly also much larger than that of sperm whale codas, which have SLs about 30 dB lower than slow clicks [44]. Slow clicks do not have the same maximum on‐axis peak−peak pressure SLs as usual clicks, but when accounting for the difference in directionality, the combined radiated energy is about the same in slow clicks and usual clicks [36, 72]. This means that male sperm whales likely click as loudly as they can when producing slow clicks to maximize their active space. Thus, male sperm whales have evolved the ability to produce this unique click type with properties that offer them long‐range communication potential much greater than any other toothed whale.

Considering the larger active space of slow clicks compared to codas, females and juveniles will be able to hear and potentially behaviorally respond to a distant male producing slow clicks. However, they will not be able to communicate back via codas or usual clicks unless they are within 3–10 km from the male sperm whale [36, 44]. Only males can exchange slow clicks with one another across distances of up to 70 km, corresponding to an area > 10,000 km² of ocean and perhaps even more if we did not infer ASL as true SLs. Ultimately, it remains to be understood whether slow clicks serve a specific role in long‐range communication and whether they are sufficiently important to explain the substantial sexual dimorphism in the relative size of the sound‐producing nose between male and female sperm whales. This would be an intriguing alternative to prior hypotheses regarding echolocation adaptations for different foraging conditions between sexes [45].

4.2. What Are Slow Clicks Potentially Communicating?

At close ranges, such as experienced by the group of females in our SL data set (Figure 2), slow clicks may carry both spectral and IPI information about the size and perhaps identity of the transmitting male individual. IPIs within individual slow clicks are longer in larger males due to a longer delay path between the reflective air sacs of their larger noses (Figures 1A and 2A,C). In addition, the band‐pass filter effect on the subsequent pulses seen in the spectrogram of Figure 2A may lead to a lower center frequency for larger spermaceti organs. Thus, larger males may encode size acoustically in a form of honest advertisement (i.e., conveying an honest signal regarding their quality to the receiver [73, 74]). If they can encode and signal body size via slow clicks, the clicks could function as an honest advertisement to females for mate attraction, or to males for competition. However, intraclick information will eventually be lost to off‐axis distortion, multipath propagation, and absorption when a slow click propagates over many kilometers, and the only information that is left at these ranges is the timing between the clicks, that is, the ICI, and potential reflections from the sea floor and surface.

Owing to their acute long‐range echolocation capabilities, where whales infer range to prey from keeping track of the time delay between outgoing clicks and returning echoes, sperm whales are likely predisposed, along with other toothed whales, to detect and use small differences in time delay between acoustic transients. This acute auditory time‐keeping capability very likely comes into play when extracting timing and rhythmicity information from codas, which are approximately 1‐s‐long bursts of 3–11 clicks. Importantly, however, due to multipath arrivals, codas cannot carry their timing information unambiguously across long ranges even if they were loud enough to be detected over wide swaths of ocean. In contrast, slow clicks can maintain their timing information, and due to multipath propagation over long ranges, slow clicks need to be at least a couple of seconds apart to allow for unambiguous interpretation of ICIs amidst reflections from the surface and sea floor (see supplementary analysis in Figure S4). Thus, it is proposed that the use of very long ICIs in possible slow click communication that is more than an order of magnitude slower than those implemented in coda repertoires, may be an adaptation to allow timing information to be maintained over a larger active space. Given that slow clicks vary in stable ICIs from 2 to 9 s (Figure S2), we speculate that such timing may encode size, maturity status, and/or dominance. Communicating dominance status at a distance may be speculated to help mitigate aggressive direct physical contact that male sperm whales are known to engage in, as evidenced by intense scarring and sometimes broken jaws in older males [75, 76]. Thus, slow clicks may not be intended for nearby conspecifics. This hypothesis, along with a potential communication function, may be addressed via carefully designed playback studies at sea with tagged male sperm whales exposed to playbacks of slow click series with different ICIs and center frequencies.

In a potential male–male interaction context, stable, long ICIs of loud slow clicks may also hold the intriguing potential to offer range cues to listening whales. As the relative distances between the groups of multipath arrivals depend on the bottom depth, a receiving whale that knows the depth from its own echolocation can, in principle, deduce the range to another slow click‐producing male from the timing of the multipath propagated pulses that follows each slow click. This concept remains entirely speculative in the absence of concrete evidence but is made uniquely possible by long stable ICIs that are longer than the time it takes for an emitted click to reach the sea floor and return to the transmitter as an echo, that is, the two‐way travel time.

4.3. How Do Sperm Whales Keep the Beat?

In support of the hypothesis that sperm whale slow clicks are highly rhythmic signals at slow rates, we find that slow click ICIs vary between 2 and 9 s (Figure S2) with individual series of slow clicks being highly rhythmic (Figure 4). While the slow clicks were predominantly organized on an isochronous grid, like the regular beat of a metronome, they were punctuated by small‐integer relationships, 1:2 and 2:1. In the absence of concrete evidence, the functionality of this rhythmicity remains entirely speculative at this stage: Most obviously, a rhythmic click train can be detected and recognized in long‐range signaling. A single broad band transient in the open ocean can stem from many sources, but only male sperm whales produce transients around 3–4 kHz at slow repetition rates of 0.1−0.5 Hz, which, together with their distinct rhythmicity, do make these unique click trains truly stand out. Consequently, however, besides conveying their sex, the only other vehicle of information transfer at long ranges is the implemented ICIs, making slow clicks an inherently low‐entropy signal.

Irrespective of the functionality of sperm whale slow clicks, this study conclusively demonstrates that male sperm whales have a very large active space and that slow clicks are highly rhythmic at rates much slower than other bioacoustic sources. Typical rates of rhythmicity in animal communication are at 1 Hz or greater and entrained by neural and biomechanical oscillators [77]. Sperm whale slow clicks are outliers by being an order of magnitude slower than both vocalizations and percussion rhythms in other mammals and birds. Some baleen species, such as blue, fin, and humpback whales, display rhythmic features of their song akin to the 2:1 pattern identified for sperm whales here [12, 16, 78], but they are not, to our knowledge, capable of maintaining the strict isochrony at very slow rates demonstrated for slow click‐producing sperm whales. Here, we have discussed the advantages of such slow rates in potential long‐range click communication of these deep‐water predators, but the fundamental question remains of how strict rhythmicity can be maintained at rates so slow. Because of varying rates both within and between individuals, it is arguably unlikely that an intrinsic biomechanical resonance in the sound production apparatus can explain slow click rhythmicity. Almost all animals display rhythmic behaviors and physiological cycles entrained extrinsically by circadian or ultradian sources, chiefly the sun, from the environment. However, such rates occur on scales 3−6 orders of magnitude slower than slow click production rates, and hence also fail as a plausible extrinsic source of entrainment. In addition, for most species, production of isochronous volitional behavior with multisecond interstimulus duration is apparently difficult, with isochrony falling off sharply at interbehavior intervals greater than three‐fourths of a second [79]. In studied mammals and birds, brain systems for short‐duration interval timing are distributed across frontostriatal and frontocerebellar circuits [3]. Precise, rapid timing is more dependent on the cerebellum (although see Ref. [80] for evidence of cerebellar contribution to suprasecond interval timing). The cerebellum has been theorized to be relevant to rapid sensorimotor integration in cetacean echolocation [81, 82, 83]. Notably, sperm whales produce slow clicks at rates 1–3 orders of magnitude slower than click intervals of smaller toothed whales and do not show the same relative cerebellar enlargement [84]. Suprasecond timing has typically been associated with basal ganglia structures and their relationship with frontal regions [85]. Here, unified interval processing precision degrades substantially above 1 s, and has long been believed to have a roughly 3 s ceiling in humans [86, 87].

To the extent humans are capable of doing so, it is typically through subdividing the intervals into shorter, manageable intervals (e.g., counting one‐two‐three‐four‐one‐two‐three‐four, etc.). There is no current evidence of nonhuman animals utilizing such recursive subdivision. Therefore, if sperm whales are using a cognitive system to track and produce slow isochronous clicks, it may involve unique brain adaptations that in turn begs for behavioral studies of slow rhythm perception in sperm whales through playbacks.

It remains uncertain how male sperm whales keep the beat when slow clicking, but beyond the possibility of unique slow neural oscillators, it can be speculated that one of two parsimonious sources, one intrinsic and one extrinsic, may allow sperm whales to have a high degree of rhythmicity when slow clicking. An intrinsic source may be interoceptive awareness of heart rate, which is both isochronous and likely very slow in diving sperm whales. While the dive response heart rates of sperm whales are unknown, scaling predictions from smaller diving marine mammals suggests that a sperm whale's diving heart rate may well be around 0.1 Hz, which is on par with the measured slow click rates. Heart rate in humans has been shown to be a poor predictor of perceiving time [88], but marine mammals may have more volitional control of, and thus perceptual sensitivity to, heart rate [89]. Perhaps more likely, a potential extrinsic source of entrainment is the ever‐present bottom and surface reflections that slow clicks of low directionality create. Previous data from biologging tags revealed that male sperm whales mainly slow click during bottom, ascent, and surface phases of their dive cycle [48]. If they maintain the same depth over a fairly flat seafloor, slow click‐producing sperm whales will receive a very stable timing cue from the returning bottom and surface reflections of the previous slow click which would allow them to maintain a very stable rhythm in their slow click production by simply producing a slow click right after receiving a particular bottom or surface echo of the previous click. In support of that hypothesis, the bottom reflected paths in Figure S4 are weak at short distances, but still detectable, and sufficient for multipath ranging. Furthermore, Backus and Schevill [90] reported an encounter with a sperm whale that seemingly adjusted its ICIs to that of their echosounder, suggesting that sperm whales can use extrinsic cues to time their ICIs. Both hypotheses can be tested with onboard heart rate and sound recording tags on slow click‐producing male sperm whales at sea, and we hope that such future experiments in concert with carefully designed playback experiments can elucidate how and why the world's biggest predators employ extremely loud and isochronous signals as part of their vocal repertoire.

Author Contributions

S.K.A.V., A.R., T.R., and P.T.M. conceptualized and designed the study. Data collection was undertaken by P.T.M., D.R., and N.C.F.Vg. Data and visualizations were analyzed and prepared by S.K.A.V., M.B.P., P.M.S., T.R., and W.M.X.Z. The funding was acquired by P.T.M., A.R., P.C., S.L.K., D.R., and N.C.F.vG, and the original draft was written by S.K.A.V., P.T.M., T.R., M.B.P., P.M.S., and W.M.X.Z. All authors reviewed and edited the final draft.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supplementary Material: nyas70289‐sup‐0001‐SuppMat.docx

Data Availability Statement

The data supporting the findings of this study are available from the corresponding author upon reasonable request.