# Nonlinear phenomena in pinnipeds: a preliminary investigation in the contact calls of northern elephant seal pups

Juliette Linossier, Isabelle Charrier, Nicolas Mathevon, Caroline Casey, Colleen Reichmuth

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## To cite this version:

Juliette Linossier, Isabelle Charrier, Nicolas Mathevon, Caroline Casey, Colleen Reichmuth. Nonlinear phenomena in pinnipeds: a preliminary investigation in the contact calls of northern elephant seal pups. Philosophical Transactions of the Royal Society B: Biological Sciences, 2025, 380 (1923), pp.20240016. 10.1098/rstb.2024.0016 . hal-05356800

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1 Non-linear phenomena in pinnipeds: a preliminary investigation in the contact calls of

2 northern elephant seal pups

3 Juliette Linossier¹,³*, Isabelle Charrier²*#, Nicolas Mathevon⁴,⁵,⁶, Caroline Casey¹ and Colleen

4 Reichmuth¹,⁷.

5 1. Institute of Marine Sciences, Long Marine Laboratory, University of California Santa Cruz,

6 Santa Cruz, CA 95060, USA

7 2. Université Paris-Saclay, CNRS, UMR 9197, Institut des Neurosciences Paris-Saclay, Saclay

8 91400, France

9 3. Biophonia, Sualello 20232, Oletta, France

10 4. ENES Bioacoustics Research Lab, CRNL, University of Saint-Etienne, CNRS, Inserm, Saint-

11 Etienne, France

12 5.Ecole Pratique des Hautes Etudes, CHArt lab, PSL University, Paris, France

13 6. Institut universitaire de France

14 7. Alaska SeaLife Center, Seward, AK 99664, USA

15 * co-first authors

16 # Corresponding author

17 Isabelle Charrier, NeuroPSI, Acoustic Communications team, CNRS & Université Paris Saclay,

18 151 route de le Rotonde, 91400 Saclay, France.

19 Email: isabelle.charrier@cnrs.fr

20

21 ORCID ID of the authors

22 Juliette Linossier, 0000-0002-0221-6708

23 Isabelle Charrier, 0000-0003-4873-2342

24 Nicolas Mathevon, 0000-0003-0219-6601

25 Caroline Casey, 0000-0003-3773-2478

26 Colleen Reichmuth, 0000-0003-0981-6842
27 Abstract

28 As acoustic markers of emotional state, non-linear phenomena (NLP) are commonly found in the
29 calls that young mammals produce to solicit attention from their parents. However, data are
30 lacking to assess the ontogeny of these NLP during early development, including the extent to
31 which these acoustic cues vary with the age and sex of the emitter. In the present study, we
32 evaluated the occurrence of NLP in the contact calls that northern elephant seal (Mirounga
33 angustirostris) pups emit to solicit maternal care during the three-week period of maternal
34 dependence. We found that five types of NLP are present at an early age.. The relative
35 occurrence of these NLP types varies with pup age, with more biphonation, chaos, and
36 subharmonics as pups get older, and fewer vibrato-like frequency-modulated components
37 varying with both age and sex. Our results suggest that developmental changes - including body
38 growth - facilitate increased flexibility in the vocal apparatus, which subsequently impacts the
39 production of certain types of NLP. The production of non-linear components within the calls of
40 rapidly growing elephant seal pups is likely linked to their arousal state, which in turn is related
41 to their high demand for maternal care. This can fluctuate throughout the lactation period and
42 vary between male and female pups.
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# 1. Introduction

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Among mammals, vocal signals can contain both static (e.g., body size, age, individual identity) and dynamic (e.g., emotional and motivational state) information about the emitter [1,2]. Non-linear phenomena (NLP) are relatively common in the acoustic signals produced by various taxa and cause vocalisations to sound more pulsative, rough, harsh, or chaotic. NLP arise from the vocal production system, which includes the nervous system, respiratory pathway, sound-generating mechanism, and vocal tract [3]. When the oscillating folds within the larynx are not in exact synchrony, disturbances to the signal can occur, which often result in changes in the tonal structure of the sound being emitted [4]. These non-periodic phenomena introduce variability and complexity into structured communicative signals, and these chaotic elements can be considered either as ‘noisy’ or potentially informative aspects of calls.

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While present across a wide range of species [5–7], the biological functions and ontogeny of NLP remain uncertain. NLP tend to be associated with physiological fluctuations and may reflect the caller’s emotional state, with harsher call components indicating heightened arousal or distress [8–10]. Receivers often perceive or interpret vocalisations containing NLP with distress, fear or pain [11–13] and thus adapt their behaviour accordingly [14,15]. Acoustic non-linearities may be more difficult for the listener to ignore, promoting sustained responsiveness among receivers and thus limiting habituation [5,16]. These features may be particularly important during mother-offspring interactions, where an infant’s ability to convey arousal may be critical for offspring survival [17]. Others have suggested that NLP may function to exaggerate body size among animals competing for resources during mate attraction [18] and agonistic encounters [2,19]. Overall, less emphasis has been placed on evaluating NLP with respect to caller individuality, developmental changes, and sex-based differences over a range of species with
66 diverse vocal tract anatomy [20,21]. Exploring these facets of NLP will improve our
67 understanding of the potential adaptive functions of these vocal irregularities during social
68 interactions.

69 In the present study, we evaluated NLP within the pup calls of a large, colonial breeding
70 mammal, the northern elephant seal (Mirounga angustirostris). The availability of high-quality
71 acoustic recordings obtained from marked individuals monitored over a rapid period of early
72 development allowed us to explore the presence of NLP within the contact calls of dependent
73 seal pups and to consider the extent to which NLP may encode meaningful information to
74 mothers.

75 Northern elephant seals are a compelling species with which to evaluate NLP due to the
76 role that vocal behaviour plays in mother-offspring interactions and the pups' rapid growth
77 during the lactation period. Mothers give birth to a single pup each winter on sheltered coastal
78 and island rookeries in California, USA and Baja, Mexico. Throughout the relatively short period
79 of dependence (>3 weeks), mothers remain ashore while fasting, and their pups stay in close
80 physical contact. The mother's milk is exceptionally thick and nutritious – containing up to 55%
81 fat. Pup mass increases by about 10% each day, growing from a birth weight of about 35 kg to a
82 weaning mass of 126 kg or more [22,23].

83 During their time ashore, females and pups repeatedly exchange vocalisations to sustain
84 contact, facilitate nursing, or maintain safety within crowded harems on the beach [24]. Pup calls
85 are variable in duration and exhibit amplitude and frequency modulation [25]. These
86 vocalisations vary with motivational context and pup age (Charrier, unpublished data).
87 Nevertheless, females can recognize the calls of their filial pups from as early as a few days post-
parturition through abandonment [26], when pups are abruptly weaned and their mothers return to life at sea [22].

Among many standard temporal, spectral, and structural-acoustic variables, NLP may encode reliable information in the calls of northern elephant seal pups during this period of maturation. Here, we report our preliminary investigation into NLP to provide one of the few assessments of how NLP vary within individuals during development. We describe five types of NLP found within the contact calls emitted by known pups over the lactation period and explore the influence of growth and sex on the expression of these acoustic characteristics.

## 2. Material and Methods

### (a) Animals and acoustic recordings

The acoustic dataset was collected at Año Nuevo Reserve (San Mateo County, California, USA) over two successive winter breeding seasons in 2018 and 2019. This site includes a breeding population of several thousand northern elephant seals grouped into harems including up to 50 adult females and their dependent pups [26]. To monitor pups from birth through weaning, we individually marked their black fur with bleach marks within 24 h of observed birth. Pups frequently produced vocalisations to elicit attention from their mothers. We recorded these calls using a Marantz PMD 670 or a PMD 661 digital recorder (sampling rate 44.1 kHz) linked to a dynamic microphone (BeyerDynamic TG 69, frequency response: 50 Hz–16 kHz ± 2.5 dB) on an extension pole placed 0.7 to 4.5 m away at pup level (Figure 1). The details of the recording procedures can be found in [26].
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Northern elephant seal pup calling its mother (left) and J. Linossier recording a pup vocalising near its mother (right). Photo: Isabelle Charrier/NMFS 23188.</figcaption></figure>

Recordings were performed following an acclimation period after microphone placement to ensure there was no influence of human presence on the focal pup's behaviour (Figure 1). Voice annotations confirming the date, pup identity, and status were recorded on a separate channel. Focal observations and recordings of each pup were obtained during periods of wakefulness that lasted from 10 min to several hours. For each call recorded, we noted the motivational state of the pup as high or medium (i.e., lost contact with their mother, bitten by another female, or disturbed by a nearby stimulus) or low (i.e., spontaneously calling to their mothers when at their side to suckle), and prioritized the collection of low arousal calls. We only included pup calls produced in a low arousal state in our analysis.

We recorded 2957 calls from 28 identified pups: 12 male and 16 female. Calls were subsampled to fit into discrete age (and associated size) classes, such that vocalisations recorded in Weeks 1, 2, and 3 (W1, W2, W3) were separated by at least four days. This dataset included at least 15 binned calls per individual and 15 individuals per age class. Subsequently, we explored the types of NLP occurring within their contact calls, focusing on the effects of age and sex on these acoustic features.
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(b) Acoustic and statistical analyses

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Using Praat software [27], we annotated the occurrence of NLP within each pup's call using the following settings (view range: 0-10 kHz; windows length: 0.01s; Dynamic range: 50 dB). Following terminology and classification from previous studies [4,6,28], we identified the following types of NLP (Figure 2): biphonation (occurrence of two sound sources), vibrato-like frequency modulation (rapid FM shown as sidebands on the spectrogram), deterministic chaos (or chaos, identified on the spectrogram as noisy parts), frequency jump (abrupt change of the frequency without transition or silence), and subharmonics (additional frequencies produced at a fractional value of the fundamental frequency). For each single call, we assessed the total number of NLP types present (from 0 to 5). For each type of NLP (biphonation, vibrato-like FM, chaos, frequency jump and subharmonics), we reported their occurrences in pups' calls (0: absence, and 1: presence). Thus, six variables were obtained for each pup call: the total number of NLP (nbNLP), the occurrence of biphonation, vibrato-like FM, chaos, frequency jump and subharmonics in the call.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Spectrograms of northern elephant seal pups showing (A) several types of NLP such as subharmonics (purple) and vibrato-like FM (green), (B) biphonation (orange), and (C) frequency jump (red), and (D) chaos (black). Spectrogram settings were FFT= 512/1024/2048/1024 for A, B, C and D respectively, 90% overlap, Hamming window. Corresponding audio files are provided in the Supplementary Material.</figcaption></figure>

To assess the effect of age and sex on the expression of NLP, we used Generalized Linear Mixed Models (GLMM) with the function *glmer*, with *age* and *sex* as fixed effects and the *individual* considered as a random effect. We conducted this analysis for each of the six measured NLP variables. For count data, we used a GLMM with a Poisson family function. For occurrence data (0 or 1), we used a GLMM with a binomial family function. When we found a

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<table><caption>**Table 2** – Summarised results of the different Generalised Linear Mixed Models applied to the six NLP features, including the significant effects, the estimated means from the models, and their corresponding post-hoc analyses (only significant pairwise comparisons are shown).</caption><thead><tr><th>NLP features</th><th>Significant Effects</th><th>Estimated means (on the response scale) ± SE values (95% CI intervals)</th><th>Post-hoc Analysis</th></tr></thead><tbody><tr><td>nbNLP</td><td>Age<br/>(χ² = 10.47, df=3, p =0.005)</td><td>W1: 1.22 ± 0.0477<br/>(1.13 - 1.31)<br/>W2: 1.35 ±0.0535<br/>(1.25 - 1.46)<br/>W3: 1.38 ± 0.0541<br/>(1.28 - 1.49)</td><td>W1&W2 (p =0.0353)<br/>W1&W3 (p =0.0066)</td></tr><tr><td>Biphonation</td><td>Age<br/>(χ² = 47.16, df=3, p <0.001)</td><td>W1: 0.05 ± 0.0113<br/>(0.0323-0.0775)<br/>W2: 0.0945 ±0.0195<br/>(0.0626 - 0.1403)<br/>W3: 0.1336 ± 0.0256<br/>(0.0909 - 0.1922)</td><td>W1&W2&W3 (p <0.05)</td></tr><tr><td>Vibrato-like FM</td><td>AgeSex<br/>(χ² = 21.4, df=5, p <0.05)</td><td>FW1: 0.802 ± 0.0452<br/>(0.699 - 0.877)<br/>FW2: 0.747 ± 0.0539<br/>(0.628 - 0.837)<br/>FW3: 0.675 ± 0.0628<br/>(0.542 - 0.784)<br/>MW1: 0.868 ± 0.0388<br/>(0.772 - 0.928)<br/>MW2: 0.883 ± 0.0361<br/>(0.792 - 0.937)<br/>MW3: 0.874 ± 0.0376<br/>(0.780 - 0.931)</td><td>FW1>FW3 (p =0.0006)<br/>FW3<MW2 (p =0.049)</td></tr><tr><td>Chaos</td><td>Age<br/>(χ² = 14.97, df=2, p<0.001)</td><td>W1: 0.209 ± 0.0330<br/>(0.152 - 0.281)<br/>W2: 0.227 ± 0.0352<br/>(0.165 - 0.303)<br/>W3: 0.289 ± 0.0407<br/>(0.216 - 0.374)</td><td>W1 < W3 (p = 0.001)<br/>W2 < W3 (p = 0.025)</td></tr><tr><td>FreqJump</td><td>Sex<br/>(χ²=14.16, df=1, p<0.001)</td><td>F: 0.065 ± 0.012<br/>(0.0453 - 0.0938)<br/>M: 0.017 ± 0.005<br/>(0.0098 - 0.0306)</td><td>F > M (p = 0.0001)</td></tr><tr><td>Subharmonics</td><td>Sex<br/>(χ²=5.46, df=1, p=0.0195)<br/>Age</td><td>F: 0.1093 ± 0.0261<br/>(0.0676 - 0.1719)<br/>M: 0.0452 ± 0.0144<br/>(0.0241 - 0.0833)</td><td>F > M (p = 0.0251)</td></tr></tbody></table>
<table><tr><td>(χ²=43.27, df=2, p&lt;0.001)</td><td>W1: 0.0430 ± 0.0101<br>(0.0270 - 0.0678)<br>W2: 0.0970 ± 0.0205<br>(0.0635 - 0.1454)<br>W3: 0.0841 ± 0.0185<br>(0.0543 - 0.1282)</td><td>W1 &lt; W2 (p &lt;0.001)<br>W1 &lt; W3 (p = 0.0009)</td></tr></table>

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Both female and male pups produced on average one or two NLP types within each call (Table 1). The generalised mixed-effect model revealed a significant effect of *age* (Table 2). The calls of older pups (W2 and W3) contained more NLP in their calls than the calls of very young pups (W1).

Biphonation occurred relatively rarely in both female and male pup calls at all ages (Table 1). The generalised mixed-effect model revealed a significant effect of *age* (Table 2). The occurrence of biphonation increased significantly with age (W1&W2&W3).

Vibrato-like frequency modulation was observed in the calls of pups of both sexes and at all ages (Table 1). The generalised mixed-effect model revealed a significant effect of *agesex* (Table 2). The occurrence of vibrato decreased significantly with age in females with younger females (FW1) showing more vibrato-like FM than the oldest ones (FW3), whereas the occurrence of this NLP stayed relatively stable in males. Moreover, we found that older males (MW2) produced more calls in which vibrato-like FM occurred more than in older female pup calls (FW3).

Chaos occurred in the calls of pups of both sexes and at all ages(Table 1). The generalised mixed-effect model revealed a significant effect of *age* (Table 2). The occurrence of chaos increased with age, with calls of younger pups (W1, W2) presenting less chaos than older pups (W3)
Frequency jumps occurred quite rarely in pup calls (Table 1). The generalised mixed-effect model revealed a significant effect of *sex*, with females producing more frequency jumps than male pups (Table 2).

Finally, subharmonics occurred rarely in all pups' calls (Table 1). The generalised mixed-effect model revealed a significant effect of *sex* and *age* (Table 2). The occurrence of subharmonics was higher in female pups than in male pups' calls and higher in older pups' calls (W2, W3) than in young pups' calls (W1)

## 4. Discussion

Northern elephant seal pups consistently produce nonlinear phenomena in their contact calls during the dependency period and NLP occur in both sexes and all age classes. Further, five types of NLP were identified in male and female pups at every developmental stage. This finding suggests new research questions, such as whether NLP can provide important information about an individual's arousal level or emotional state, or the individual identity of a pup, potentially providing both dynamic and static information on these callers.

In this study, we compared NLP for pups of different ages and sex in a similar motivational context to avoid potential confounding effects. Calls were primarily recorded when pups were in a low motivational state, while vocalising before suckling or to elicit attention from their nearby mother. We can expect that under higher arousal states when pups are searching for their mothers after a separation (due to the disruptive movements of adult males in the harem, challenging weather conditions, or after the pup has been bitten by another female), more instances of NLP may occur. Calls recorded from pups in heightened arousal states need to be further investigated to assess which types of NLP would appear or increase in such situations.
218 From what we have informally observed in our recordings, pups in high arousal states seem to
219 produce calls with more chaos, vibrato-like FM, or subharmonics. As vocalisations produced
220 under high arousal states tend to be louder and rougher [31], these NLP can be considered by-
221 products of the high intensity of the calls that increase the vocal saliency and convey a sense of
222 urgency to listeners [32].

223 Our findings indicate that pups tend to produce more NLPs in their contact calls as they
224 become older and increase in size. This could be potentially explained by increased vocal power
225 and control with maturation. Given increasing energetic needs before weaning and decreasing
226 attention from their mothers, pups have been shown to demand more maternal attention and
227 suckling time later in the dependency period [33,34]. Elephant seal pups may thus produce more
228 NLP in their calls during development to solicit more maternal attention and thus more suckling
229 time. Four out of the five types of NLP changed with age. Biphonation, chaos and subharmonics
230 occurred more in calls with age. A sex effect was also found for three out of the five types of
231 NLP. We found that vibrato-like FM occurred more in males' than in females' calls, but the
232 occurrence of subharmonics and the number of frequency jumps were higher in females' than in
233 males' calls. Whether these are meaningful changes or attributable to our relatively small sample
234 size remains to be determined.

235 Vibrato-like frequency modulation is frequently associated with high arousal and
236 developmental changes. In dependent sea lion or fur seal pups, such vibrato is common in young
237 individuals; it tends to disappear with maturation [35-37] but can be found in older pups when
238 calls are produced in high arousal states (Charrier, pers. obs.). The difference found in vibrato-
239 like FM between male and female elephant seal pups is intriguing. While the occurrence of
240 vibrato decreased with age in female pups, it stayed constant in male pups. Males might produce
241 more vibrato-like FM to gain more attention from their mothers, as it can be associated with very
242 young pups or pups in high arousal state. Northern elephant seal male pups show longer nursing
243 periods than female pups, and they are more persistent and more successful at milk stealing [34].

244 Subharmonics occurred only weakly in the seal pups' calls; this may be attributable to the
245 selection of calls during low arousal states. Subharmonics have been observed more often in
246 calls recorded under high arousal states, i.e., in calls produced at high intensity [4]. We found
247 that subharmonics occurred more in female pup calls than in male pup calls

248 The production of chaos in the pup calls increased with age, being highest in the oldest
249 pups (W3). In other mammal species, chaos is mostly found in the vocalisations of neonates
250 [4,38] and thus may be related to lower motor control in young individuals. In adults, chaos is
251 associated with sounds produced under extreme arousal states [4,6,39]. It is possible that higher
252 levels of chaos in calls of the oldest age (W3) might be a strategy of pups to increase the
253 maternal attention just before weaning (higher energetic needs). Alarm calls in many species are
254 produced to attract attention of conspecifics and initiate a group flight response [14,40], and they
255 often contain chaotic elements due to the high pressure at the level of the vocal fold.

256 Some studies have suggested that NLP could be used for individual vocal recognition.
257 For example, in wolf (*Canis lupus*) howls, subharmonics seem to be specific to some individuals
258 [41]. Biphonation has also been suggested to facilitate individual recognition as the two
259 frequencies produced will be linked to the anatomy of the vocal tract and thus will be individual-
260 specific. The whistle component within the contact calls of African wild dogs (*Lycaon pictus*) is
261 a high-frequency cue that could be used for recognition [4] but also to estimate the distance of
262 the emitter, as high frequencies are more degraded than low-frequency during propagation [42].
263 In dholes (*Cuon alpinus*), the high-frequency component in biphonic calls contributes to better
264 acoustic discrimination among individual calls and thus could be used for individual vocal
265 recognition [21]. Asian elephants (Elephas maximus) and killer whales (Orcinus orca) also
266 produce biphonic calls, and the two sources increase individual vocal distinctiveness [17,43].
267 Anatomical differences in the vocal tract and potential abnormalities of voice generators (e.g.,
268 vocal folds) may also lead to individual-specific NLP vocalisations (e.g., biphonation, chaos,
269 subharmonics), and thus will be strong markers of individual identity [28]. Northern elephant
270 seals have been studied to determine the importance of individual vocal recognition. For
271 example, it has been shown that females recognize their pup's voice and that this recognition
272 occurs as early as two days after birth and extends over the period of rapid growth during the
273 period of dependency [26]. The acoustic cues that support this recognition of offspring are not
274 yet resolved. It will be now interesting to consider what role, if any, NLP play in forming the
275 individual acoustic signatures of pups.

276 The extent to which listeners may gain information from NLP remains an open question.
277 In the present case, it may be interesting to determine whether female northern elephant seals are
278 sensitive to the occurrence of NLP contained in the calls of their filial pups. For instance,
279 playback experiments could be conducted to reveal whether females are more responsive and
280 react faster to the calls of their pups that contain more chaos, vibrato-like FM, or subharmonics
281 than to those without. The presence of NLP increases the attention of the receivers and elicits
282 stronger behavioural responses in several species, including (meerkats (Suricata suricatta) [44],
283 yellow-bellied marmots (Marmota flaviventris) [14], and Nile crocodiles (Crocodylus niloticus)
284 [45]. Moreover, testing different types of NLP in structured playback experiments would also be
285 interesting, as they might not encode the same information. In koalas (Phascolarctos cinereus),
286 the relative amount of NLP in female rejection calls has been tested on the males, revealing that
males were more reactive to calls with a higher proportion of subharmonics or more deterministic chaos, but their looking responses decreased when calls contained higher levels of biphonation [46]. In our case, vibrato-like FM may be a good candidate for further exploration as it is the most common NLP type in the calls of northern elephant seal pups, and it is found in calls produced by pups of all ages and in both sexes. Playback experiments might test the hypothesis that a higher proportion of vibrato-like FM in pups calls would increase their mothers' responsiveness.

In conclusion, northern elephant seal pups are good candidates for studying non-linear components within vocal signals. Based on their presence and expression in the calls of dependent pups, further research could clarify the importance of these non-periodic elements in the development and survival of young mammals.

## Acknowledgements

We thank Dan Costa, Roxanne Beltran, and Patrick Robinson for coordination of research activities and authorizations, and Emma Levy and Ines Agosto for essential support in the field. Andrey Anikin and two anonymous referees provided helpful and constructive comments on our manuscript.

## Ethics

Research was conducted with minimal disturbance and without harm to animals, with permission and support from Año Nuevo State Park and Año Nuevo Reserve. We recognise that this field site is in the unceded homelands of the Quiroste Tribe. Animal research authorization was granted by the United States National Marine Fisheries Service under marine mammal research
310 permit 23188. Animal protocols were reviewed and approved by the Institutional Animal Care

311 and Use Committee at the University of California Santa Cruz.

312

313 **Funding**

314 Funding was provided by the Fyssen Foundation (JEL) and CNRS (IC).

315
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