An exploration of Menzerath's law in wild mountain gorilla vocal sequences

Abstract

Menzerath's law, traditionally framed as a negative relationship between the size of a structure and its constituent parts (e.g. sentences with more clauses have shorter clauses), is widespread across information-coding systems ranging from human language and the vocal and gestural sequences of primates and birds, to the building blocks of DNA, genes and proteins. Here, we analysed an extensive dataset of ‘close-call' sequences produced by wild mountain gorillas (Gorilla beringei beringei, no. individuals = 10, no. sequences = 2189) to determine whether, in accordance with Menzerath's law, a negative relationship existed between the number of vocal units in a sequence and the duration of its constituent units. We initially found positive evidence for this but, on closer inspection, the negative relationship was driven entirely by the difference between single- and multi-unit (two to six unit) sequences. Once single-unit sequences were excluded from the analysis, we identified a relationship in the opposite direction, with longer sequences generally composed of longer units. The close-call sequences of mountain gorillas therefore represent an intriguing example of a non-human vocal system that only partially conforms to the predictions of Menzerath's law.

1. Introduction

A common biological principle that has been found to hold true across information-coding systems as diverse as a human language [1,2], music [3], the vocal [4–9] and gestural [10] communication systems of non-human animals and even structures such as DNA, genomes and proteins [11–14] is known as ‘Menzerath's law' [15]. This law states that, as the relative size of a construct increases (e.g. a word, song or gene), so too do its constituent parts decrease in size (syllables, calls and exons accordingly). Menzerath's law represents just one way in which the principle of ‘compression' (minimization of the length of a code) can manifest in information systems [4,16]. Despite its broad phylogenetic distribution, continued exploration of Menzerath's law across systems and species remains an important endeavour, as outlier cases that demonstrate exceptions or nuances to the law may be highly informative. For instance, another linguistic law related to compression, known as Zipf's law of brevity [17], predicts that the most frequently used words in a language are also the shortest. Zipf's law has been upheld across languages [18] and in the vocal systems of a number of non-human species [7,10,19–21], yet some notable exceptions have been identified [9,22]. Such variation allows us to examine the potential factors that may drive a system's convergence towards, or deviation from, compression.

Mountain gorillas possess a rich vocal repertoire that is characterized by a highly combinatorial system of close-call sequences [23], namely at least 159 different call structures consisting of recombinations of five acoustically distinct vocal units (four ‘tonal' units and a single ‘atonal' unit, figure 1) produced primarily during social and feeding contexts. This system therefore represents an ideal testbed in which to explore Menzerath's law. To this end, we analysed a large dataset of 2189 vocal sequences (a total of 4294 call units) recorded from 10 individuals (described by Hedwig et al. [23]) to determine whether, in accordance with Menzerath's law, the number of units in a sequence had a negative relationship with the average duration of those units. Owing to the widespread presence of Menzerath's law in non-human vocal systems, including closely related ape species [5,6], we predicted that wild mountain gorilla close-call sequences would adhere to its predictions.

Figure 1.

Spectrograms of representative gorilla close-calls recorded in this study, their subdivision into units and categorization into unit types. Spectrograms (a–f) illustrate typical examples of syllabled calls: (a–e) double grunts, (f) single grunt. Spectrograms (g–k) illustrate non-syllabled calls: (g) grumble; (h,i) hums; (j,k) mixed calls. Calls were subdivided into units (indicated by black lines) based on the occurrence of periods of silence of less than 2 s duration (a–e,h,i) or abrupt changes in the distribution of energy (j,k). The units were categorized as atonal or tonal according to the presence/absence of harmonic frequency bands. Indicated above the lines are the unit type each unit was assigned to via cluster analysis: a1: atonal grunts; t1: short hums; t2: short tonal grunts; t3: long hums; t4: grumbles. Reproduced with permission from Hedwig et al. [23].

2. Material and methods

(a). Study site and species

This analysis was performed using a pre-existing dataset [23] of close-call vocalizations recorded from 10 adult mountain gorillas (five female : five male, mean age in years = 21, s.d. = 8, range = 11–31) living in a single group of 16 individuals in Bwindi Impenetrable National Park, Uganda. Mountain gorillas are a primarily herbivorous species of great ape that live in stable single- or multi-male groups ranging from 2 to 34 individuals in size [24]. Mountain gorilla close-calls are a group of short-range, low-pitch, inter-graded vocalizations that comprise nine acoustically distinct types (e.g. grunts, grumbles, hums) which are often combined in different ways and primarily produced in feeding and resting contexts, described in detail by Hedwig et al. [23].

(b). Data collection

Data were collected over a period of 312 days between October 2007 and October 2008 using a combination of focal-follows (average 33 h per individual) and opportunistic recordings of individuals in proximity to the focal gorilla. Vocalizations were recorded at 48 kHz sampling rate with a Marantz PMD670 digital recorder and Sennheiser ME66 shotgun microphone. Call types were classified according to the descriptions of Harcourt et al. [25,26]. Calls were selected for analysis based on their signal-to-noise ratio determined through inspection of the spectrograms in Avisoft SASLab Pro Version 5.1.23 [27]. This final dataset consisted of 2189 close-call sequences (composed of one to six ‘vocal units' for a total of 4294 units: see electronic supplementary material, figure S1; figure 1). Durations of units were measured from spectrograms with a 20 Hz frequency and 1 ms temporal resolution using Avisoft SASlab Pro [27]. Acoustic parameters were also semi-automatically extracted from the units (using ‘LMA’ software developed by K. Hammerschmidt [28]) in order to categorize them according to a cluster analysis detailed in Hedwig et al. [23]. Reliability of manually extracted measurements was ascertained through comparing the results of manual with automatic measurements on a subset of tonal units (Spearman correlation; ρ > 0.92, N = 55, p < 0.001). A sequence was defined as a series of units separated by less than two seconds of silence between each unit and the next. Individual units were identified by either a period of silence (min. 10 ms, max. 2000 ms, 95% of intervals less than 550 ms, see electronic supplementary material, figure S2) or sudden spectral shifts between them [23,29–33]. The distribution of the occurrence of each of the five different types of vocal units across sequence lengths is illustrated in electronic supplementary material, figure S3. Sequence lengths for which we only had a single example were excluded from analysis (although the outcome of our analyses remained similar if these were included, see electronic supplementary material, analysis S1). Additional details regarding acoustic analyses and categorization of close-call call types can be found in Hedwig et al. [23].

(c). Statistical analysis

We used Bayesian Markov chain Monte-Carlo (MCMC) linear mixed effects models (using the package ‘rethinking' [34]) to examine the relationship between the number of units in a vocal sequence (as a predictor) and median duration of units within that sequence (as the dependent variable). Since median duration was not normally distributed, we performed a log-transformation and used the transformed variable in our model. For each analysis, a full model including a fixed effect of ‘number of units in sequence' (outcome = log-median unit duration, fixed effect = number of units in sequence, random effect = caller ID) was compared with a null model (identical to full but without a fixed effect of ‘number of units in sequence') to determine which had the best out-of-sample predictive fit (ascertained by Watanabe–Akaike information criterion (WAIC) weights). Evidence for effect of a variable in the best fitting model was determined according to whether the 89% credible intervals (the distribution within which there is an 89% probability that the population mean lies) crossed zero [35,36]. All models were fitted with a varying intercept for individual identity to control for pseudo-replication. The data and R scripts used to produce our analysis and related figures can be freely accessed from our Open Science Framework repository: https://osf.io/5u3jf/ [37].

3. Results

In an initial analysis using the full dataset, we found that a full model with ‘number of units in sequence' as a predictor was a substantially better fit for the data than the null model (full model WAIC weight: >0.99) and identified a strong negative relationship between the number of units and their log-median duration (beta: −0.29, 89% CI: −0.31, −0.26), which is consistent with Menzerath's law. However, based on visual inspection of the data, it seemed plausible that this effect was being driven by the change in the median duration of units between single- and multi-unit sequences (figure 2), as opposed to generalizing across sequence lengths in true adherence to Menzerath's law. To test this, we conducted a follow-up analysis that excluded single-unit sequences (1777 sequences remained). Here, the full model once again fitted the data substantially better than the reduced model (full model WAIC weight: >0.99), but now the relationship between length and log-median unit duration was weakly positive, with longer sequences predicted to have a greater log-median duration relative to shorter sequences (beta: 0.05, 89% CI: 0.03, 0.06). Because Gorilla 5 had a single outlier datapoint (figure 2, unusually long duration for length = 6 units), we reran these analyses excluding this sequence to make sure that our results were not driven by it and found that its presence or absence did not substantively impact our outcomes (electronic supplementary material, analysis S2).

Figure 2.

(a) Median duration of units (in seconds) composing sequences of each length (in number of units) for each individual. Averages computed across all call types. (b) Median duration of units composing sequences of each length across individuals. Error bars indicate ±1 standard error.

Finally, we ran additional analyses (detailed in electronic supplementary material, analysis S3) to determine whether the length of a sequence predicts which type of unit would occur within it. Results suggest that atonal units were more likely to occur in shorter sequences, as were tonal-2 and tonal-4, whereas tonal-1 and tonal-3 were more likely to occur in longer sequences. Given the respective average durations of each unit type (atonal: 25 ms, tonal-1: 13 ms, tonal-2: 20 ms, tonal-3: 81 ms, tonal-4: 82 ms; see electronic supplementary material, figure S4), this would therefore indicate that the effect identified was not a result of longer sequences being disproportionately composed of longer unit types.

4. Discussion

We tested Menzerath's law in a thus far unexplored system—the vocal sequences of mountain gorillas—and found that, while there was a substantial reduction in unit duration between single- and multi-unit sequences, this relationship did not generalize across sequence sizes. In fact, quite the opposite was found: vocal units comprising structurally larger multi-unit sequences were of slightly greater average duration. The positive relationship between length and duration reported by our model is weak, so caution should be taken in interpreting the biological significance of this directionality. However, our data do at the very least show an absence of a negative relationship between median unit duration and sequence length. The close-call sequences of mountain gorillas therefore represent an intriguing example of a non-linguistic system that does not strictly adhere to the predictions of Menzerath's law.

Compression is expected to self-organize in any information system [4,11,38], so exceptions such as this provide especially intriguing datapoints allowing exploration of factors that may act against compression in signals. Compression may be selected against in particularly urgent contexts, where survival is at immediate risk, to make signals conspicuous and ensure unambiguous transmission, for example: signals given in the context of predator detection (alarm calls), or sexual solicitation in extreme cases of intra-sexual competition [39]. However, the mountain gorilla vocal sequences analysed here are predominantly produced in feeding and resting contexts [23]. These constitute low-risk and relaxed activities, as they occur in an environment characterized by low seasonal variation, high food abundance, non-monopolizable food sources and low predation risk [23,40,41]; we would thus expect compression to have acted upon this system, much as it has been found to in the close-call sequences of gelada monkeys [4]. One possible explanation for its absence is that compression is maladaptive in systems where signals are relatively difficult to disambiguate, creating a trade-off between saliency and efficiency [22]. For example, the accurate reception of acoustic signals in mountain gorillas may be confounded by environmental factors, such as their dense forest habitat, which obscures the transmission of sound [16], contrasting with the open grassland habitat of gelada monkeys [42]. Alternatively, saliency may be confounded by acoustic properties of the calls themselves: mountain gorilla close-calls are graded, relatively quiet, low-pitch vocalizations (as illustrated by labels such as ‘grunts', ‘grumbles' and ‘hums' [23]) which may, from the receiver perspective, not be easy to differentiate. The saliency of individual units may also be particularly important in larger sequences of mixed unit types, where disambiguation between units and unit types would be necessary to determine the function of the overall sequence. The convergence of these potential factors within the same system may have led to the observed relationship, the inverse of that conventionally reported for Menzerath's law [4,9,10]. However, until further research reveals more about the specific function and information expressed by the call combinations of mountain gorillas, understanding the evolutionary pressures that may have acted against the conventional pattern of Menzerath's law in this case will remain speculative.

Interestingly, while the inversion of Menzerath's law identified in gorilla close-calls runs contrary to the basic prediction of a negative relationship between sequence length and element-size, there is evidence that similar trends exist in spoken language since the pioneering work of Menzerath [15] and more recently verified again in the oral corpuses of English [2], Spanish and Catalan [43]. In a more sophisticated formulation of Menzerath's law, known as the Menzerath–Altmann law [44], Torre et al. [2] identified a negative correlation between the number of words spoken in a single breath and their average duration holds until a ‘tipping point’ is reached, whereupon the relationship reverses. It could be argued, therefore, that the close-calls of mountain gorillas do indeed adhere to Menzerath's law, albeit differently to the more linear negative relationship between sequence and unit length described in other non-human species [4,7,8,10]. Torre et al. [2] suggest that the relative rarity of this inversion in human language may be because the likelihood of this ‘tipping point' (at which the law inverts) being reached is limited by the constraints of human lung capacity on the number of words that can reasonably be produced in a single breath. It is plausible that this constraint is relaxed in a species as large as mountain gorillas, allowing them to reach the point of inversion more easily, or reducing the urgency of compression within single breaths. This is speculative, however, since the lung capacity of gorillas has only been crudely estimated [45]. Furthermore, to our knowledge, the breathing activity accompanying vocal behaviour in gorillas is unknown, making it unclear whether vocal sequences are indeed analogous to breath-groups in human speech, or instead themselves comprise multiple breath-groups, hindering direct comparisons with the phenomena in humans [2]. As further research sheds light on the physiology of gorilla vocal production, the respective constraints on this system may become clearer and new avenues of analysis become available.

In conclusion, mountain gorillas present an intriguing vocal system that demonstrates mixed evidence for Menzerath's law. Continued work searching for Menzerath's law in a broad range of non-human systems will shed light on (i) the relative rarity of possible outlier cases such as mountain gorillas and (ii) the potential pressures selecting for and against this powerful law of compression.

Ethics

This research complies with the American Society of Primatologists principles for the ethical treatment of animals as well as the ethical guidelines of the Department of Primatology of the Max Planck Institute for Evolutionary Anthropology and was conducted in accordance with the animal care regulations and national laws of Uganda and Germany.

Data accessibility

The data and R scripts used to produce our analysis and related figures can be freely accessed from our Open Science Framework repository: https://osf.io/5u3jf/ [37].

Authors' contributions

R.H., S.K.W. and S.W.T. conceived and designed the study. D.H. collected the data. S.K.W. and R.H. analysed the data. All authors contributed towards interpretation of the data and writing of the manuscript. All authors approved the final version of the manuscript and agree to be held accountable for the content therein.

Competing interests

We declare we have no competing interests.

Funding

This research was financially supported by the Leakey Foundation, the Max Planck Society, the University of Warwick and the Swiss National Science Foundation (grant PP00P3_163850 to S.W.T.). S.K.W. and S.W.T. were also partially by NCCR Evolving Language, Swiss National Science Foundation Agreement no. 51NF40_180888.