Across diverse systems including language, music, and genomes, there is a tendency for longer sequences to contain shorter constituents; this phenomenon is known as Menzerath’s law. Whether Menzerath’s law is a universal in biological systems, is the result of compression (wherein shortest possible strings represent the maximum amount of information) or emerges from an inevitable relationship between sequence and constituent length remains a topic of debate. In nonhuman primates, the vocalizations of geladas, male gibbons, and chimpanzees exhibit patterns consistent with Menzerath’s law. Here we utilize existing datasets of three duetting primate species (tarsiers, titi monkeys, and gibbons) to examine the widescale applicability of Menzerath’s law. Primate duets provide a useful comparative model to test for the broad-scale applicability of Menzerath’s law, as they evolved independently under presumably similar selection pressures and are emitted under the same context(s) across taxa. Only four out of the eight call types we examined were consistent with Menzerath’s law. Two of these call types exhibited a negative relationship between position of the note in the call and note duration, indicating that adherence to Menzerath’s law in these call types may be related to breathing constraints. Exceptions to Menzerath’s law occur when notes are relatively homogenous, or when species-specific call structure leads to a deterministic decrease in note duration. We show that adherence to Menzerath’s law is the exception rather than the rule in duetting primates. It is possible that selection pressures for efficient long-range communication of duets was stronger than that of compression. Future studies investigating adherence to Menzerath’s law across the vocal repertoires of these species will help us better elucidate the pressures that shape both short- and long-distance acoustic signals.

Clink and Lau Electronic Supplementary Material: Data collection and acoustic analysis protocols for all datasets included in the present analysis.

Tarsiers [1]
Data collection
Data were collected July and August 2018 in Tangkoko National Park, Sulawesi, Indonesia. We collected data using a combination of focal recordings and autonomous recorders. For focal recordings, we used a RØDE NT-USB Condenser Microphone (Røde Microphones, Sydney, Australia) connected to a 32 GB Apple iPad Air (Apple Inc., Cupertino, CA) and the Voice Record Pro application at a sampling rate of 44.1 kHz and 16 bits. We used 2 different autonomous recording devices, an ARBIMON portable recorder which recorded at 44.1 kHz and 16 bits, or a SWIFT recorder which recorded at 48 kHz and 16 bits.

Acoustic analysis
We downsampled the data with a 48 kHz sampling to a sampling rate of 44.1 kHz using Audacity(R) 2.3.0 software (2018). We created spectrograms using Raven Pro 1.5 Sound Analysis Software. Spectrograms were created with a 1600- point (33.3 ms) Hann window (3 dB bandwidth . 43.1 Hz), with 50% overlap, and a 2048-point discrete Fourier transform, yielding time and frequency measurement precision of 16.7 ms and 24.1 Hz.

Titi monkeys [2,3]
Data collection
Titi monkey duets were recorded opportunistically at the California National Primate Research
Center (CNPRC), Davis, CA, USA each morning between 06:00 and 07:30 from March 2017 to March 2019. We used a Marantz PMD 660 flash recorder and a Marantz Professional Audio Scope SG-5B directional condenser microphone. We recorded at a sampling rate of 44.1 kHz and 16-bit resolution.

Acoustic analysis
We created spectrograms using Raven Pro 1.5 Sound Analysis Software. We generated spectrograms with a 512-point (11.6 ms) Hann window (3 dB bandwidth = 124 Hz), with 75% overlap, and a 1024-point DFT, yielding time and frequency measurement precision of 2.9 ms and 43.1 Hz. 

Gibbon duets (female introduction and trills; male codas [4,5])
Data collection
We collected recordings from gibbons at seven sites across Sabah, Malaysia during multiple field seasons from January 2013 to September 2016. We recorded
vocalizations at a sampling rate of 44.1 kHz and 16-bit size using a Marantz PMD 660 flash recorder (Marantz, Kawasaki, Kanagawa Prefecture, Japan) equipped with a
Røde NTG-2 directional condenser microphone (Røde Microphones, Sydney, Australia).

Acoustic analysis
We created spectrograms using the Raven Pro 1.5 sound analysis with a 512-point (11.6 ms) Hann window (3 dB bandwidth ± 124Hz), with 75% overlap, and a 1024-point discrete Fourier transform, yielding time and frequency measurement precision of 2.9ms and 43.1 Hz. For the female calls we used the band-limited energy detector in Raven Pro to identify individual notes from each great call.

Gibbon male solos [6]
Data collection
We collected data using Swift autonomous recording units in Danum Valley Conservation Area (11 recording units; March–July 2018) and in Maliau Basin Conservation Area (four recording units; August 2019), Sabah, Malaysia. The units in Danum Valley Conservation Area recorded at a sampling rate of 16 kHz and the units in Maliau Basin recorded at a sampling rate of 48 kHz. For both recording locations, we recorded at a sample size of 16 bits and at a gain of 40 dB.

Acoustic analysis
We created spectrograms in Raven Pro 1.6.We downsampled the 48 kHz recordings to 16 kHz.  We then made spectrograms with a 1024-point (64.0 ms) Hann window (3 dB bandwidth = 22.5 Hz), with 50% overlap, and a 1024-point discrete Fourier transform, yielding time and frequency measurement precision of 32 ms and 15.6 Hz.

Works Cited
1.    Clink DJ, Tasirin JS, Klinck H. 2019 Vocal individuality and rhythm in male and female duet contributions of a nonhuman primate. Curr. Zool. 0, 1–14. 
2.    Clink DJ, Lau AR, Bales KL. 2019 Age-related changes and vocal convergence in titi monkey duet pulses. Behaviour 156, 1471–1494. (doi:10.1163/1568539X-00003575)
3.    Lau AR, Clink DJ, Bales KL. 2020 Individuality in the vocalizations of infant and adult coppery titi monkeys (Plecturocebus cupreus). Am. J. Primatol. (doi:10.1002/ajp.23134)
4.    Lau A, Clink DJ, Crofoot MC, Marshall AJ. 2018 Evidence for High Variability in Temporal Features of the Male Coda in Müller’s Bornean Gibbons (Hylobates muelleri). Int. J. Primatol. 39, 670–684. 
5.    Clink DJ, Grote MN, Crofoot MC, Marshall AJ. 2018 Understanding sources of variance and correlation among features of Bornean gibbon (Hylobates muelleri) female calls. J. Acoust. Soc. Am. 
6.    Clink DJ, Hamid Ahmad A, Klinck H. 2020 Brevity is not a universal in animal communication: evidence for compression depends on the unit of analysis in small ape vocalizations. R. Soc. Open Sci. 7.