Review articlesTransitions and tricks: nonlinear phenomena in the avian voice
Abstract
Birds evolved a novel vocal organ, the syrinx, that exhibits a high anatomical diversity. In the few species investigated, the syrinx can contain up to three pairs of functional syringeal vocal folds, acting as independent sound sources, and eight pairs of muscles. This rich variety in vocal structures and motor control results in a wide range of nonlinear phenomena (NLPs) and interactions that are distinct to avian vocal physiology, with many fascinating mechanisms yet to be discovered. Here, we review the occurrence of classical signatures of nonlinear dynamics, such as NLPs, including frequency jumps and transitions to chaos in birds. However, birds employ several additional unique tricks and transitions of inherent nonlinear dynamical nature that further enrich their vocal dynamics and are relevant for understanding the motor control of their vocalizations. Particularly, saddle-node in limit cycle (SNILC) bifurcations can switch sounds from tonal to harmonically rich and change the physiological control of fundamental frequency. In mammalian phonation, these bifurcations are mostly explored in the context of register transitions but could be equally relevant to altering vocal fold dynamical behaviour. Due to their diverse anatomy compared to mammals, birds provide unique opportunities to explore rich nonlinear dynamics in vocal production.
This article is part of the theme issue ‘Nonlinear phenomena in vertebrate vocalizations: mechanisms and communicative functions’.
1. Introduction
Bird vocalizations are crucial for mate choice, resource competition, territorial defence and fitness [1,2]. Within the 11 000 species of birds, there is a tremendous diversity in vocal signals. While some species use a variety of simple calls, other taxa are capable of acoustic imitation learning and stringing together highly complex sequences of syllables [3].
Birds do not generate sound with vocal folds in their larynx but instead evolved a completely new vocal organ, the syrinx, that is located around the tracheobronchial junction (figure 1). The syrinx evolved either with the occurrence of birds around 65 Ma or even before [8,9]. The syrinx as an evolutionary novelty coincided with an explosive radiation of species numbers [4]. In contrast to the mammalian larynx, the morphological diversity of the avian vocal organ is exceptionally high in extant species [7,10,11]. It ranges from a simple tube with thickened walls without any intrinsic syrinx muscles, in common ostriches (Struthio camelus) [12,13], to highly modified tracheobronchial structures with two or even three sound sources under fine control of up to 16 muscles as in most songbirds [8,14,15]. This rich variation in source number and motor control gives rise to a rich palette of nonlinear phenomena (NLPs) and interactions uniquely found in avian voice physiology, with many exciting mechanisms awaiting discovery.
Figure 1. The high diversity of evolved sound sources in birds compared to all vertebrates. (a) Evolution of sound sources in vertebrates based on Kingsley et al, [4]. (b) The syrinx can have 0–3 sound sources. There is currently no evidence for sound production in the avian larynx. (c) Examples of syringeal morphologies with physiologically confirmed sound sources: 0 (white stork), 1 (pigeons, parrots), 2 (songbirds) and 3 (suboscine ‘tracheophones’). Asterisks indicate the location of the sound sources. Rock dove and cockatiel syrinx from Elmans et al. [5]; zebra finch syrinx render made with three-dimensional PDF from Düring et al. [6]; syrinx of the red-billed scythebill (Campylorhamphus trochilirostris), a tracheophone after Ames [7]. Figure made in BioRender and Adobe Illustrator.
Here, we review the occurrence of classical signatures of nonlinear dynamics, such as NLPs, including frequency jumps and transitions to chaos in birds. In addition, coupled oscillators can give rise to additional behaviours rooted in nonlinear dynamics that may not be so salient but equally relevant for understanding vocal motor control. Due to their diverse anatomy compared to mammals, birds employ several additional unique tricks and transitions of inherent nonlinear dynamical nature to further enrich their vocal dynamics. The large anatomical diversity in birds thus provides unique opportunities to explore rich nonlinear dynamics in vocal production.
2. Vocal source diversity
For the purpose of this article, we consider a sound source to be tissue that demonstrates flow-induced (self-sustained) oscillations and thereby causes pressure and flow fluctuations in the tract downstream. These fluctuations can be approximated as acoustic mono/di/quadrupoles which are termed sound sources in acoustics. However, here we refer to the tissues as sound sources.
The 450-year history of studying syrinx anatomy since Duverney [16] includes many speculations on sound source location across taxa. Birds were thought to make sounds via aerodynamic whistles or small amplitude vibrations of thin membranes leading to low harmonic content of vocalizations in many species. Only in the last 20 years, mounting evidence has pointed towards sound sources following myoelastic aerodynamic principles; endoscopic observations in parrots and songbirds demonstrated vibrations [17] and glottal-like closure [18], independent of sound frequency with air density [19]. In vitro and ex vivo studies of phonation finally established the presence of caudocranial tissue waves essential to sustain self-sustained oscillations according to myoelastic-aerodynamic theory (MEAD) [5,20] just as in mammalian vocal folds. The shared physical mechanism underlying voiced sound production between birds and mammals further strengthened the applicability of nonlinear dynamical systems and their characteristic signature transitions, including NLPs.
There is currently experimental (imaging or bronchial flow) evidence for at least three configurations of sound sources in birds (figure 1). Because of the high diversity of syringeal anatomy, the vibrating structures have also received many names within and between different taxa. We will here use the term syringeal vocal folds for all oscillating syringeal tissues. First, this is to simplify terminology. Second, we do this also because the low-dimensional models that are instrumental in understanding the nonlinear dynamical behaviour of vocal systems do not and cannot differentiate between laryngeal or syringeal vibrating structures and are equally applicable to both. In figure 1, we show examples of the diversity within vocal sound sources:
| — | Absent functional syringeal sound source (figure 1b, zero sound sources). Several mute species of birds with little anatomical adaptation in tracheobronchial bifurcation. For example, the white stork (Ciconia ciconia) [10,21] and new-world vultures [10,22]. | ||||
| — | Single syringeal sound source consisting of two bilateral syringeal vocal folds (figure 1b, c, one sound source). Examples are rock dove (Columba livia) and cockatiel (Nymphicus hollandicus) [5,17]. Intrinsic syringeal muscles insert into the syringeal vocal folds directly in Barbary doves (Streptopelia risoria) [23] or on cartilages and syringeal vocal folds in budgerigars (Melopsittacus undulatus) [24]. | ||||
| — | Dual syringeal sound sources, one in each bronchus (figure 1b, c, two sound sources). These sources typically consist of a pair of bilaterally asymmetrically shaped syringeal vocal folds that can be connected to tracheobronchial rings and cartilaginous extension. These latter structures are mobile, and their position, rotation and tension are controlled by a highly variable number of muscles; from single (e.g. oilbirds (Steatornis caripensis) [25]) to eight pairs of syringeal muscles (e.g. zebra finch (Taeniopygia guttata) [6]). Taxa with dual sound sources include oscines, suboscines, penguins and oilbirds [7,10]. In some species, the left and right sources are highly asymmetrical in tissue properties, e.g. providing a complementary extended frequency range in Bengalese finches (Lonchura striata var. domestica) or canaries (Serinus canaria) [5,26]. | ||||
| — | Triple syringeal sound sources, one in each bronchus and an additional tracheal membrane (figure 1b, c, three sound sources). Endoscopic imaging established three sound modulators in the several species of suboscines called ‘tracheophones’, whose syrinx contains an additional tracheal membrane [27]. Anatomical evidence suggests that a tracheal sound source may be present in more taxa, including Furnariidae, Thamnophyilidae, Formicariidae, Rhinocryptidae and whistling ducks (Dendrocygna spp. [7,10]), but this remains to be tested. | ||||
Figure 2. Established NLPs as signatures of nonlinear dynamical systems in bird phonation. (a) Single source/double oscillators. Left: asymmetry in left and right vocal syringeal vocal folds in Patagioenas pigeons that cause substantial roughness (bottom panel) in comparison to a more symmetric pair of vocal folds in a sister species (top panel) [42]. Middle: deterministic chaos in sulfur-crested cockatoos (Cacatua galerita) [43] as commonly observed in mammals (see other contributions in this special issue). Right: period doublings are often visible in spectrograms, but topological analysis using recurrence and phase-space plots did not support proper period doublings in zebra finches [41]. (b) Left: dual source left and right frequency specialization is a salient feature of many songbirds as demonstrated by in vivo bilateral bronchial flow measurements in canaries [26]. Right: left–right coupling between two different frequencies produces sidebands in chickadees [44] that disappear after unilateral nerve cuts. (c) Three sound source interactions in several species of suboscine ‘tracheophones’ lead to pulsatile amplitude modulation (AM) (left) that disappears when the third source is experimentally disabled (right) [27].
The two sound source configuration is currently thought to be ancestral [8], but this depends on agreement on the number of sources in ostriches [9] and is not relevant for the concepts presented here.
3. Acoustic filters in birds
The position of the syrinx at the tracheobronchial junction has several consequences for the vocal filter and potentially nonlinear dynamics of the source. The upper vocal tract includes the oral and nasal cavities as in mammals, but also the larynx and the entire trachea from syrinx to larynx. Apart from parrots [28], most birds have an immobile tongue that does not allow formant tracking by tongue motion. However, northern cardinals (Cardinalis cardinalis) and zebra finches can shape a resonant cavity downstream from their larynx, the oro-oesophageal cavity (OEC), to track the resonance of the fundamental frequency generated at the source [29–31]. Dynamical modelling also showed that zebra finches use the OEC filter to emphasize a certain band of harmonics essential for recognizing their own song in neurophysiological experiments [32]. This OEC filter is potentially generally present and used by songbirds and perhaps even all birds, but this remains unknown. If so, the OEC filter could play an important role in making birds sound like birds by steeply reducing the harmonics produced in the source.
Vocal tract acoustic filters may add complexity to the sounds and specific harmonic modulations, but also richer sound dynamics may emerge from source–tract interaction found in mammals [33]. Indeed, computational models suggest that some acoustic signatures may emerge from source–tract coupling (e.g. [34,35]). However, in the few species investigated, there is little experimental evidence that vocal tract configurations can change syringeal dynamics. The syringeal sound source vibrations are thus not strongly coupled to the upper vocal tract resonances, and source and track are typically considered uncoupled. This lack of experimental evidence certainly does not exclude the possibility that such interactions occur, as supported by voice break due to tracheal elongation during growth [36]. However, we will focus here on NLPs generated by the sound source alone without vocal tract interactions.
4. Evidence of NLPs caused by sound sources
(a) Single source
Some of the classical NLPs have also been proposed to occur in birds. Here we list first the NLPs attributed to a single source (either single source species or one source of a dual source species).
(i) Period doubling/subharmonics
Additional frequency bands occur often in the spectrograms of bird vocalizations, e.g. in the northern mockingbird (Mimus polyglottos) [37] and African penguins (Spheniscus demersus) [38]. However, their dynamical origins have rarely been investigated. Notably, subharmonics were suggested to occur in adult song of zebra finches [39] and used to match fundamental frequency during song learning in juvenile zebra finches [40]. However, close investigation of the song in 130 adult zebra finch individuals using topological analysis of the acoustic waveforms before and after the bifurcation falsified the presence of true period doublings in zebra finch song ([41]; figure 2a, right panel). Only in one call was evidence found for a true period doubling. Rapid acoustic transitions in the order of milliseconds were instead attributed to modulation of frequency by superfast syringeal muscles [45] or left–right switching [46,47]).
(ii) Deterministic chaos
Confirmed transitions to chaotic regimes seem surprisingly uncommon in birds compared with mammalian screams and cries [38,48], but their prevalence across birds has not been quantified systematically. The first mention of NLPs and deterministic chaos was in zebra finch phonation in vitro [39], however, these conclusions were later falsified and attributed to erroneous flow conditions in the experiments (41). The calls of parrots can be loud and noisy. Acoustic analysis using various tools from nonlinear dynamics (e.g. Lyapunov exponents and recurrence plots) suggested deterministic chaos in two species of cockatoos (figure 2a, middle panel) [43]. Noisy sounds are produced on one side of the dual source syrinx in the northern mockingbird [37], but these signals were not tested with nonlinear tools to be deterministic chaotic signals. In mammals, the prevalence of deterministic chaos is caused by increased driving pressure and source level. Interestingly, the screaming piha (Lipaugus vociferans) and the three-wattled bellbird (Procnias albus)—currently the loudest birds and among the loudest terrestrial vertebrates with source levels of 116 and 125 dB re 20 µPa at 1 m, respectively [49,50]—have calls that are low in harmonics and without obvious signs of deterministic chaos. These species may have specific anatomical and physiological adaptations to produce loud calls that remain currently unknown; however, it is reasonable to assume the calls are made with high driving pressures. If correct, this suggests that even at high driving pressures, the syrinx of these species operates in regimes without deterministic chaos.
(iii) Biphonation
Literally defined as two (bi) simultaneous, harmonically unrelated sound frequencies (phonation), there are multiple ways biphonation could potentially manifest itself physically within a one-source syrinx. In spectrograms, there is ample evidence for biphonation (e.g. [38,51]). The syrinx in rock doves consists of a pair of opposed syringeal vocal folds that move in synchrony in vitro [5,20]. Spot-winged pigeons (Patagioenas maculosa), however, show side bands in their spectrogram indicative of biphonation (figure 2a, bottom left panel). A low-dimensional dynamical model suggested that a large size/mass asymmetry between the left and right syringeal vocal folds prevents their synchronization, leading to independent dynamics of each syringeal vocal fold [42]. In contrast, a sister species, the picazuro pigeon (Patagioenas picazuro) with more symmetrical syringeal vocal folds capable of synchronizing, produces more tonal sounds (figure 2a, top left panel). Thus, desynchronization of the two syringeal vocal folds could lead to biphonation [42]. In northern mockingbirds, one source of the dual-source syrinx is also reported to produce sidebands in the spectrogram [37]. This species could potentially use desynchronization as a biphonation mechanism, but this remains untested.
In humans (Homo sapiens), there is evidence for multiple dorsoventral modes on vocal folds [52,53], and the co-occurrence of such multiple modes can manifest as sidebands in the acoustics. However, simultaneously occurring different vibrational modes that lead to biphonation have not been observed in birds to our best knowledge.
(b) Dual source
The species with two bilateral sources that are physically close provide additional complexity.
(i) Biphonation
There are multiple ways biphonation can manifest itself physically with a two-source syrinx. First, the two sources vibrate at two different frequencies without any physical coupling, which will result in two independent frequency contours in the acoustic signal. This phenomenon is common and one of the salient features of birdsong by oscine songbirds (figure 2b, left panel). Second, two sources vibrate at two different frequencies with some degree of physical coupling, which will show up in the spectrogram as sideband modulation around a carrier frequency [38,54]. It was shown in black-capped chickadees (Parus atricapillus) almost 40 years ago [44] that unilateral nerve lesions could eliminate phonation in one of the sources (figure 2b, right panel).
(ii) Entrainment/injection locking
When two mechanical oscillators have similar resonance frequencies and are physically close, they can become mechanically coupled by energy injections. Such injection locking, or injection pulling, can force one oscillator to oscillate at the resonance frequency of the other depending on the coupling strength [55,56]. Because the two syrinx sides are physically close, we cannot exclude that the two sides become mechanically coupled by injection locking if the two sides have tissue resonance frequencies that are sufficiently similar. This is similar to the phenomenon in single-source biphonation in spot-winged pigeons as described above [42].
(iii) Period doubling/subharmonics
Measurements of bilateral airflow in zebra finches suggested that with both left and right sources vibrating at the same frequency but π radians out of phase also manifests in the sound as a period doubling [46]. Zebra finches are capable of generating low-frequency pulse tones with each of their two sound sources. If the two sound sources are synchronized and oscillate in phase, the total sound generated will have a period equal to the time difference between successive pulses. Since the two sources are in phase, the period in the sound time trace matches the periodic motion of each labium. However, if the oscillations are out of phase by π radians, the radiated sound will be the superposition of the sounds generated by each source, and the time difference between successive peaks will be half the period of each sound source. Consequently, if the system parameters change such that an out-of-phase solution loses stability and the system transitions to in-phase dynamics, it will appear as though a period-doubling bifurcation has occurred. However, the observed change is due to the synchronization of the two sound sources, not a true period-doubling bifurcation.
(c) Triple source
‘Tracheophones’ are a suboscine group that does not exhibit vocal learning [57]. Until recently, it was believed that they phonated with tracheal membranes instead of the two independent sources found in other passerines [10]. However, a recent study revealed that several species of suboscines possess three sound sources [27]: two oscine-like labial pairs and the unique tracheal membranes, representing the largest number of sound sources described for a vocal organ (figure 2c). Endoscopic observations showed that the ventral and dorsal tracheal membranes were drawn into the tracheal lumen upon pressurization and began oscillating under specific flow conditions. Additionally, it was found that birds in this group possess a labial sound source in each bronchus. Various experimental manipulations and modelling demonstrated that in an intact tracheophone syrinx, all three sound sources can interact nonlinearly to produce complex acoustic features (see [27] for further details).
5. Biomechanical models of song production in birds
The mechanics of voice production are well described by coupled oscillators, and these give rise to the well-known NLPs as described above and throughout this special issue (e.g. [52,56]). These abrupt behaviour or state changes are thus deeply rooted in nonlinear dynamics. However, coupled oscillators can give rise to additional behaviours caused by their nonlinear dynamics that have large effects on vocal output. Although not characterized by transient, salient features such as frequency jumps or period doubling, these behavioural transitions are equally relevant for understanding vocal motor control and communicative systems.
Here, we will present different phenomena in voice production that can be explained by nonlinear dynamical models of coupled oscillators:
| — | switching from a tonal to a spectrally rich sound source; | ||||
| — | switching between frequency modulation mechanisms via nonlinear material properties; | ||||
| — | forcing of source-synchronization by superfast muscles. | ||||
The use of low-dimensional dynamical models has been particularly fruitful for uncovering the rich dynamics found in sound production in birds. A low-dimensional model based on minimal assumptions can highlight the essential biological elements that generate complex vocal behaviours. Additionally, it can provide insights into the degree to which the complexities of behaviour arise from nervous control versus biomechanical factors.
(a) Switching from tonal to spectrally rich sound sources
The physical mechanism underlying voiced sound production is shared between birds and mammals [5]. Self-sustained oscillations of the soft tissue are generated when the airflow provides sufficient energy to the system to overcome dissipation (figure 3a). A minimal model for song production assumes that two basic modes are active: a flapping-like motion and a lateral displacement of the tissues, appropriately out of phase [60–66]. To minimize the number of parameters involved in the description, the dynamical model can be reduced to its normal form. The normal form is a minimal mathematical representation of the dynamics that presents the same bifurcation diagram as the original model [67,68]. In this way, if the variable describes the departure from the equilibrium point of the mid-point position of the tissue (figure 3a), its dynamics can be described using the following differential equations:
Figure 3. Other features of nonlinear dynamics that affect source behaviour. (a) The oscillating tissue is modelled as a mass, m , with damping, b , and restitution force, k, together with other nonlinear terms in equations (5.1) and (5.2). (b) The bifurcation diagram of the dynamical system described in equations (5.1) and (5.2) is set with the parameters (, ) proportional to bronchial pressure and tissue tension, respectively. The insets represent the phase portraits indicating different dynamical regimes: 1, one attracting fixed point; 2, limit cycle; 3, three fixed points: saddle, node and repulsor. The bars indicate Hopf (H) bifurcation and SNILC (S) bifurcation. In region 2, the oscillations indicate that phonation occurs. (c) The synthetic sounds generated by the dynamical model (equations (5.1) and (5.2)) could be almost tonal when emerging from a Hopf bifurcation (H, top panel) or spectrally rich if a SNILC bifurcation is involved (S, middle panel). (d) Linear correlation between pressure and sound frequency during song in kiskadee with full motor control (top panel), a denervated kiskadee, i.e. no syringeal muscle control (middle panel) and a synthetic song generated with the dynamical system (bottom panel). (e) A nonlinear restitution force allows frequency modulation with as opposed to a linear force. (f) This property is used to generate synthetic copies of the kiskadee songs using recorded air sac pressure that is proportional to . Figures reproduced with permission from [58–60].
where is a time scale factor, and (t) and are time-dependent parameters proportional to the tissue tension and to the bronchial pressure, respectively. This model captures the physiological mechanism of sound initiation in birds or mammals: increasing bronchial pressure past the phonation threshold pressure generates self-sustained oscillations of the (syringeal) vocal folds that modulate the airflow to produce sound.
In this model, phonation onset can occur in two distinct dynamical ways: through a Hopf bifurcation [56] or a saddle-node in limit cycle (SNILC) bifurcation (figure 3b). The Hopf bifurcation generates tonal sounds characterized by sinusoidal oscillations, and these oscillations are born with a defined frequency and zero amplitude. As the control parameter (in this case ) moves away from the bifurcation point into the oscillatory regime, the amplitude increases (figure 3c, top panel).
The SNILC bifurcation is called saddle-node bifurcation in the human voice literature [33,69,70]. Due to the different naming, the parallel use has remained overlooked. The SNILC bifurcation generates oscillations that are born with an infinite period and a rich spectrum (figure 3c, middle panel). The bifurcation occurs when a stable stationary state (node) is annihilated by an unstable state (saddle), generating a limit cycle. When the control parameter takes the system through the bifurcation, the variable (t) starts to oscillate and spends a significant amount of time in the phase-space region where the saddle-node annihilation occurred. This is due to the presence of a saddle-node remnant [71]. When the parameter space is close to the bifurcation point, the system predominantly visits the remnant of the saddle-node pair, causing the periodic solution to resemble a sharp peak during a small fraction of its period. Consequently, this mechanism produces oscillations with rich spectral content (figure 3c, middle panel). As the control parameter moves further away from the bifurcation point, the oscillation becomes more tonal and the frequency increases.
Zebra finch vocalizations generally include both tonal and spectrally rich sounds. The spectral content and fundamental frequency of the sound elements unveil a specific relationship, which could emerge from source dynamics, therefore being less dependent on direct control of the upper vocal tract (see [68] for further details). Such a speculative hypothesis requires experimental validation. The response of selective neurons in the cortical areas of the song system to synthetic songs and the response in syringeal muscles were examined and compared to the response to the bird’s own song [32,72,73]. Additionally, the response of wild birds defending their territories was tested using recordings of conspecific birds and synthetic songs of the same themes [74]. In all these experiments, physiological and behavioural responses elicited by synthetic songs were similar to those produced by real songs, showing that low-dimensional models captured essential features of the song. In this way, dynamical models can be used as tools to study songbird production and perception.
(b) Switching between frequency modulation mechanisms via nonlinear material properties
Around the Hopf bifurcation, dynamical models for vocal production transition from silent to phonating. The bronchial pressure drives the model through the bifurcation and determines the source level, but the pressure has only a small effect on the frequency of the oscillation fo. This is consistent with experimental observations in human and avian phonation, where bronchial pressure does not have a large effect on fo [32,75,76]. Around this bifurcation, fo is controlled with the value of the parameter , related to tissue tension that can be controlled with syringeal muscles [77,78].
On the other hand, the dynamical properties of the SNILC bifurcation are different. In two-mass models in humans and one-mass models in birds, the SNILC bifurcation transitions between different vibratory regimes of the masses. In human models, SNILC is used to model transitions between vocal registers (e.g. [69,70]). Interestingly, in models describing vocalizations of the great kiskadee (Pitangus sulphuratus), the SNILC bifurcation allows the fundamental frequency (fo) of the oscillations to be modulated by the bronchial pressure [59]. This behaviour is very distinct from the Hopf bifurcation. In this species, muscle activity does not control fo and bronchial pressure is used for fo modulations (figure 3d). The novel key element introduced in the model to reproduce this feature was a nonlinear restitution force: (figure 3e). When the control parameter is increased near a SNILC bifurcation, the fo of the oscillations depends on the value of (figure 3e). Measurements of air sac pressure in singing kiskadees were used as input parameters to generate synthetic kiskadees song matching fo for all the syllables (figure 3f). For further details, see Amador et al. [59].
The change from control of fo from stiffness parameter k to pressure parameter p can thus be explained by simply changing the mechanical properties of the vocal fold tissue from linear to nonlinear. Vocal fold tissues in both mammals [79] and birds [80,81]—or any biological tissues for that matter—have intrinsically nonlinear stress–strain properties that can be approximated to be linear over a short range around their resting length. The above dynamical models thus strongly suggest that SNILC bifurcations may also play a major role in the dynamical behaviours of mammalian vocal folds.
(c) Forcing of source synchronization by superfast muscles
In songbirds, syringeal muscles, particularly the ventral syringealis muscle, modulate the fundamental frequency of vocalizations [5,77,81]. In great kiskadees, however, syringeal muscles do not modulate fundamental frequency [82], which raised the question of what the function of syringeal muscles in this species is. Syringeal muscle electromyography showed that peaks of muscle activity correlated with sound amplitude modulation in the range of 160−190 Hz [82]. The simultaneous study of the electromyographic syringeal activity shows bursts of activity occurring at the same rate as the modulation of the sound envelope. These modulations, resulting from the lack of synchrony between the sound sources, are accentuated by the action of the obliquus ventralis muscle. A series of denervation experiments showed that this muscle produces a controlled detuning between the two sound sources during the execution of certain syllables of the song (see details in [82]). These amplitude modulations are at low frequencies compared with the phonation frequencies but are likely generated by superfast syringeal muscles that can achieve modulation rates of up to 200−250 Hz [45].
The myosin isoform that enables superfast contraction by avian syringeal muscles (MYH13) is encoded by an ancient gene, shared by all tetrapods [83,84]. Superfast syringeal muscles are thus very likely present in all birds, and the ability to force synchronization between sources may be much more common than currently known.
6. Conclusions
The syrinx exhibits rich and complex dynamical behaviour, enabling a wide range of acoustic features and modulations. The syrinx has several sources of potential NLPs, and we conclude that many of these are exploited in avian communication and sound production. The classical period-doubling and deterministic chaos transitions typically observed in mammals seem not as common in birds, but only very few species have been investigated. Other signatures of nonlinear dynamics are clearly present. For instance, the locking between the syringeal vocal folds can exhibit a certain degree of asymmetry, and the different spectral properties of syringeal vocal fold oscillations have been found to be consistent with various bifurcations.
Because MEAD principles underlie vocalizations in both birds and mammals, the framework of nonlinear dynamics and low-dimensional dynamical models are powerful tools for hypothesis generation to study the underlying physiology and motor control of vocal production in both groups. The diverse anatomy of the syrinx offers distinctive opportunities to investigate complex nonlinear dynamics in vocal production.
Ethics
This work did not require ethical approval from a human subject or animal welfare committee.
Data accessibility
This article has no additional data.
Declaration of AI use
We have not used AI-assisted technologies in creating this article.
Authors’ contributions
A.A.: conceptualization, funding acquisition, investigation, visualization, writing—original draft, writing—review and editing; G.B.M.: conceptualization, funding acquisition, investigation, writing—original draft, writing—review and editing; C.P.H.E.: conceptualization, investigation, visualization, writing—original draft, writing—review and editing.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.
Conflict of interest declaration
We declare we have no competing interests.
Funding
This work was supported by Novo Nordisk grant NFF20OC0063964 to C.P.H.E, and by UBACyT, ANCyT and CONICET grants to A.A. and G.B.M.
