Most anurans are highly vocal but their vocalizations are stereotyped and simple with limited repertoire sizes compared with other vocal vertebrates,presumably because of the limited mechanisms for fine vocal motor control. We recently reported that the call of the concaveeared torrent frog (Amolops tormotus Fei) is an exception in its seemingly endless variety, musical warbling quality, extension of call frequency into the ultrasonic range and the prominence of subharmonics, chaos and other nonlinear features. We now show that the major spectral features of its calls, responsible for this frog's vocal diversity, can be generated by forcing pressurized air through the larynx of euthanized males. Laryngeal specializations for ultrasound appear to include very thin portions of the medial vocal ligaments and reverse sexual size dimorphism of the larynx - being smaller in males than in females. The intricate morphology of the vocal cords, which changes along their length,suggests that nonlinear phenomena probably arise from complex nonlinear oscillatory regimes of separate elastically coupled masses. Amolopsis thus the first amphibian for which the intrinsic nonlinear dynamics of its larynx - a relatively simple and expedient mechanism - can account for the species' call complexity, without invoking sophisticated neuromuscular control.
Most vertebrate species use sound to communicate intra- and inter-specifically. The vocal repertoires of vertebrate groups range widely,with mammals and especially primates having greater repertoires and call complexity than amphibians. It is often assumed that an increase in vocal complexity requires a corresponding increase in the neuromuscular machinery involved in phonation (e.g. Gaunt,1983; Simpson and Vicario,1990). According to this view, animals that lack sophisticated mechanisms for motor control of the vocal system are limited to producing relatively simple vocal signals. An alternative means for increasing vocal complexity involves the intrinsic nonlinear dynamics of the oscillators in the larynx or syrinx (Fee et al.,1998). The nonlinear properties of the vocal source enable very small, gradual changes in a control parameter (such as the driving respiratory pressure or rate of airflow across the oscillator) to produce abrupt changes in the vibratory mode, resulting in such nonlinear phenomena as period doubling, biphonation, abrupt frequency jumps and deterministic chaos. The relatively recent application of nonlinear dynamics theory to animal communication has fostered a growing interest in the possible importance of nonlinear phenomena in acoustic communication(Fee et al., 1998; Wilden et al., 1998; Banta-Lavenex, 1999; Fee, 2002; Fitch et al., 2002).
We investigated the inherent nonlinear properties of the larynx of a remarkable frog, Amolops tormotus (Ranidae). Whereas most frogs produce relatively simple calls, the vocalizations of A. tormotus are unusual in several respects. First, males of this small species produce a seemingly endless variety of warbling calls that typically contain both upward and downward frequency modulations (Feng et al., 2002). Second, this frog is unique among those studied in using ultrasound for communication. Many A. tormotus calls extend well into the ultrasonic frequency range(Narins et al., 2004). It has been shown that these frogs can detect and respond to ultrasound(Feng et al., 2006). By extending its vocal communication to include these high frequencies, A. tormotus minimizes masking by the generally lower frequency noise from the fast-flowing streams in its habitat. Third, nonlinear acoustic phenomena -including period doubling, frequency jumps and chaos - are prominent components of their acoustic signals and dominate the spectral properties of many calls (Feng et al., 2002; Narins et al., 2004).
Frog vocalizations, except for species that vocalize underwater, are powered by respiratory airflow. Pulmonary air is compressed by the trunk muscles and forced from the lungs through the larynx into the oral cavity and vocal sac. As air passes through the larynx it generates sound by causing oscillation of the vocal cords, which are located upstream from the glottis(Gans, 1973). In some frogs,sound may also be produced by forcing air in the vocal sac back through the larynx into the lungs (Bradbury and Vehrencamp, 1998; Gerhardt and Huber, 2002; Walkowiak,2006). Four pairs of laryngeal muscles control the glottal aperture as well as the position and tension of the vocal cords, which are composed of elastic tissue and lack intrinsic muscles(Martin, 1972; Schneider, 1988). In ranid frogs, partial or total surgical removal of the vocal cords abolishes or substantially modifies the vocalizations(Weber, 1976).
In the following experiments we show that most of the variety and acoustic complexity in the vocal repertoire of A. tormotus can be attributed to the intrinsic nonlinear properties of its vocal periphery. The complex spectral and temporal acoustic features of normal vocalizations can be replicated postmortem by forced airflow though the isolated larynx. A. tormotus thus appears to have achieved its exceptionally large vocal repertoire primarily by exploiting the passive nonlinear dynamics of its laryngeal oscillators, reducing the need for complex and sophisticated mechanisms of vocal motor control.
Materials and methods
Preparation and set-up
Experiments were performed in Huangshan Hot Springs, China on three males of Amolops tormotus Fei collected along Tao Hua Creek(Feng et al., 2002; Narins et al., 2004; Feng et al., 2006). The frogs were euthanized in tricaine methanesulfonate (MS-222). Most of the viscera including the liver, lungs and heart were removed through a large incision along the ventral midline of the abdomen. The primary bronchi were transected as close to the lungs as possible, and a piece (a few mm long) of polyethylene tubing (PE 60; 0.76 mm i.d., 1.22 mm o.d.; Clay Adams Inc., New York, NY, USA)was inserted into the cut end of each bronchus to ensure that it did not collapse during the experiment. The PE tubing was held in place by applying a small amount of tissue adhesive around the end of the bronchus. The frog was then placed on a small piece of wet gauze and positioned with its head extending out of the opening of a celluloid centrifuge tube (25 mm diameter× 85 mm long). The open end of the centrifuge tube was closed with an airtight seal constructed by inserting the frog's head through a small slit in the middle of a disc-shaped plastic membrane (made from a Zip-lock bag). The outer edge of the membrane was folded over the rim of the centrifuge tube and held tightly in place with an elastic band. Silastic medical adhesive silicone Type A (Dow Corning, Midland, MI, USA) was applied between the plastic membrane and the centrifuge tube to make an airtight seal. Tissue adhesive and silastic medical adhesive were use to achieve another airtight seal between the slit in the membrane and the frog's head just behind the hinge of the jaw. The mouth was open.
During the experiment, air was forced through the frog's larynx and upper vocal tract by an experimenter blowing through an 18 cm length of silicone tubing (silastic medicalgrade tubing 602-305; 2.0 mm i.d., 3.2 mm o.d.; Dow Corning), one end of which was sealed into a small hole in the bottom of the centrifuge tube. Owing to the relatively small diameter of the tube, the maximum pressure in the centrifuge tube was only a few cmH2O (1 cmH2O=98 Pa). The air pressure inside the tube, i.e. the sublaryngeal pressure of the frog, was monitored by a miniature piezoresistive pressure transducer (model FPM-02PG; Fujikura, Vista, CA, USA) attached to a silastic tube (silastic medical-grade tubing 602-175; 0.8 mm i.d., 1.7 mm o.d.; Dow Corning), 17 mm long, inserted into the side of the centrifuge tube. Silastic medical adhesive was used to seal the space between the outside of these silicone tubes and the centrifuge tube.
Sound produced during airflow through the larynx was recorded by a microphone (model AT835b; Audio Technica, Stow, OH, USA) placed 1-2 cm from the frog's mouth. The microphone output was amplified (MS1b preamplifier;Rane, Mukilteo, WA, USA). Audible sound and the simultaneous amplified output of the pressure transducer were recorded on separate channels of a DAT tape recorder (model RD135T; TEAC, Montebello, CA, USA). The nominal frequency response of this complete recording system was approximately 50 Hz to 20 kHz±4 dB. In the first experiment (frog #4) we recorded only this audible sound and pressure. During subsequent experiments (frogs #2 and #5) we added an ultrasonic microphone to extend the recorded frequency range. We used a custom-built PC-based recording device (PC Tape) and a custom-built ultrasonic microphone (Department of Animal Physiology, University of Tübingen,Tübingen, Germany) with a frequency response from 15 to 120 kHz(±3 dB) and a roll-off of 10 and 6 dB/octave for <15 kHz and >120 kHz, respectively. The ultrasonic microphone was placed next to the audible microphone so that both microphones were 1-2 cm in front of the frog's mouth.
`Audible' sound and subglottal pressure recorded on DAT tape were reproduced at half speed, sampled at 20 kHz using a 12-bit A/D converter(2821-G; Data Translation, Marlboro, MA, USA) and saved as `Signal' files(Signal v. 3.1; Engineering Design, Belmont, MA, USA) with an equivalent real-time digitization rate of 40 kHz. The ultrasonic signals were digitized using a 16-bit A/D converter (AD 7723; Analog Devices, Norwood, MA, USA) at a sampling rate of 256 kHz, with 8× oversampling. Ultrasonic data were saved as WAV files. Audible sound recordings and measurements of air pressure were aligned in time with ultrasonic recordings using cross-correlation. Fast Fourier transform (FFT) length was 1024 points for both sonic and ultrasonic vocalizations.
The larynges from one male and one female frog, preserved in 10% formalin,were decalcified, embedded in paraffin, serially sectioned at 10 μm in the horizontal plane and stained with Gomori's aldehyde-fuchsin elastic fiber stain and counterstained with Haematoxylin and Eosin (male) or Masson's trichrome (female) using standard histological methods.
Airflow in an expiratory direction through the larynx of euthanized Amolops tormotus generated a variety of sounds in the human audible and ultrasonic frequency ranges. Some sounds had their fundamental frequency(f0) in the audible range whereas others were entirely ultrasonic (i.e. f0>20 kHz). Although the sounds produced in this manner were emitted at a much lower sound level than that of A. tormotus vocalizations, many of them were similar in their spectral and temporal properties to the advertisement calls recorded from this species in the field (Feng et al.,2002; Narins et al.,2004).
Nonlinear dynamics of the frog larynx
A typical sequence of the sounds produced with gradually rising subglottal pressure usually began with a periodic limit cycle containing multiple harmonics. The sublaryngeal threshold `phonation' pressure varied between approximately 1.3 and 2.0 cm H2O in different trials and subjects. As the sublaryngeal pressure continued to increase, a sequence of bifurcations occurred that eventually led to chaos. A typical example of this is shown in Fig. 1A, where the gradually rising subglottal pressure produced a sequence of sounds that began as a fundamental at 16 kHz with multiple harmonics (i.e. a periodic limit cycle),followed by a period doubling bifurcation resulting in a 1/2 f0 subharmonic regime(Fig. 1A, arrow a; Fig. 2A). This was followed by a period quadrupling bifurcation that produced subharmonics in a 1/8 f0 pattern (Fig. 1A, arrow b) and then by apparent deterministic chaos (e.g. last half-second of Fig. 1A; Fig. 1B, arrow d and Fig. 2B). The chaos was often interrupted by subharmonic windows, such as the window at 1/6 f0 (Fig. 1A, arrow c) in this example.
As sublaryngeal pressure decreased toward ambient pressure from its maximum value during the pressure cycle, chaos usually gave way to another series of subharmonic regimes. In the example shown(Fig. 1B), a frequency at 19 kHz abruptly appeared in the final 0.25 s of chaos(Fig. 1B, arrow d and Fig. 2B). At 0.5 s chaos ended,the 19 kHz fundamental rose to approximately 20 kHz and strong harmonics at 2 f0 and 3 f0 appeared. Period doubling occurred briefly at 0.7 s and again at approximately 0.9 s. Sidebands indicating biphonation appeared on each frequency component for a short time centered at approximately 1 s. This appears to be followed by 3/5 mode-locking transition that resulted in a subharmonic regime of 1/10 f0 (Fig. 1B, arrow e and Fig. 2C), which was followed in turn by low amplitude apparent chaos beginning at approximately 2.3 s. In some pressure cycles, chaos continued until sound production ceased.
Sublaryngeal pressure and nonlinear phenomena
The general pattern of nonlinear acoustic phenomena shown in Fig. 1 was typical of the sounds produced during cycles of gradually increasing, followed by decreasing,sublaryngeal pressure, independent of the frog preparation and the experimenter applying the sublaryngeal pressure. This is consistent with the hypothesis that subglottal pressure, or the resulting changes in glottal airflow, serves as a control parameter for the nonlinear dynamics of the vocal oscillators. However, bifurcations also occurred when there was no measurable change in the driving pressure (e.g. the abrupt increase in sound level and bifurcation to chaos at approximately 2.2 s in Fig. 1A).
In order to examine in more detail the relationship between sublaryngeal pressure and nonlinear dynamics of the sound source, we plotted pressure immediately before and after various nonlinear bifurcations for several different pressure cycles. Fig. 3 shows the detailed fluctuations of sublaryngeal pressure during a period beginning 20 ms before a bifurcation until 20 ms after the bifurcation for limit cycles (Fig. 3A,B), subharmonics (Fig. 3C,D) and chaos (Fig. 3E,F). The left panel in each row shows the first onset of the nonlinear phenomenon with rising pressure during the beginning of the pressure cycle. The right panel in each row shows the last occurrence of the nonlinear event as pressure declines toward ambient pressure in the latter part of the pressure cycle. In some cases there was a gradual slight pressure increase or decrease over the 40-ms time interval centered on the bifurcation, but the slope could be either positive or negative. In other cases there was no detectable change in pressure exceeding the background `noise'. None of the regression lines for the mean pressure had a significant slope. Pressure values at the time of the bifurcations in Fig. 3 are summarized in Table 1, which shows that as pressure rises, limit cycles and subharmonics first appear at a lower mean pressure than chaos, but interestingly, as the pressure declines subharmonics and limit cycles disappear at higher mean pressures than does chaos.
|Sound .||Onset, first occurrence during rising pressure (cmH2O) .||End, last occurrence during falling pressure (cmH2O) .|
|Limit cycle||1.71±0.25 (10)||1.79±0.35 (6)|
|Subharmonics||1.73±0.10 (7)||1.86±0.36 (7)|
|Chaos||2.04±0.21 (6)||1.69±0.13 (6)|
|Sound .||Onset, first occurrence during rising pressure (cmH2O) .||End, last occurrence during falling pressure (cmH2O) .|
|Limit cycle||1.71±0.25 (10)||1.79±0.35 (6)|
|Subharmonics||1.73±0.10 (7)||1.86±0.36 (7)|
|Chaos||2.04±0.21 (6)||1.69±0.13 (6)|
Sublaryngeal pressure was measured at the onset of the first occurrence of different nonlinear phenomena during rising pressure and at the last occurrence during falling pressure. 1 cmH2O=98 Pa.
Mean ± s.d. (N=number of pressure cycles measured).
Occasionally, a bifurcation was accompanied by a discrete change in pressure, suggesting a direct causal relationship. An example of this is the small transient increase in pressure accompanying the appearance of subharmonics together with an increase in fundamental frequency and increase in sound level (Fig. 4B).
Nonlinear dynamics below 12 kHz
The sounds in Fig. 1 were recorded with an ultrasonic condenser microphone, which had a frequency response that rolled off at 10 dB/octave below 15 kHz, attenuating the low-frequency `audible' sounds. Recordings made using a microphone with a frequency response restricted to the human audible range (up to 20 kHz) showed nonlinear dynamics similar to those described above in the ultrasonic range. These included the occurrence of a frequency-modulated fundamental with harmonics (Fig. 4A,C); what appears to be a mode-locking transition from 1/8 f0 to 1/7 f0 (preceded by a faintly visible period doubling)(Fig. 4B); and subharmonics,frequency jumps and chaos (Fig. 4C). Fig. 4A also illustrates one of the uncommon cases in which there was a clear positive correlation between subglottal pressure and frequency modulation.
Occasionally, a discrete periodic signal consisting of a fundamental plus its higher harmonics is superimposed on a chaotic signal. Fig. 5A,B shows an example of this in which signals from the ultrasonic(Fig. 5A) and audible(Fig. 5B) microphones were recorded simultaneously on separate channels. We hypothesize that separate audible and ultrasonic oscillators or portions of the vocal cords may be responsible for generating the chaos and the low-frequency periodic harmonic signals, respectively.
The basic structure of the A. tormotus larynx is similar to that of other ranids, except that the male's larynx is approximately half as large as that of the female. This sexual dimorphism in laryngeal size is the reverse of that reported for other frogs(Trewavas, 1933; Schmid, 1978; Schneider, 1988; McClelland et al., 1996). The T-type vocal cords are composed of elastin and fibroblasts. A venule runs along the length of the posterior edge of the caudal part of the medial vocal ligament.
Approximately the dorsal third of the length of the vocal cords(Fig. 6A) consists of a narrow,thin lateral vocal ligament that is attached to the caudal edge of the arytenoid cartilage. (In the horizontal histological sections, the length of the ligament indicates its width in the three-dimensional larynx. Vocal ligaments that appear short or long in the cross-section are referred to here as being `narrow' or `wide', respectively.) The vocal cord has a thick,triangular cross-section where the lateral vocal ligament joins the medial vocal ligament. The caudal and cranial portions of the medial vocal ligament are approximately the same width, but the cranial ligament tapers to a thin edge, whereas the caudal medial ligament maintains a uniform thickness.
Ventral to the dorsal region described above, the morphology of the middle portion of the vocal cords (equivalent to approximately half their total length) is different (Fig. 6B). The lateral vocal ligament has increased in width and thickness. The cranial portion of the medial vocal ligament is thin and approximately four times wider than its caudal portion. The width of the caudal medial vocal ligament is reduced compared with that in the dorsal part of the vocal cord. The middle portion of the vocal cord, like its more dorsal region, is attached to the caudal edge of the arytenoid cartilage, but unlike the dorsal region, the relatively thick base of the lateral vocal ligament also extends laterally to form an attachment on the medial edge of the cricotrachealis cartilage. This anatomical arrangement suggests that contraction of either the inferior branch of the laryngeal dilator muscle (Schmid,1978) or of the laryngeal sphincter muscle, or simultaneous contraction of both these muscles, will exert tension on the lateral ligament,causing it to pivot around the caudal edge of the arytenoids. This action presumably initiates phonation by rotating the cranial portion of the medial vocal ligaments toward the midline and into the air stream, where the two vocal cords might contact each other along part or all of their length. According to this scenario, both the laryngeal constrictor muscles and the inferior branch of the laryngeal dilator muscles may function as vocal cord adductors.
The posterior laryngeal pouch along the middle portion of the vocal cords is filled with a highly vascularized network of serous secretory cells surrounding air-filled passages or chambers(Fig. 6B, vn). Their position at the base of the vocal cords is well situated for their presumed function of lubricating the vocal cords with serous fluid. Lubrication of mammalian vocal folds by laryngeal secretions is essential for normal vibration during phonation (Fukuda et al.,1988; Nakagawa et al.,1998).
The vocal behavior of all frogs is sexually dimorphic, but in other species the female has a smaller larynx than the male. The converse is true for A. tormotus in which the female's larynx is approximately twice the size of the male's larynx. Her vocal cords are larger and her medial vocal ligament is thicker compared with the male. The nature of her vocalizations is not known.
The vocalizations of Amolops tormotus are remarkable for their variety, the prominence of nonlinear phenomena and the presence of ultrasonic frequencies. The experiments we report here provide insight into the mechanistic basis for these unusual properties of anuran vocal signals.
Nonlinear vocal phenomena
Subharmonics, frequency jumps and deterministic chaos are common in the natural vocalizations of A. tormotus(Feng et al., 2002; Narins et al., 2004) and in the sounds produced by blowing air through the larynx of euthanized frogs. As the driving sublaryngeal pressure was gradually increased, a periodic sound consisting of a fundamental and its higher harmonics characteristically appeared when the phonation threshold was reached. As sublaryngeal pressure continued to increase, a series of bifurcations occurred from the initial limit cycle to period doubling and other subharmonic bifrucations, followed by apparent chaos. Although subharmonics and chaos typically occurred at successively higher driving pressures above the phonation threshold, there were exceptions and chaos was often interrupted by windows of periodic behavior. Only occasionally was a bifurcation accompanied by a detectable inflection in the driving pressure.
The sounds we elicited in the present experiments were much fainter than the vocalizations produced by living frogs. Subglottal pressure is one of the factors that determine vocal intensity and the subglottal pressures we used(<4 cmH2O) may be lower than those that normally accompany phonation. In addition, since in our experiments the mouth was open, there was no inflation of the vocal sacs, the acoustic properties of which have been shown to amplify (and modulate) the laryngeal signal in live frogs(Rand and Dudley, 1993; Bradbury and Vehrencamp, 1998; Rand, 1999). Paulsen reported that subglottal pressures below 10 cmH2O elicited no sound from the isolated larynx in three other species of Rana whose calls consist of a series of short pulses (Paulsen,1965). At higher pressures, air in the caudal pouch of the vocal cords pushed them together in the midline, blocking airflow until the rising pressure behind the vocal cords caused them to pop open and oscillate in the escaping air. With a sustained source of airflow this process repeats itself,generating a series of pulsed vocalizations. It is interesting that the caudal pouches of the vocal cords in A. tormotus, which produce continuous calls of relatively long duration, are small because of a short caudal vocal ligament of the cord's medial segment and are partially filled with a network of glandular serous cells along much of their length. The presence of secretory tissue in the caudal pouch may also facilitate the production of long calls by preventing the driving pressure from pushing the cords together.
Why are nonlinear phenomena so prominent in the vocalizations of A. tormotus? The complicated morphology of the T-type vocal cords would seem to be well suited for producing complex oscillatory behavior. Vocal cords of this type are present in the Ranidae, Hylidae and Pelobatidae, but nonlinear oscillatory dynamics are not a common, much less a dominant, part of the natural vocal repertoires of these other species. Airflow through the isolated larynx of tree frogs can produce some nonlinear sounds, but these sounds are not present in the normal vocalizations and were attributed to mucus on the vocal cords (Gridi-Papp et al.,2006). Based on its shape in cross-section, the vocal cords of A. tormotus do not fit well into any of the several basic morphological types (Schmid,1978) described for other genera. We speculate that the distinctive morphology of A. tormotus vocal cords, perhaps involving the very different shape of its dorsal and ventral segments compared with its middle portion (Fig. 6A,B), may cause the vocal cords to oscillate as a dynamic system comprising two or more coupled masses capable of sudden transitions between different nonlinear modes of vibration.
Nonlinear phenomena in mammalian vocalizations arise from complex interactions between aerodynamic and biomechanical forces on the vibrating vocal folds behaving as coupled nonlinear oscillators(Wilden et al., 1998; Fitch et al., 2002). Fee et al. showed that the nonlinear dynamics of oscillation, which are responsible for much of the acoustic complexity in zebra finch (Taeniopygia guttata)song, can be reproduced in the isolated syrinx and accounted for by a two-mass model consisting of a heavy medial labium coupled to a flexible medial tympaniform membrane (Fee et al.,1998). A two-mass model of the avian labia in which the upper and lower portions of each labium function as separate elastically coupled masses has been discussed by Mindlin and Laje(Mindlin and Laje, 2005).
Occasionally, airflow through the A. tormotus larynx produced simultaneous periodic and aperiodic chaotic sounds(Fig. 5). It is not clear whether these arise from coupled different oscillatory modes in the same oscillator (biphonation) or are from two independent sets of oscillators (two voices). The simultaneous production of two independent sounds has also been reported in the leptodactylid frog, Physalaemus pustulosus(Drewry et al., 1982). Some advertisement calls of this species consist of two components: a whine accompanied by one or more chucks. It is hypothesized that the whine is produced by vibration of the vocal cords and the chuck is produced by vibration of a large fibrous mass that is loosely coupled to the vocal cord by a ligament (Drewry et al.,1982; Ryan and Drewes,1990). This hypothesis was recently verified by surgically removing the fibrous mass resulting in the inability of males to produce the chuck (Gridi-Papp et al.,2006).
Source of ultrasound
Microchiropteran bats and other mammals that produce ultrasonic fundamental frequencies in air have thin membranes on their vocal folds(Suthers and Fattu, 1973; Mergell et al., 1999). In the big brown bat, Eptesicus fuscus, this membrane is approximately 6-8μm thick, 500 μm wide and 2 mm long(Suthers and Fattu, 1973). In A. tormotus, ultrasound is most likely produced by oscillation of the cranial portion of the medial vocal ligament, based on its dimensions. This ligament varies in width and thickness along the length of the vocal cord, but is at its thinnest and widest along the middle portion of the cord where it is approximately 20-30 μm thick and approximately 200 μm wide(Fig. 6B). Although this ligament is approximately three to four times thicker than the vocal membrane of the big brown bat, the fundamental of the bat's frequency-modulated sonar pulses extends to considerably higher frequencies than does the fundamental of the frog's communication calls.
It would be interesting to know how the dimensions of A. tormotusvocal cords compare with those of other small frogs, which share T-shaped vocal cords but do not produce ultrasound. Quantitative comparative data of this type are not, to our knowledge, available. In male cricket frogs(Acris crepitans) the caudal portion of the medial vocal ligament is relatively wide and thin (McClelland et al., 1996), suggesting a high natural frequency of oscillation. The authors give the estimated volume of the vocal cord, but not the dimensions of its ligaments (McClelland et al., 1996).
Whereas males of other frogs have a larger larynx than the females, the opposite is true in A. tormotus. Although not universally true, the mass of the vocal cords tends to be correlated to body size so large frogs usually produce calls with a lower dominant frequency(Narins and Smith, 1986; Marquez, 1995; McClelland et al., 1996; Gerhardt and Huber, 2002); for some species, the females have been shown to prefer males with lower frequency calls (Marquez, 1995). In male A. tormotus, however, natural selection may have favored a small larynx in order to produce higher frequencies where there is less environmental noise.
Vocalizations of female A. tormotus have not been described. Most female frog vocalizations consist of low intensity, simple release calls,although females of a few species produce advertisement calls(Emerson and Boyd, 1999).
Vocal diversity in the absence of central control
One might predict that the importance of central control of sound production should be directly related to the variety and complexity of the vocal repertoire. This is not the case for A. tormotus, however. Contrary to that prediction, our experiments with A. tormotus show that despite the richness of its vocal repertoire, most of the acoustic features present in normal vocalizations can be generated by airflow through the larynx of a euthanized frog. Our data suggest that A. tormotus'diverse vocal repertoire depends on the interaction between the aerodynamic forces, normally generated by respiratory muscles, and the intrinsic biomechanical properties of the laryngeal oscillators. Laryngeal muscles presumably gate phonation, but their participation does not appear to be required in order to achieve either the vocal diversity or complexity that characterizes the acoustic signals of this species. We do not know, however,whether within this highly nonlinear vocal system males are able to control the acoustic structure of their calls or have individual vocal signatures that may involve neuromuscular control.
Nonlinear dynamics have been found to contribute to the vocal repertoire of several vertebrates (e.g. Fee et al.,1998; Wilden et al.,1998; Fee, 2002; Fitch et al., 2002), but A. tormotus appears to be unique in the extent to which it depends on the inherent nonlinear oscillatory properties of its vocal cords. This ability,together with the long duration of most vocalizations, may have evolved as a relatively simple and inexpensive way of broadening the calls' bandwidth and shifting their energy to ultrasonic frequencies in order to be heard over the background noise of the mountain streams along which they live(Narins et al., 2004).
We thank Chen Qi-Lin, Weng Jun and Yu Xinjian for their assistance in the field experiments. Sandra Ronan, Sue Childress, Mica Terrell, Brian Nelson and Rhonda Burgoon assisted with various aspects of data analysis and manuscript preparation. We are indebted to Rodrigo Laje for his constructive comments on a previous version of this article. This work was supported by grants from the National Institutes of Health (NS-29465 to R.A.S., DC04998 to A.S.F., DC00222 to P.M.N.), a DFG grant (SFB 550) to H.U.S. and a grant from the State Key Basic Research and Development Plan [G1998010100 (China)] to C.H.X.