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First published online December 1, 2006
Journal of Experimental Biology 209, 4984-4993 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02594
Voices of the dead: complex nonlinear vocal signals from the larynx of an ultrasonic frog
1 School of Medicine, Department of Biology, and Program for Neuroscience,
Jordan Hall, 1001 E. Third Street, Indiana University, Bloomington, IN 47405,
USA
2 Departments of Physiological Science and Ecology and Evolutionary Biology,
University of California, Los Angeles, CA 90095, USA
3 Department of Molecular and Integrative Physiology, University of
Illinois, Urbana, IL 61801, USA
4 Lehrstuhl Tierphysiologie, Zoologisches Institut, Universität
Tübingen, D-72076 Tübingen, Germany
5 Shanghai Institutes of Biological Sciences, The Chinese Academy of
Science, Shanghai, P. R. China
* Author for correspondence (e-mail: suthers{at}indiana.edu)
Accepted 16 October 2006
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Summary |
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Key words: vocal cord, nonlinear dynamics, vocal communication, Amolops
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; 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.
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Materials and methods |
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;
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
x 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.
Data analysis
`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 8x 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.
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Results |
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; Narins et al.,
2004).
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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.
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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.
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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.
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Laryngeal anatomy
The male
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.
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) 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 female
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.
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Discussion |
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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 6-8
µm 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. tormotus
vocal 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).
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Acknowledgments |
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0.003. 1 cmH2O=98 Pa.
