Riede, Tobias : Vocal changes in animals during disorders

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Chapter 5. Vocal tract length and acoustics of vocalization in the domestic dog

This chapter is a revised version of: T. Riede, W.T. Fitch: Vocal tract length and acoustics of vocalization in the domestic dog (Canis familiaris). J. Experimental Biology 202: 2859-2867 (Riede, Fitch 1999).

The sound production systems of all mammals exhibit a number of fundamental anatomical and acoustical similarities. The primary acoustic signal is generated at a source, typically the vocal folds of the larynx (the glottal source), which are driven into rapid mechanical oscillations by an expiratory air flow from the lungs. Opening and closing, the vocal folds modulate the airflow through the glottal opening, producing a time-varying acoustic signal: the glottal source signal. Many mammals produce a nearly periodic signal in the larynx, which can be represented as a Fourier series, with a fundamental (lowest) frequency and integer multiple harmonics. A narrowed but non-oscillating larynx can also generate turbulent noise.

All mammals also have a supralaryngeal vocal tract (hereafter simply referred to as "vocal tract"), through which the sound generated at the glottal source must pass. The column of air contained in the vocal tract, like any tube of air, has resonant modes, which selectively allow certain frequencies in the glottal source to pass and radiate out through the mouth or nostrils into the environment. In other words, the vocal tract acts as a bank of bandpass filters, each of which allows a narrow range of frequencies to pass. These resonances of the vocal tract, along with the spectral peaks they produce in the vocal signal, are given the special name "formants" (from Latin formare "to shape"; after Hermann 1890). This term has a long history of use both in speech science (Fant 1960; Titze 1994) and bioacoustics (Lieberman et al. 1969; Nowicki 1987; McComb 1988; Fitch & Hauser 1995).

In an anatomical investigation of the non-human vocal tract, Lieberman et al. (1969) discovered important differences between non-human and human vocal tract shapes, and concluded that the production of the full range of vowels found in human speech are impossible without a modern human vocal tract. For a long period after this there was little research on formants in animal communication (although see Andrew 1976). Recently, however, there has been a resurgence of interest in animal formant production and perception.


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In terms of perception, it has long been known that various animals can discriminate human vowels (baboons: Hienz & Brady 1988; dogs: Baru 1975, cats: Dewson 1964; blackbirds and pigeons: Hienz et al. 1981; macaques: Sommers et al. 1992). Because vowels are perceived and classified primarily on the basis of the two lowest formant frequencies (Peterson & Barney 1952; Bogert & Peterson 1957; Kent 1978, 1979), this work suggests that animals can perceive formants. More directly, Sommers et al. (1992) documented the ability of Japanese macaques to discriminate formant frequencies with an accuracy rivalling that of humans. Finally, Owren (Owren & Bernacki 1988; Owren 1990) used operant techniques to show that spectral features potentially related to formants are discriminated by vervet monkeys in their own species-specific calls. A number of studies have demonstrated the potential communicative relevance of formants in several mammal species (cats: Shipley et al. 1991; rhesus macaques: Hauser et al. 1993; baboons: Owren et al. 1997). A more detailed discussion of the importance of formants for acoustic communication in animals is given by Fitch (1997) and Owren & Rendell (1997).

In terms of production, formant frequencies are strongly influenced by vocal tract length and shape (Fant 1960; Titze 1994). Carterette et al. (1979) found a good correspondence between isolation call formant frequencies in domestic kittens and the formant frequencies predicted theoretically for a uniform tube (closed at one end) of the same length as the kitten vocal tract. The effect of vocal tract length was further studied by Fitch (1997), who measured vocal tract length, body size and formant frequencies in rhesus macaques (Macaca mulatta), and found that formant frequency spacing is a reliable correlate of body size in that species. Further investigations on the relationship between vocal tract length, body size and formant characteristic suggest that the prediction of body size from the acoustic signal (and vice versa) may also be applicable to humans (Fitch & Giedd 1999). Given the Baru (1975) study, which indicated that formants in human speech can be perceived by dogs, it is reasonable to ask if formant frequencies could potentially be used in intraspecific size assessment in this species. In canid communication, the advertisement of body size and strength plays an important role, mentioned as early as Darwin (1872). In dominant dogs, large size is exaggerated by the stiff upright threat posture, while the crouched posture of submission decreases apparent size. Low frequency, broad-band barking or growling often accompanies threats, vocalizations ideally suited for accurately outlining the vocal tract transfer function. If vocal tract length is related to body size in canids, growls could thus possibly convey an accurate impression of size to listeners. In contrast, high frequency whining that accompanies the crouched posture of submission, provides little information on body size as such a high frequency source contains energy at only a few, widely spaced frequencies (Ryalls & Lieberman 1982).


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At least 12,000 years of domestication (Clutton-Brock 1995; Vila et al. 1997) have resulted in a remarkable diversity of dog breeds, differing in behavioural traits and overall body size parameters. Dogs range in mass from Chihuahuas to Saint Bernards, a 100-fold difference. However, this difference in body size does not necessarily imply an equivalent difference in proportions (Clutton-Brock 1995). Most dog skulls are actually quite similar in proportion, except for the extreme long-faced breed like the Borzoi, or short faced breeds, like the Boxer. Morey (1992) gives evidence that skull proportions have been relatively constant since prehistoric times. Because of these significant size differences in breeds, it is not obvious that the correlation between body size, vocal tract length and formant frequencies documented for macaques by (Fitch 1997) will hold for domestic dogs of different breeds. The goal of this study was thus to analyze the correlation between vocal tract length ("VTL"), body mass and formant frequencies in the domestic dog, and to determine if the huge intraspecific size differences generated by selective breeding have affected the relationship between body size and the acoustic cues related to vocal tract length.

5.1 Formant frequencies and vocal tract length

Acoustic theory predicts that formant centre frequencies will relate to simple anatomical measures of the vocal tract, mainly its length and shape (particularly variations in cross-sectional area along the length of the tract). The length is the single most important anatomical parameter which influences the frequencies of the formants. As a first approximation, we can consider the resonant frequencies (natural modes) of an air-filled tube which does not vary in cross-sectional area: a "uniform tube". For a uniform tube with one end closed, resonant frequencies are described by:

equation 1

and with both ends closed:

equation 2


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where, i = 1 to the number of formants; c is the speed of sound (350 m/s); VTL is vocal tract length (in m) and Fi frequency (in Hz) of i-th formant. It will be noticed that, for a uniform tube regardless of end conditions, the frequency difference between the successive resonances is constant, given by:

equation 3

Thus if formants from a uniform tube can be measured (which requires an excitatory signal with appreciable energy at the formant frequency), their frequencies provide direct access to the length of the tube. Specifically, the difference between successive resonances should theoretically provide an accurate estimate of tube length. The only effect of the boundary conditions (whether the tube is open or closed at the ends) is to shift the entire pattern up or down in frequency, offsetting the absolute frequencies of the formants (e.g., of the lowest formant F1) but not changing their spacing. A measure of formant spacing thus overcomes the need to make assumptions about these vocal tract boundary conditions, which are known to vary in humans but which are unknown for nonhumans. These factors led Fitch (1997) to introduce a measure he termed "formant dispersion" which is the averaged difference between successive formants :

equation 4

where Df is the formant dispersion (in Hz), and N is the total number of formants measured. Formant dispersion is the mean of the formant spacings; a reasonable choice since the mean is theoretically the best predictor (in a least squared error sense) of a normal distribution. Averaging the differences should make the measure less sensitive to deviations from the first approximation (caused for example by non-uniform shape) and thus provides an overall estimate of spectral dispersion. Higher order statistics, for example the standard deviation of


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the formants intervals {Fi+1 - Fi}, can be used to evaluate the extent to which the uniform tube approximation holds. For example, four formants of 500, 1500, 2500, 3500 Hz (as in a 17.5 cm long uniform tube) would yield a Df of 1000 Hz. However, a set of formants of 700, 1200, 2200, 3700 Hz (as in the human spoken vowel \a\) also yields Df = 1000 Hz, but does not approximate those of a uniform tube, which has evenly spaced formants. The uniform tube approximation is a good one to the extent that the intervals between F1 - F2, F2 -F3, F3 - F4 etc. are nearly equal, in which case the standard deviation of the formant intervals will be small.

In summary, the spacing between resonant frequencies of a uniform tube decreases as its length increases, implying that individuals with longer vocal tracts should show exhibit formant dispersions. In this study we tested this prediction by measuring VTL from radiographs (x- rays) of domestic dogs. We then used linear prediction to measure the formant frequencies from the growls of the same dogs, calculating the formant dispersion using Eq. 4 and comparing it with the predicted formant dispersion from Eq. 3. Finally we tested the correlation between these variables and body mass to see how closely these acoustic variables predict body size.

5.2 Materials and Methods

5.2.1 Subjects

The subjects were 47 domestic dogs of various ages representing 21 different breeds. These dogs were patients at a veterinary practice (Clinic for Small Animals, Freie Universität Berlin). All dogs were treated for broken legs, an affliction unlikely to have a substantial impact on the vocalizations of the animal. The animals were between 0.5 and 15 years old, and between 2.5 and 50 kg in mass. Dogs were weighed using a 100 kg scale (accuracy 100 g). All animals were in the mass range typical of their breed (according to Clark & Brace 1996).

5.2.2 Anatomical Measures

Radiographs were taken of 33 anaesthetised dogs immediately after surgery. Each animal was placed on its side on a radiographic table and lateral images were made of the head and the neck region. For calibration, a 1 cm-lead-reference-square was positioned at the midsaggital level of the head. Vocal tract length (VTL) was determined from tracings of the X-ray images that were scanned using a Microtek MRS-600Z scanner and measured using NIH Image (version 1.58). Image clarity was sufficient to delineate the outlines of the oral vocal


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tract, although the glottis itself was not visible in all cases. Therefore the midpoint of the thyrohyoid bone, which was always visible, was used as the origin of our vocal tract length measurement. The thyrohyoid always appears on such radiographs just on the cranial side of the glottis (Gaskel 1974; Kneller 1994). Thus, our measure was slightly less than the actual vocal tract length, but in a manner consistent from dog to dog. A curvilinear line from the midpoint of the thyrohyoid cartilage along the line of the soft and hard palates to the front of the incisors was drawn and measured (Fig. 5.1). The VTL was determined with reference to the calibration square. The skull length was measured as the distance between the front of the incisors and the Protuberantia occipitalis externa of the Os occipitale; the latter was sometimes off the radiograph and thus the skull length measurement was missing in some cases. The repeatability of these measurements was high: in 10 animals the measurements were repeated ten times, which yielded standard deviations of 0.5 cm (2.8%) for VTL and 0.1 cm (< 1%) for skull length.

Figure 5.1: Schematic drawing of the anatomical features and the morphometric features used in this study as observed by radiography. The lines represent 1 vocal tract length (VTL) and 2 skull length and were measured on digitized images of the radiographs in NIH image with reference to a 1 cm calibration square.

5.2.3 Acoustical Measurements

Dog vocalisations were recorded using a Sony-WMD3 Walkman Professional cassette recorder and Sennheiser microphone (ME80 head with K3U power module) on BASF ChromeSuper II tapes whilst the animals were in their stalls in the clinic. Only growl vocalisations were considered for analysis, since growls are uttered with a nearly closed mouth and therefore use the full length of the vocal tract. Growling is a low-frequency, broadband signal, which is uttered in sequences of variable duration consisting of growls with interspersed pauses. Because of their low frequency and broad bandwidth, growls are well-


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suited for formant estimation. Growling was induced by staring into the dog's eyes (a mild threat to the animal). If growling could not be provoked in this way, only radiographic data were used for that individual. This opportunistic approach led to an overlap of anatomical and acoustical data sets for 12 dogs representing 8 breeds. To enlarge the acoustical data set, we also recorded growling of 14 dogs from which we did not take radiographs.

Recordings were digitised at 16-bit quantization and 24-kHz sampling rate using an Audiomedia II sound card and Sound Designer 2 software (Digidesign, Palo Alto, CA).

Linear predictive coding ("LPC") is a spectral modelling technique widely used to estimate formant frequencies in human speech. LPC uses least-squares curve fitting to estimate the value of a point in a time-domain waveform based on the past N points, where N is the order of the LPC analysis. LPC algorithms then construct the best-fitting all-pole model to account for the waveform. "All-pole" means that only vocal tract resonances ("poles") are estimated, and not anti-resonances ("zeroes"). Such a spectral model appears to be a valid first-approximation for most human speech (Markel & Gray, 1976), as well as for the dog growls we analysed here. The specifics of the many algorithms used to do LPC are well-documented elsewhere (see Markel & Gray, 1976 for the mathematical details, or Owren & Bernacki, 1998 for applications in bioacoustics); we used the autocorrelation technique provided by the signal processing toolbox of MATLAB 4.2 (The Mathworks, Natick, MA) in the current analysis. This technique provides as output the coefficients of an Nth-order all-pole digital filter whose frequency response best approximates (in a least-squares sense) the spectrum of the input signal. Given a broadband source signal and an appropriate model order (approximately, two plus twice the number of formants), LPC analysis can provide an extremely accurate estimate of formant center frequencies in both human speech and in animal sounds (e.g. Fitch, 1997). Signal analysis was done using MATLAB with 18 to 26 coefficients and preemphasis settings of 0.8 to 0.99. All LPC measurements were visually verified by superimposing the LPC-derived frequency response over a 512-point fast Fourier transform (FFT) of the same time slice, allowing the user to select the optimum number of coefficients for each call by trial and error. When possible, we measured 5 formants in each growl, but the number of formants which could be extracted was highly subject dependent.


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5.3 Results

Raw data are presented in Table 5.1 and a summary of the data is presented in Table 5.2.

Table 5.1: Raw morphological and acoustic data for 47 individual dogs. VTL - vocal tract length; Df - formant dispersion; CV - coefficient of variation; F1, F2 - first and second formant


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Table 5.2: Basic descriptive data for acoustic and anatomical variables of the dogs used in the study. (n - sample size, d - the standard deviation, S.E. - standard error of the mean, ’min‘ and ’max‘ - minimum and maximum values, respectiveliy; VTL - vocal tract length, Df - formant dispersion, F1 - lowest formant frequency).

 

 

n

mean

d

S.E.

min

Max

 

age (years)

45

5.4

4.2

0.6

0.5

15

 

mass (kg)

45

19.3

13.7

2.0

2.5

50.0

 

log10 body mass (kg)

45

1.15

0.37

0.055

0.39

1.69

 

skull length (cm)

25

16.0

5.27

1.08

8.1

25.1

 

VTL (cm)

33

15.7

4.05

0.71

6.9

22.4

 

Df (Hz)

26

1101

429

88.6

568

1910

 

F1 (Hz)

26

585

239

49

234

1173

Of the 33 dogs, vocal tract length varied between 6.9 cm (a Yorkshire terrier) and 22.4 cm (a Rottweiler). In 12 of these 33 dogs, growls were elicited for acoustic analysis. There were no significant differences between females and males (unpaired t-test, t= -1.08, nf=19, nm=26 p=0.57) and therefore for further analysis the data for both sexes were combined. Normality testing indicated that head length, VTL and body mass measurements were not normally distributed while formant dispersion and age were. All correlation analyses were thus performed with both Pearson parametric correlation and Spearman non-parametric. No significant differences in the results of these two analyses were found, so we report only the

Pearson values. Correlation analyses are presented in Table 5.3. High and statistically significant correlation was found between all of the variables measured except for skull length and the lowest formant frequency (F1) and VTL and F1. In contrast to F1, correlation between formant dispersion and VTL or skull length were highly significant (P< 0.001). VTL increased with body mass and the formant dispersion decreased with increasing size and with increasing VTL (Fig. 5.2)


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Table 5.3: Pearson correlation coefficients between the various acoustic and anatomical variables measured in this study. *** - significant at P<0.001; ** - significant at P<0.01; * - significant at P<0.05; ns - not significant p>0.05. (F1 - lowest formant frequency, VTL - vocal tract length, Df - formant dispersion)

 

 

 

log 10 body

mass

skull length

VTL

F1

 

skull length

 

0.96***

(N=25)

1.00

 

 

 

VTL

 

0.93***

(N=33)

0.95***

(N=25)

1.00

 

 

F1

 

-0.53**

(N=26)

-0.37ns

(N=12)

P=0.117

-0.38ns

(N=12)

P=0.107

1.00

 

Df

 

-0.88***

(N=26)

-0.87***

(N=12)

-0.87***

(N=12)

0.62***

(N=26)

For 12 dogs (where both anatomical and acoustical data were available) the theoretical value calculated using the VTL obtained from the radiograph and equation 3 was compared with that calculated from vocalisation recordings using equation 4. The predicted and measured formant dispersion were not significantly different (paired t-Test: t= 0.26; n=12; p=0.79).


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Figure 5.2: Relationship between (A) vocal tract length, VTL and body mass (m in kg), (B) VTL and formant dispersion, Df and (C) formant dispersion and body mass. The lines represent the linear regression lines, with the equations and r² values given in each case.


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Figure 5.3: Waterfall representation of the LPC curves of a growling utterance showing the formant distribution over approximately one second. This 3-D spectrogram display shows the Fourier transform spectra of several time slices. The actual time slices are 75% overlapping.

The longest growl that we recorded lasted up to 3 s. The length of the growl sequences from different dogs varied from a few seconds up to several minutes. In four animals with very long growl sequences, the stability of formant frequencies was investigated. Within a single growl utterance, the formant pattern was rather stable (Fig. 5.3 gives a representative example). In the four animals for whom multiple growls were examined, the formant distribution was found to vary at least slightly between growls. In particular, certain formants sometimes "dropped out" of the signal (Fig.5.4), suggesting that the dogs were able to modify their source characteristics or vocal tract configuration (e.g., via lip or tongue movements) somewhat during a growl sequence.

Standard deviations of formant spacing ("formant deviation") was quite variable between dogs ranging from 11% to 71% of the formant dispersion (mean: 42%). Thus some dogs closely approximated the uniform tube approximation (e.g. dog 1 in Fig. 5.4) while others deviated from this approximation considerably (e.g. dog 4 in Fig. 5.4).


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Figure 5.4: Consistency of formant frequencies, measured across different growls for each of four individual dogs. Each growl is represented by a set of formant frequencies. For instance the first growl of dog 1 has four formant frequencies at approximately 500 Hz, 1800 Hz, 3000 Hz and 4200 Hz.(dog 1: Dachshund; dog 2: Rottweiler; dog 3: Irish Setter; dog 4: Mix (mass 10kg))

5.4 Discussion

The results presented above indicate that formant frequency spacing (as measured by Df) is closely correlated to vocal tract length (VTL) (Fig. 5.2b). Because VTL is in turn related to body size (Fig. 5.2a), the growling signals analysed here provide a reliable indication of the size of the animal that produced them (Fig. 5.2c). Below, we consider some of the acoustical, anatomical and methodological issue raised by our data, and end with a brief consideration of some implications of this data for canine communication.

Formant frequencies are held relatively constant across the duration of an individual growl (Fig. 5.3), but show some change across growls produced by the same animal (Fig. 5.4). These changes may result from a process paralleling that used in human speech: active variation of the shape (mid-saggital cross-sectional area function) of the vocal tract. Vocal tract shape can be changed voluntarily by a vocaliser by differing the amount of mouth opening (Stevens & House, 1955; Ohala, 1984), as has been shown in both monkeys (Hauser et al., 1993) and birds (Westneat et al., 1993, reviewed in Gaunt & Nowicki, 1998).


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Mouth opening in humans has a stronger effect on the first formant than on other formants (Stevens & House, 1955). Vocal tract shape can also be modified by movements of the tongue body or blade, raising or lowering of the larynx or using the velum to open or close the nasal passages. Although such changes have not been documented in nonhumans, the comparative anatomy suggests that dogs may have similar capabilities to those of humans in these respects.

The notion that dogs can vary their vocal tract shape receives further support from the data on deviation from even spacing of the formants. For a uniform tract the formant spacing is expected to be constant. This is not the case in all of the dogs' growls we recorded. The standard deviations of formant spacing show considerable variability for an individual dog, with some individuals approaching uniform spacing and others having quite high deviation from even spacing. For example, in figure 5.4 we can see that dog 1 has approximately equal formant spacing (in growls 1 to 4) while dog 4 does not. Because our radiographs clearly demonstrate some deviations from uniform cross-sectional areas in many dogs' vocal tracts, we hypothesise that the deviations observed in the acoustic signal result from non-uniform vocal tract shapes. Unfortunately, our data provides only static images of the vocal tract of anaesthetised dogs, while the relevant vocal tract shape is obviously that adopted during vocalisation. We are thus unable to determine if different degrees of formant deviation result from differences across dogs in the vocal posture adopted during growling, though this seems a plausible hypothesis. Testing this will require anatomical images of the vocal tract of dogs taken during vocalisation; cineradiography (moving picture radiography) would be ideally suited for this task. Another useful extension of our results would involve 3-D reconstruction of the vocal tract using non-invasive imaging techniques such as MRI. Such techniques have proved exceedingly valuable in understanding human speech acoustics (e.g. Baer et al. 1991, Story et al. 1996), and could be used with other species as veterinary use of non-invasive imaging techniques increases.

Due to deviations from even spacing, the amount of information contained in any one formant is less than that contained in the entire ensemble of formants. A good illustration is that the lowest formant F1 provided a much less reliable indication of body size than did formant dispersion (Table 5.3). The correlation coefficient between log body mass and F1 was only -0.53 (N=12), compared to that between Df and log body mass of -0.88. In addition, there was a negative correlation between F1 and VTL, it was not statistically significant (r = -0.38, p = 0.1), while the correlation between VTL and Df was highly significant (r = -0.87, p < 0.01). However, it should be noted that the sample size for this analysis is too small (N= 12) to reliably reject an inverse correlation between F1 and VTL, the difference between the


84

findings for F1 and for Df (which had the same sample size) invites some comments. One possibility for the higher variance in F1 is measurement error: LPC estimates of lower formants can be effected by low-frequency or DC poles due to radiation, room reverberation characteristics or other phenomena. Also, variability in the amount of low frequency energy in the source signal will have the effect of decreasing the accuracy with which F1 can be measured (though this decrement would also be suffered by perceivers, and is thus not restricted to our algorithm).

Physiological explanations for the low reliability of F1 include the deviations from uniform vocal tract shape mentioned above (changes in mouth opening have a disproportionate effect on F1, and potential nasal resonances might also play a role in obscuring F1). Another important factor may be the effect of tissue compliance. At low frequencies, the tissues in the walls of the vocal tract absorb energy, and thus tissue compliance places a bound on F1 below which it cannot fall (approximately 180-200 Hz for humans, Fujimura & Lidqvist, 1970). Finally, variation in the end conditions (e.g. from a half-open to a fully open tube) will have a large effect on individual formant frequencies but none on formant spacing (see Introduction). In summary, an algorithm for estimating body size from formant locations (whether on a computer or in a perceiver) will be most reliable if it includes information from all formants, and not focus on a single formant, and especially not on F1, which for the reasons detailed above is likely to be the least reliable formant of all.

Although dog breeds exhibit high variability in skull shape (Miller, 1964), our results indicate that this variability does not obscure the strong negative relationship between formant dispersion and VTL and/or body size. Formants therefore provide an indication of a growling dog's body size. These results parallel those reported for rhesus macaques by Fitch (1997), who further discusses the implications of these relationships for acoustic communication. The artificial selection for brachycephalic or dolichocephalic skull shapes over the course of domestic breeding seems not to have had a pronounced effect on VTL/body size correlations. However, there are indications from other work that the shortening of the skull during domestication in some breeds has had an impact on vocal tract shape, particularly in the pharyngeal area. In extreme cases of head shortening (brachycephalic breeds such as bulldogs) a pharyngeal constriction is often observed which is well known to cause respiratory problems (Wykes, 1991; Hendricks, 1992). More research is required to determine what acoustic effects might result from this skull and vocal tract shape diversity in domestic dogs.


85

Although the current work has focused only on formant production in canines, earlier work by Baru (1975) clearly demonstrated that dogs are also capable of perceiving formants with high accuracy. It would be quite surprising if dogs could perceive formants in synthetic human speech but not in their own species-specific vocalisations. Thus we hypothesise that formants could play a role in canine communication. In particular, the information that formants in growls convey about body size should be available to other listening dogs, and may well play a role in social behaviour. Perceptual experimentation will be necessary to determine if this in fact the case. For example, a dog could be given the choice between entering two darkened enclosures. From one of these, a synthetic growl stimulus with low, narrowly-spaced formants would emanate, while a growl with widely-spaced formants would come from the other. All other acoustic aspects of the stimuli would be held identical. If dogs perceive formants as cues to body size, we would predict the dogs to be more willing to enter the chamber with the "small" dog (widely-spaced formants).

5.5 Conclusion

We found clear evidence that vocal tract length is correlated with body size in domestic dogs, despite the apparent variation in skull and vocal tract shape induced by selective breeding. As predicted by acoustic theory, vocal tract length was inversely correlated with the spacing between formant frequencies, which means that formant spacing provides a reliable cue to body size (log body mass) in the sample of dogs studied here. Single formants were less reliably related to body size or vocal tract length than the ensemble, suggesting that acoustic estimates of body size will be most reliable by integrating information from multiple formants rather than just one. We found some deviations from the first order approximation of a uniform tube, which likely result from deviations from uniformity in vocal tract shape, as visible in the radiographs. However, further data is necessary to test this since our radiographs came from anaesthetised (not vocalising) dogs. Because dogs have been shown to perceive formants in synthetic human speech sounds, it seems plausible that they could perceive formant data in their own species-specific vocalisations, implying that formants could play a role in vocal communication between canids.


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