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We performed two sets of propagation measurements: the first set was performed in Australia in a typical environment of the wild zebra finch, and the second set was performed in France in an open field. The measurements in Australia were performed with a limited database of zebra finch calls and can be considered as a pilot study for characterizing the acoustic properties of the species' natural environment. The background noise distributions and the frequency transfer functions obtained in both environments were compared to assess both the ecological relevance and some of the limitations of these analyses. The propagation experiments performed in France included multiple call exemplars of each individual, and aimed to fully characterize the acoustic features that carried information about the caller's identity. The experimental protocol for the recording of distance calls of our zebra finch subjects was approved by the Jean Monnet University's animal care committee (authorization n°42-218-0901-38 SV 09 to the ENES lab).
Calls database used in the experiments and recording locations: For the pilot experiments performed in Australia, we used distance calls from both wild and domesticated zebra finches (16 calls used: 2 samples each from 2 wild males, 2 wild females, 2 domesticated males and 2 domesticated females). The domesticated zebra finches had been previously recorded in France (see protocol below). The distance calls from the wild birds were recorded at the University of New South Wales Arid Zone Research Station at Fowlers Gap, 112 km north of Broken Hill in far western New South Wales, Australia (Gap Hills; 30°57′S, 141°46′E). Here, a large zebra finch colony is established, with birds breeding both in natural vegetation and in nest-boxes [24]. We recorded calls using omnidirectional tie-microphones (AKG C417) placed inside nest-boxes and connected to a portable solid state recorder (Marantz PMD670; sampling frequency: 44100 Hz; D&M Holdings Inc., Kanagawa, Japan). These recordings were conducted under the authorities of the Animal Ethics Committees at the University of New South Wales and Macquarie University and a Scientific Research Permit from the New South Wales Parks and Wildlife Service. For the propagation measurements performed in France, we used calls from 32 domesticated zebra finches (16 distance calls from each of 16 females and 16 males = 512 calls). The domesticated birds were bred in the ENES laboratory aviary (14L/10D photoperiod with adapted wavelengths; food and water ad libitum; temperature between 23 and 25°C). They were recorded in a soundproof room using a Sennheiser MD-42 microphone placed 0.2 m above the cage and connected to a Marantz PMD 670 recorder (sampling frequency: 44100 Hz). Each bird was recorded in the presence of two female zebra finches placed 3 m away and used as an audience to minimize stress [25]; the bird was stimulated with playbacks of distance calls that had previously been recorded from conspecific birds. During the recording, conditions of temperature, food and water availability were the same as in the aviary. All the calls were normalized by matching the maximum values of the sound pressure waveforms using Goldwave (version 5.57), prior to the propagation experiments. The frequency power spectra of wild and domesticated zebra finches were similar: we did not observe any consistent differences that could have been due to our use of different recordings methods or to different vocal outputs of the two populations. The two types of vocalizations were thus combined in our analysis of the pilot experiment in Australia.
Recording and processing of propagated calls: 1. Sound transmission experiments in Australia: The transmission experiments in Australia were performed in November 2008 at two locations, next to the research station. The first experimental location was an open environment deprived of vegetation. On this site, experiments were performed during the day with light wind. The weather was clear and the temperature was around 30°C (Australia site 1). The second location was a subarid environment with sparse vegetation including small trees, the landscape being open with little relief [18]. Experiments at this location were performed on a completely windless evening. The weather was clear and the temperature was around 25°C (Australia site 2). For both Australian recordings, the sounds were played back via an amplified loudspeaker (Minivox Lite PA System, Anchor Audio, Inc.) connected directly to a laptop computer. The loudspeaker was placed at a height of between 1 and 1.3 m. The volume of the speaker was set such as to match the intensity typical of zebra finch calls, around 70 dB at 1 m [9]. Sounds were recorded using an omni-directional microphone (Sennheiser MD 42) connected to a Marantz PMD670 recorder (sampling frequency: 44100 Hz). The microphone was held at 1 m above the ground. We recorded the calls sequences 2 m, 5 m, 10 m, 20 m, 50 m and 100 m away from the speaker.
2. Sound transmission experiments in France: The transmission experiments in France were performed in October 2010 in the afternoon on a level field in Bellegarde-en-Forez, Loire, France. This recording site was chosen to match the open environment of the Australian desert. The weather was cloudy, there was little wind and the temperature was 11°C. The complete calls database was broadcast from a portable solid state recorder (Marantz PMD671) connected to a MegaVox speaker (PB-35W) placed on a stool, 1.3 m high. The speaker volume was set to obtain a sound level of 70 dB SPL at 1 m (Velleman Sound Level Meter DVM 1326). The sounds were recorded with a Schoeps microphone (MK4 cardioid, on a CMC6-U base) equipped with a Schoeps Basket-type Windscreen (W 20) and set 1.3 m high. The microphone was connected to a second Marantz recorder (PMD671; sampling frequency: 44100 Hz). We recorded the calls 2 m, 16 m, 64 m, 128 m and 256 m away from the source, twice for each distance.
3. We used a custom-made Matlab (Mathworks) script to cross-correlate the propagated recordings with the original sequences. For the recordings performed in France, we then compared the signals of the propagated calls from the two recording sessions, by ear or by a visual assessment of spectrograms when necessary, and selected the better of the two recordings for each call and at each propagation distance. This selection allowed us to exclude recordings that had been impaired by unexpected transient sounds that were not relevant to the study (e. g. birds calling in the vicinity).
1. Visualization of the spectro-temporal properties of the environmental noise and the propagated calls: a. Using custom-made Matlab scripts, we calculated the frequency spectra (FS, in dB units) for all calls from the same sex at each propagation distance. We also calculated the FS of the background environmental noise that was present during these recordings.
Spectral transfer function can be used to quantify signal attenuation (or gain) and phase shifts as a function of frequency for a given propagation distance. Here we calculated, the gain of spectral transfer function by normalizing the cross-spectrum between a propagated sound and the reference sound by the FS of the reference sound. We used the recordings obtained at 2 m as the reference sounds, and the recordings at 50 m (Australia) and 64 m (France) as the second propagated sound. In other words, we estimated the gain of the transfer function resulting from 48 m of propagation in Australia and 62 m in France. Estimates of the standard error in the gain function were obtained using the Jackknife resampling technique [26]. The empirical transfer function was compared to the attenuation expected from spherical radiation and atmospheric absorption. The sound level of a source emitting at a sound level Ls (in dB) and recorded at a propagation distance r, Lr, can be written as:where the −20 log10(r) term corresponds to the spherical distribution of energy (also known as the inverse square law and yielding a 6 dB attenuation per distance doubling), K′ is a constant equal to −10 log10(4π) for spherical radiation and −10 log10(2π) for hemi-spherical radiation and Aa is the atmospheric absorption. Atmospheric absorption depends on frequency, temperature, humidity and atmospheric pressure and its magnitude can be estimated analytically using the equations published by the International Organization for Standardization (ISO 9613–1:1993). These equations were implemented in a Matlab script that was validated by comparing its output to the tables provided in the ISO publication. For example, at 1 atm, for 50% humidity and at 4 kHz, the atmospheric attenuation is 4.5 dB/100 m, 2.6 dB/100 m and 2.5 dB/100 m at 11°C, 25°C and 30°C, respectively.
In order to visualize the joint spectro-temporal modulations of the distance calls propagated in France and their evolution with propagation, we calculated the modulation power spectra (MPS) of the calls: the joint second order statistics of the spectro-temporal amplitude envelopes obtained from a spectrographic representation of the sound [27]. The MPS is obtained as follows. We first calculated the spectrogram of each call using a Gaussian window (symmetric in time and frequency domains) 70 Hz wide in the frequency domain or 2.27 ms wide in the time domain. The MPS is then simply the 2-D power spectrum of the log spectrogram [27]. The time-frequency scale of the spectrogram (70 Hz) determines the spectral and temporal Nyquist limits of the modulation spectrum (7.14 cycles/kHz for spectral modulations and 220 Hz for temporal modulations). MPS were obtained for each propagation distance and each sex.
2. Parameters used for the statistical analysis of individual signature: We used two distinct sets of acoustic parameters to test for the presence of a vocal signature in the propagated calls: (a) a set of parameters that separately describe the amplitude in the spectral domain (the spectral envelope) and the amplitude in the time domain (the temporal envelope, often simply called amplitude envelope); (b) the spectrogram. Since our spectrographic representations are invertible, using a complete spectrogram not only circumvents the use of a priori assumptions on the nature of the information-bearing acoustical features but also provides an upper bound for discriminability. Prior to these analyses, the sounds were band-pass filtered between 0.5 to 8 kHz in order to reduce irrelevant environmental background noise. Those frequency cutoffs were chosen based on the zebra finch's audiogram [28]. a.
Parameters used to describe the separate spectral and temporal features: We extracted the spectral amplitude envelope (amplitude as a function of frequency) and temporal amplitude envelope (amplitude as a function of time) of each call. Each amplitude envelope (spectral and temporal) was then converted to a density function by dividing each value of amplitude by the sum of all amplitude values. We quantified the shape of these normalized envelopes by estimating the moments of the corresponding density functions: their mean (i.e. the spectral centroid for the spectral envelope and temporal centroid for the temporal envelope), standard deviation (i.e. spectral bandwidth and temporal duration), skewness (i.e. measure of the asymmetry in the shape of the amplitude envelopes), kurtosis (i.e. the peakedness in the shape of the envelope) and entropy. The entropy captures the overall variability in the envelope; for a given standard deviation, higher entropy values are obtained for more uniform amplitude envelopes (e.g. noise-like broad band sound and steady temporal envelopes) and lower entropy values for amplitude envelopes with high amplitudes concentrated at fewer spectral or temporal points (e.g. harmonic stacks or temporal envelope with very fast attack and decay). The spectral envelope was obtained with the Welch's averaged, modified periodogram estimation of the power spectral density using a Hann window of 23 ms and an overlap of 99%. The temporal envelope was obtained by rectifying the sound pressure waveform and low-pass filtering below 50 Hz. With these procedures, we obtained 10 acoustical parameters, 5 describing spectral features and 5 describing temporal features. Since these parameters had different units, Z-scores were calculated prior to using them in the multivariate discriminant analyses.
b. As stated above, we calculated an invertible spectrogram of each call using a Gaussian window and a time-frequency scale of 70 Hz-2.27 ms. Because the dimensionality of this representation was higher than the total number of calls in our database, we used a Principal Component Analysis (PCA; using the princomp function of Matlab) for dimensionality reduction. The discriminant analysis was then performed using the coefficients of a subset of the principal components. These two complementary approaches enabled us to compare the acoustical nature of vocal signatures, using discrete and more easily interpretable envelope parameters that have proven to be useful, if somewhat subjective, in the investigation of information-bearing features [29], as well as more complex parameters (principal components coefficients) extracted from a complete and invertible representation of the signals. To be concise, we will refer henceforth to the 5 pairs of separate spectral and temporal parameters as the “envelope parameters” and to parameters describing the spectrogram as the “spectrogram principal component parameters”, or more simply “SPC parameters”. The extraction method for each set of parameters is summarized in Fig. 2a.
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0102842.g002 Overview of the acoustical analysis.This figure summarizes the procedure for extracting both sets of parameters (a), and the subsequent discriminant function analysis (b). The discriminant functions were calculated using the fitting dataset, and we tested the validating dataset against these to obtain the percentages of correct classification.
3. Statistical analysis of the vocal signature in calls: To test for the presence of an acoustic signature in the propagated distance calls, we used cross-validated linear discriminant function analyses (DFA), performed separately for each sex. The DFA finds the linear combinations of parameters that maximally separate the data points (the calls) that belong to different categories (the birds identities); these linear combinations are called discriminant functions (DFs) and the significant DFs define a Euclidian subspace where calls can be projected. The cross-validation consists of first calculating a set of discriminant functions using a fitting dataset, and then testing these functions on a validating dataset (non-overlapping with the fitting dataset) by assessing the number of calls that had been correctly classified for each individual, the percentage of correct classification (Fig. 2b). We performed this DFA using either the 10 envelope parameters or the SPC parameters. Prior to the final calculations, we performed a series of preliminary analyses to determine the number of principal components (PCs) used for the SPC parameters and the number of discriminant functions (DFs) used for quantifying the discrimination for both the envelope and SPC parameters. We found optimal values for these hyper-parameters using the data at 2 m as a reference, and applied them for all other conditions. We first aimed to define the number of PCs to be used to reduce the dimensionality of the data while representing a reasonable amount of variance; to do this we estimated the percentages of correct classification using the 10 first significant DFs (at 2 m using the SPC parameters, 13 were significant for the females, and 15 were significant for the males as assessed by the Wilks Lambda test statistic) and a varying number of PCs from 10 to 100. We found that using 25 PCs captured most of the information about identity as witnessed by a saturation of the percentages of correct classification around that number (94.9% with 25 PCs and 95.4% with 100 PCs, using 10 DFs). We then compared the eigenvalues for each DF (fixing the number of PCs to 25) and found that using the first 4 DFs (DF1 to DF4) was an appropriate tradeoff, as it accounted for 83.9% for the females and 82.6% for the males of the variance between birds. Furthermore, in all our discriminant analyses (described below), we found at least 4 significant DFs. We were thus able to always use the same number of DFs in all our calculations and directly compare results. Finally, we assessed the number of cross-validation iterations required to obtain robust values for the percentage of correct classification; we found that 250 iterations were largely sufficient to reach stable values. We quantified the discriminability by calculating the percentage of correct classification. We also determined which acoustical features were the most important for individual discrimination by examining the form of the significant DFs (for the SPC parameters) or the effect of each set of parameters independently (for the envelope parameters). The discriminant analyses were only performed for the more complete data set of propagated calls obtained in the experiments in France.
4. Extraction of the most important parameters for individual discrimination: A different procedure was used for identifying the relative importance of the envelope parameters and the SPC parameters in the individual discrimination task. For the envelope parameters, we simply repeated the DFA with only the temporal envelope parameters or only the spectral envelope parameters. For the SPC parameters, we represented the first 4 DFs in the spectrographic space: since both the discriminant analysis and the PCA decomposition of the spectrogram are linear operations, the inverse rotation and scaling can be applied on the discriminant functions to represent them in a spectrographic space, allowing us to describe them as we would on a spectrogram.
5. Comparisons between the percentages of correct classification: To compare the results obtained with different set of parameters, at different distances and for both sexes, we performed analyses of covariance (ANCOVA), using a general linear model framework (Statistical Toolbox in Matlab), with the percentage of correct classification as the dependent variable, the sex (male vs. female) and the type of parameters used (SPC vs. envelope) as factors, and the propagation distance as a covariate.
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