A generalized model for communicating individuality through teleost swim bladder modulation

The swim bladder model for resonance as defined in Ladich (2015) is understood to be one of the most widely accepted approaches to characterizing vocalization from fish who apply muscle contractions across the swim bladder to generate sound. Normal mode analysis can yield varied outputs for any particular geometry being actuated by a source (Frisk, 1994). Evidence has been found to support that some fish are at least sensitive to the effects of envelope modulation (McKibben and Bass, 2001). Researchers are also presenting challenges to the conventional resonating bubble model (Fine, 2012) in terms of understanding how fish apply its use in vocalizing. When considering the possibility of a time and envelope modulation dependent strategy in terms of the findings in McKibben and Bass (2001), it becomes of interest to consider possible biological rationale for developing such proclivities.

Observations were made on a controlled dataset, where multiple records were collected using 4 inch long standard PVC pipe sections of 1.5, 2, 3 and 4 inch diameter.

This paper presents a methodology for isolating envelope modulation characteristics associated with resonance of air cavities in water being impulsively excited by an external source. As a means of controlling the signal output, an identical test reference vocalization with no variation in power was played through four varying air volumes, and each air volume was correctly assessed by both methods considered. The intent of showing two methods is to corroborate each other. Further, the air volumes were static, implying the most consistent possible modulation scheme as described in Eqn 2 with respect to radius of the air volume. It is important to consider some of the assumptions in developing a successful strategy for accurately estimating the air volumes used as test targets.

With respect to static power, this was intentional with respect to the candidate fish species selected for vocalization; no references on signal power (IV) characteristics of the red hind were discovered in the literature review. Relatives of the red hind have been analyzed from a transmission power standpoint (Hazlett and Winn, 1962), but not with enough detail to differentiate size between referenced power sources. With respect to the pivotal behaviors typically seen as associated with vocalization, specifically territorial assertion and mating ritual, Some fish have indeed exhibited correlations in mass and swim bladder size (Fine et al., 2001; Suthers et al., 2016; Ali et al., 2016). If the frequency is indeed coupled with the radius of the swim bladder, then the frequency drop indicated in Suthers et al. (2016) could potentially be indicative of an attempt to maintain a particular modulation effect about an increasing swim bladder volume.

Multipath effects of the pipes were completely neglected in consideration. The pipes may be expected to act as nearly perfect Von Neumann boundaries for the frequencies of interest and have relatively long periods of bounce along the pipe walls affecting linear summing at the receiver. This does not preclude multipath interference from contributing to variations in spectral profile, though none were visibly observed in the collected records.

The resonant bubble model does not strictly require a spherical reverberation, though in the classical form in Ladich (2015) it does not consider the complete effects of normal modes transferring in the wall as lobed or otherwise geometrically defined waves. All of these effects, should they be present, could contribute to variations in the signal envelope in either time or time-frequency analysis. The air bubble effect of a rubber balloon in a pipe does not provide the same biological controls as a fish in terms of damping, movement, etc.

The implication of the absolute value for M(t) indicates the form of a raised cosine modulation as the format for the idealized filter. Presuming on a modulation/demodulation strategy in a given species, McKibben and Bass (2001) provides the basis for the presence of an identifying feature used by gravid female midshipmen to identify high value mates – the filter model idealizes with age as a function of the males' swim bladder. The model also presents the possibility that a swim bladder can be used to infer mass of an individual conspecific. If the characteristic modulation can be used to identify a range of bladder volumes associated with mass, then identifying traits of the vocalizing fish species associated with various masses may be extractable features to the observing conspecific. The consequence of this modulation leads to potential value in vocalizing at low frequencies, even in environments inhospitable to low frequency acoustic transmission, as described in Fig. 2.

With regard to a static tone, as radius increases in a swim bladder, the proposed model function takes on a decaying epoch toward unity with an increase in ripple frequency but a decrease in ripple amplitude. An implication of this model is that the peak modulation amplitude drops off significantly as frequency F of the forcing function increases. The next pair of figures illustrates these decay models over a single period of unit vocalization time for a hypothetical raised cosine distribution strategy, where a magnitude operator is applied to (1) for a radial variation of 1–10 cm.

Within the model described, it is possible to estimate any number of resonant modulation strategies on the part of the fish, including variable compression of the air bladder to vary the output of M(t). The swim bladder modulation effect is essentially an all-pass filter for the vocalization, with passband ripple and natural curvature over the ideal 1-D filter envelope [it is important to note that M(t) is a 1-D function, the previous figure would a line drawn through it somewhere to define M(t)]. As the frequency increases, peak cyclical effects associated with the swim bladder approach unity, indicating that the function described in (2) will be driven to unity – essentially an ideal all-pass filter. This supports the evolutionary strategies described in Ladich (2015) regarding low frequency acoustic communication and shallow running teleost fishes if swim bladder modulation features do in fact help identify attractive mates.

The proposed modulation is expected to be, relatively speaking, highly overshadowed by the information signal. As such, in the following section, we consider a well-defined and strong red hind grouper vocalization played through several increasing diameters of pipe filled with a roughly spherical and equally increasing air volume in a typical rubber balloon. It should be noted that any acoustic signal could be applied as the input to the model; the intent is to measure effects of an increasing air volume on the sound passing through it.

In order to measure effects in a controlled setting, a physical analog was constructed to allow variations in the air volume for a static test audio file to be played through. Fig. 3 shows a diagram of the test set-up.

With a general framework for analysis and an absence of live specimens to work with, we consider the model thus far in terms of a static volume with fish vocalizations played back through the static volume increased sequentially. The original file is shown below in Short Time Fourier Transform (STFT) – often referred to as spectrogram – format. The reference signals' spectral content is shown in Fig. 4.

In analyzing the signal, methods as described in work by E. C. Like (Non-Cooperative Modulation Recognition Via Exploitation of Cyclic Statistics, MSc Thesis, Wright State University, 2007), A. F. Jr. Lima Analysis Of Low Probability Of Intercept (Lpi) Radar Signals Using Cyclostationary Processing, MSc Thesis, Naval Post-Graduate School, 2002] and Antoni (2007) are applied as well as a general twist on classical demodulation schemes. In terms of general STFT analysis, the demodulation of the signal across the time–frequency domain is expected to yield the base information of the fish vocalization. If the modulation characteristics are consistent with a modulo-resonance model such as the one put forth, a separable impulse response should remain after removing information signal.

As an assumption in developing the demodulation strategy, the same methods in McKibben and Bass (2001) are presumed upon regarding amplitude modulation. The blind demodulation estimate also presumes on the fish applying Single Side Band (SSB) amplitude demodulation. The Amplitude Modulation SSB (AM-SSB) model as shown in Fig. 5 is attractive not only as a possible physiological effect of the damping swim bladder wall but also as a carrier suppression tool. The intent of this operation is to decorrelate impulse and impulse response to extract a hypothetical carrier identification signal. The demodulation routine then becomes the signal multiplied by a cosine function using the fundamental of the presumed vocalization [this is readily achieved for red hind vocalization – potentially any communication signal – with peak-finding in energy detectors following a front-end speech detection process, see Matthews and Beaujean (Edge Detection of Red Hind Grouper Vocalizations in the Littorals, Society for Photonics and Imaging Electronics, Buried and Obscured Objects Detection Session, Defense Security Systems, 2016) and C. A. Matthews (Acoustic Tonal And Vector Properties Of Red Hind Grouper Vocalizations, Doctoral Thesis, Florida Atlantic University, 2017)]. The following flow diagram describes the process in detail, which consists in low-pass filtering the modulated signal through a 5th order Butterworth filter as described in Bianchi and Sorrentino (2007).

The authors would like to thank Dr Michael Fine (Virginia Commonwealth University) and Dr Andrew Bass (Cornell University) for their valuable insights and multiple papers on fish vocalizations. This paper was prepared in conjunction and partial fulfillment of a Doctorate in Ocean Engineering at FAU, and was developed under training provided by the United States Navy (USN).