Support for the beam focusing hypothesis in the false killer whale

Odontocetes, or toothed whales, dolphins and porpoises, produce intense, directional, ultrasonic echolocation signals and use the information in the returning echoes to identify, localize and track prey. Unlike most mammals, which use the larynx for sound production, odontocetes have evolved an elaborate sound production mechanism in their nasal cavity. Air is pressurized in a bony cavity and pushed upwards across soft tissue structures called the phonic lips. As air passes across these lips, the lips hit each other, presumably causing the associated fatty bursae structures to vibrate, creating the echolocation pulses. These pulses reflect anteriorly off both the curvature of the skull and associated posterior air sacs, and propagate through the melon before being transmitted to the water (Cranford et al., 1996).

The origin of the term ‘melon’ may be traced back to Captain David Gray, Commander of the Whaling Steamer Eclipse, who, in describing the anatomy of a Bottlenose whale (Hyperoodon rostratus) remarked, ‘In the males, instead of oil there is a solid lump of fat similar in shape to, and about twice the size of, a large water-melon’ (Gray and Flower, 1882). The unique structure of the melon was further described by A. Ohlin, who remarked on the structure ‘…somewhat resembling the cells of a bee-hive. The rooms between the fibrous bands are filled with a clear thin-floating oil’ (Ohlin, 1893). Since these early reports, we now have a better understanding of the structure and composition of the melon. The melon is ovoid in shape and located slightly right of the midline in the forehead (Heyning, 1989). The melon itself has both an outer core, composed of acoustic fats and connective tissue, and an inner core, composed mainly of acoustic fats (Heyning, 1989; Litchfield and Greenberg, 1973; Mead, 1975; Norris and Harvey, 1974). The acoustic fats are composed primarily of wax esters, which are metabolically toxic to the animal. This toxicity reinforces the importance of the melon to odontocetes; despite representing a significant investment of energy, individuals maintain the structure of the melon during periods of starvation (Cranford et al., 1996; Koopman et al., 2003). This implies that the melon serves a crucial functional role for odontocetes. Within the melon, the lipids are distributed in such a manner that there is a variable topography of chemical properties and sound speeds, which together help collimate the sound anteriorly (Litchfield and Greenberg, 1973; Norris and Harvey, 1974). Surrounding the melon is a network of facial muscles (Cranford et al., 1996; Heyning, 1989; Huggenberger et al., 2009; Mead, 1975), which may change the size and/or shape of the melon and associated air sacs (Harper et al., 2008; Huggenberger et al., 2009).

The melon has been hypothesized to act as an acoustic lens, shaping and focusing the emitted sound beam (Evans and Prescott, 1962; Norris, 1964). Some studies have attempted to investigate this hypothesis with a modeling approach, and found that the melon does play a role in beam formation (Aroyan et al., 1992; Cranford et al., 2014). Limitations of the modeling studies include using tissue properties from post-mortem specimens (Aroyan et al., 1992) and ignoring any conformational changes to the melon produced either intentionally or coincidentally by the animal (Cranford et al., 1996). Recently, this beam focusing hypothesis was empirically tested in a live animal during echolocation (Kloepper et al., 2012). The results from that study showed that the beam area changed with range in a manner that could not solely be predicted by changes in the center frequency. This suggested that active focusing might be playing a role in determining beamwidth, but because of the design of the experiment, the focusing of the beam across distance could not be directly tested.

Sound commonly propagates in a divergent manner, with the same energy spreading over a larger surface area as it propagates away from the source. The simplest divergent propagation is spherical spreading, where the acoustic energy is equally distributed across all azimuths and elevations. In this model, the pressure field amplitude decays with 1/r and the intensity decays as 1/r² (where r is range from the source) to account for spreading the same energy over a larger surface area as the wavefront propagates away from the source. Many marine mammals transmit sound with a directional characteristic, where the pressure (and intensity) at certain azimuths and elevations is greater than at others. The far field pressure for directional propagation is modeled as a product of two terms: one term for the angular dependence and the other term representing the 1/r spreading (Au and Hastings, 2008; Kinsler et al., 2000; Urick, 1983). The beam pattern is the angular dependence term normalized for the maximum on-axis pressure at a given range. This directional propagation model predicts that the beam will have constant angular width but increasing beam area as the sound propagates away from the source. Consequently, the intensity, or energy per unit area, must decrease as the distance from the source increases. The 1/r spreading term in the pressure results in a 1/r² decay in intensity, conserving energy as the constant width beam propagates to greater range.

The alternative to divergent propagation is convergent propagation, or focusing. In this case, the wavefronts converge to interfere constructively. The location of this convergence is known as the focal range (FR). One method for creating convergent propagation is to cause the sound to propagate through a region of reduced sound speed, or increased index of refraction (Kinsler et al., 2000; Urick, 1983). Such a region acts as an acoustic lens, as illustrated in Fig. 1. Depending on the distance from the sound generator to the lens, and also the size, shape and sound speed of the lens, this acoustic lens can produce a beam that is still divergent (Fig. 1A), constant in area (Fig. 1B) or converging to a FR then diverging again beyond the FR (Fig. 1C). A consequence of focused propagation as shown in Fig. 1B and C is that the angular beam width decreases with increasing range from the animal (up to the FR in Fig. 1C), and the intensity pressure does not display the 1/r² spreading behavior (or 1/r behavior in pressure). Instead, the focusing results in an intensity that increases closer to the FR (Fig. 1C) or remains constant (Fig. 1B) with range.

The propagation of sound through the head of a marine mammal is more complicated than the simple optical lens shown in Fig. 1. However, the underlying refraction mechanism and fundamental nature of acoustic propagation (divergent, convergent or constant width) are the same. For the case of convergent propagation (Fig. 1C), the distance from the sound generator (the phonic lips) to the focusing lens (the melon) is fixed by anatomy. However, changing the shape of the melon will alter the propagation characteristics of the sonar beam, including the FR.

In this study, we tested whether the false killer whale Pseudorca crassidens (Owen 1846) uses an unfocused or a focused beam during echolocation. Specifically, we tested two hypotheses: first, does the whale focus its beam, and second, if so, does the whale focus its beam adaptively (i.e. according to target distance and condition)? While the whale echolocated on targets at three distances (2, 4 and 7 m), the sonar beam was recorded with three linear arrays at the three target distances. The intensity and beamwidth were calculated at each distance and compared with the divergent propagation model. When the target was located at distances of 4 m or greater, the echolocation beam width narrowed with distance, and the pressure was greater than predicted by 1/r spreading. During target absent trials, the whale adapted its beam similar to the farthest expected distance. These results support the hypothesis that the false killer whale focuses its sonar beam according to target distance, producing a convergent beam with an adaptable FR.

To determine the near-to-far field transition, the sound pressure level (SPL) was recorded along the beam axis from 0.5 to 7 m while the whale performed a target detection task with the target located at 8 m. At distances less than 2 m, the relative SPL (SPL at 2 m subtracted from the SPL at distance r) deviated from the spherical spreading function, but at distances greater than 2 m the relative SPL approximated a spherical spreading function (Fig. 2). Therefore, when a target is located at 8 m the acoustic far field for the subject begins at a distance between 1.5 and 2 m away from the blowhole, and all three linear array distances are located in the far field of the whale.

To test the first hypothesis that the whale uses a focused convergent beam, and not a constant width divergent beam, we measured the beamwidth at each of the three arrays. We performed the multivariate T² test for all three target ranges (2, 4 and 7 m) and for both target conditions (present and absent). For each of the six tests, the width of the known constant width beam was the average beamwidth over all trials and measurement arrays for that target range and condition. This choice for the known constant beamwidth is the most conservative. Any other choice for constant beamwidth would bias the tests towards significance. For the target present condition, the focusing was significant for the 2 m target (⁠⁠, P<0.01), 4 m target (⁠⁠, P<0.001) and 7 m target (⁠⁠, P<0.001). For the target absent condition, the focusing was significant at P<0.001 for all three target ranges: 2 m (⁠⁠), 4 m (⁠⁠) and 7 m (⁠⁠).

To test the second hypothesis that the whale not only focuses its sonar beam but also adapts the focus to target distance and condition, we used a multivariate ANOVA (MANOVA) to determine the effect of target distance, target presence and click number on beamwidth, normalized voltage and center frequency. For beamwidth, the multivariate result was significant for target distance (Pillai's trace=0.171, F_6,570=8.867, P<0.001), but not significant for target presence (Pillai's trace=0.011, F_3,284=1.082, P=0.357) or click (Pillai's trace=0.060, F_15,858=0.06, P=0.293). The interaction of target distance and target presence was significant (Pillai's trace=0.236, F_6,570=12.68, P<0.001). For most of the target conditions, beamwidth narrowed with increasing array distance (Fig. 3). For normalized voltage, the multivariate result was significant for target distance (Pillai's trace=0.137, F_6,570=6.982, P<0.001), target presence (Pillai's trace=0.086, F_3,284=8.962, P<0.001), the interaction of target distance and target presence (Pillai's trace=0.155, F_6,570=7.970, P<0.001), and click (Pillai's trace=0.138, F_15,858=2.763, P<0.001). For most of the target conditions, the normalized voltage increased with increasing array distance (Fig. 4). For center frequency, the multivariate result was significant for target distance (Pillai's trace=0.112, F_6,570=5.651, P<0.001), target presence (Pillai's trace=0.061, F_3,284=6.170, P<0.001) and the interaction of target presence and target distance (Pillai's trace=0.243, F_6,570=13.112, P<0.001), but not significant for click (Pillai's trace=0.075, F_15,858=1.458, P=0.114). For most target conditions, there was a slight decrease in center frequency with increasing array distance (Fig. 5).

Our results support the hypothesis that the false killer whale focuses its echolocation beam onto a target. By recording the same echolocation click as it propagates through the water, we determined that the emitted beam of the false killer whale has a narrower beam and higher intensities at distance than would be predicted by spreading losses alone. For the target conditions where we saw a consistent beam narrowing with distance (7 m present and all absent conditions), the angular beamwidth decreased by an average of 13.92% and source levels increased by an average of 1.73 dB between the 2 m and 7 m array. Beamwidth, intensity and center frequency are linked, such that higher intensity signals have higher center frequencies and narrower beamwidths (Au et al., 1995; Kloepper et al., 2012).

If the focusing observed is caused by changes in the signal spectrum decreasing the center frequency with range, the beamwidths should increase at the more distant arrays, not decrease, because lower frequency signals have broader beamwidths. If the decreases in beamwidth and increases in normalized voltage were due to changes in the signal spectrum and center frequency as the click propagates out in range, the center frequencies across the arrays should increase for the target conditions. Instead, we measured a small (200–400 Hz) decrease in center frequency over the distance of the arrays (Fig. 5). This decrease may be caused by the preferential attenuation of the higher frequency portion of the signal with range, which would result in a decrease in the center frequency. Because lower frequency signals have wider main lobes, this decreasing trend in center frequency over array distance would predict the beamwidth increasing with distance. Instead, we observed a decrease in beamwidth over distance, which further supports the hypothesis that the whale is actively focusing its echolocation beam to decrease beamwidth.

If the whale did not focus its beam, the beamwidth would be constant at all distances, and small noise perturbations and experimental errors would produce an equal distribution of beam types across all target conditions. If the animal did focus its beam, we would expect two outcomes depending on the method of focusing: (1) if the whale consistently narrowed her beam with distance, or had a FR much larger than any of the target ranges, we would expect an equal distribution of Type 1 beams across all target conditions; (2) if, however, she used a strategy of creating a FR according to target distance, as hypothesized by previous work (Kloepper et al., 2012), we would expect the beam to be narrowest at the target distance, with the other array distances intermediary in size, as illustrated in Fig. 1C – thus, we would expect a higher proportion of Type 2 signals when the target is at the 2 m distance, a higher proportion of Type 5 or 6 signals when the target is at the 4 m distance, and a higher proportion of Type 1 signals when the target is at the 7 m distance. Consistent with the distribution of pulse types according to target condition in Fig. 6B, it appears the animal is using both strategies for beam focusing. For the 7 m target present and target absent conditions at all distances, the whale overwhelmingly produces Type 1, or narrowing with distance, signals (Fig. 6B). These data are consistent with prior work indicating that when there is a target absent condition, odontocetes attend to the farthest expected target range (Kloepper et al., 2014). For the other target present distances, the whale produces some Type 1 signals, which suggests the whale is still searching at the farthest target range, but the most frequently produced pulse types are Type 3 and 4 for the 2 m target distance and type 5 for the 4 m target.

We may take a cue from optics to help explain these results. The ovoid melon of the odontocete forehead may be roughly modeled as a biconvex lens. These lenses are thicker in the center and thinner at the periphery, which causes a convergence of light, or a focal point (Sharma, 2006). This focusing results in a narrowing of the beam to a certain region, then an expansion of the beam beyond that FR. Changing the curvature or thickness of this lens can cause the FR to move closer to or farther from the lens. In odontocetes, changes in the curvature of the melon could be accomplished by manipulating the network of muscles that surround the melon (Mead, 1975).

The results for the 4 and 7 m target support the idea that the whale is narrowing the beam onto the target, but the results for the 2 m target do not. Particularly perplexing is that, for the measurements with the target at 2 m, the beam is narrowest at 2 m, widens at 4 m and then narrows again at 7 m. There are several possible factors that might be contributing to these results. These include physical interactions in the near field, and biological limitations of the whale's focusing mechanism.

The acoustic near field is the region close to the source where the pressure field experiences complicated constructive and destructive interference patterns due to the sound radiating from different elements of the source. In the near field, the acoustic pressure is not well described by the product of a range term and an angular term as it is in the far field (Foote, 2014; Urick, 1983). As a result, in the near field there is no clearly defined beamwidth, and the intensity of the sound does not obey 1/r spreading seen in the far field. Instead, the acoustic intensity in the near field varies rapidly as even small changes in frequency or distance can move from constructive to destructive interference. We determined the near-to-far field transition for the animal to occur between 1.5 and 2 m when the target is located at 8 m distance (Fig. 2). If the animal were changing the shape of its melon depending on target distance, deformations in the melon would change the effective size of the transducer, which would also change the near-to-far field transition distance. Because our original near-to-far field region of 1.5–2 m was determined from a target distance of 8 m, we cannot rule out that the 2 m array is within the near field of the whale when the whale is echolocating on a target at 2 m.

The likelihood of the 2 m array being located in the near field for the 2 m target condition is further supported by a comparison of center frequency for the click types. For the Type 1 signals, which are presumably produced when the near-to-far field transition is greater than 2 m, there is no significant difference of center frequency between the clicks recorded on the 2 and 4 m arrays. For the Type 3 and Type 4 signals, however, there is a significant difference of center frequency between the clicks recorded on the 2 and 4 m arrays (Type 3, t₉₈=3.0861, P=0.0026; Type 4, t₉₆=3.0551, P=0.0029), with a higher center frequency recorded on the 2 m hydrophone array compared with the 4 m array. Because frequency and beamwidth are inherently related (Au et al., 1995), this rise in frequency would be consistent with a narrowing of the beam and may reflect interference patterns from being in the near field. Furthermore, as the intensity and frequency of echolocation signals are related (Au et al., 1995; Kloepper et al., 2010a), if we were in the acoustic far field we would expect to find an associated significant difference in voltage between the 2 and 4 m arrays for the Type 3 and Type 4 signals. The fact that there is no significant difference (P=0.7332 and P=0.7561) is further evidence that we may be operating in the acoustic near field for the 2 m array, which would explain the anomalous beam results.

A second explanation for the results at the 2 m distance might be the practical limitations of the focusing mechanism. If the focusing is caused by muscular deformation of the melon, there may be a physical limitation for a minimum FR. FRs are reduced by increasing the curvature of the lens (Sharma, 2006), or equivalently reducing the radius of curvature. If there is a maximum curvature possible for the melon as a result of anatomical limitations, this would impose a minimum FR for the transmitted sonar waveform. Many odontocete species produce low-amplitude, high-repetition clicks (termed ‘buzzes’) when prey are within one body length (DeRuiter et al., 2009; Johnson et al., 2004; Verfuss et al., 2009; Wisniewska et al., 2014). These buzzes are distinctly different from the clicks made when prey are at greater distances, and their rapid production rate may eliminate any need for focusing. When prey are at such close distances and echolocation clicks are produced at a rapid rate, there may be no advantage in focusing at a close range.

Using a focused echolocation beam has important ecological functions for odontocetes. By using internal structures to narrow the sound beam, the animal increases the intensity of the signal impinging on a target, which results in a louder returning echo. Changing the FR according to the target distance means the animal adapts its signal to ensure the returning echo, regardless of target distance, is as loud as possible, which may help in species that discriminate between target species or forage on prey with weak echoes (Au et al., 2009; Kang et al., 2005). Additionally, the surface temperature of seawater can vary by as much as 20°C over Pseudorca's range, with a consequent change in sound speed of 90 m s⁻¹ (Kinsler et al., 2000). This temperature driven sound speed change can alter the index of refraction significantly for the water surrounding the animal throughout the year. From this point of view, the animals are likely to alter their melon to compensate for the changes in refraction due to seasonal temperature variations. If the melon were fixed in shape, the animal would suffer from a sonar beam that widened and narrowed in angle and moved its FR nearer and further as the water temperature varied annually.

The results from this study further raise an interesting question of what is the ‘default’, or relaxed, state for an echolocating animal that focuses its sound beam. Based on the results from the target absent condition – that is, the whale focuses its sonar to the farthest expected target distance – one hypothesis is that the natural state is to focus the beam at long range. Intuitively this makes ecological sense, as the whale will likely first detect an object at far range, then track and discriminate as the animal comes closer to the object. If this is indeed the strategy used by echolocating odontocetes, it suggests there is some cost associated with focusing its sonar beam.

Because of the similarity of sound producing structures across all odontocetes (Cranford et al., 1996), this sonar focusing strategy is likely not unique to the false killer whale. Instead, this may be an adaptive mechanism shared by all odontocetes. By using their unique sound focusing structures, odontocetes can optimize the energy impinging on a target, which would result in increased target detection, discrimination and overall foraging success. Anatomical adaptation is common in many other animals and across sensory modalities (Estes, 1972; Forrester et al., 1996; Gao et al., 2011). Therefore, our proposed focusing mechanism for odontocetes is not unusual, but rather is consistent with adaptive sensory behavior clearly demonstrated in many other animal species.

This project was approved under permit from the National Marine Fisheries Service to P.E.N. Work was approved under the University of Hawaii Institutional Animal Care Committee Protocol 93-005-15.

The experiments were conducted at the floating pen complex of the Marine Mammal Research Program of the Hawaii Institute of Marine Biology off Coconut Island, Kaneohe Bay, Oahu, Hawaii. The water surrounding the pens is approximately 22°C, 12 m deep, and has a thick mud substrate 1 m thick. The experimental subject was a female false killer whale (P. crassidens) named Kina, measuring 3.96 m and weighing 540 kg. The exact age of Kina is unknown; she was brought to Hawaii as an adult in 1987.

The setup for the experiment is shown in Fig. 7A. The experiment utilized two separate pens: the experimental pen, a wire enclosure that measured 9.14×12.19×4.11 m, width×length×depth, and contained the whale; and the target pen, a wireless structure consisting of a floating dock that measured 6.10×9.14 m, width×length, and contained the echolocation targets and the recording equipment. During the experiment, the subject would keep her body in the experimental pen but station her head through a hoop located 1 m below the surface of the water and ensonify the targets located in the target pen. An underwater camera (SCS Enterprises, Montebello, NY, USA) was used to monitor her hoop behavior. An acoustically opaque metal screen was located in front of the animal to prevent her from echolocating prematurely on the targets. An acoustically transparent, yet visually opaque polyethylene screen was placed in front of the acoustically opaque screen to ensure that the subject was not utilizing visual cues.

The subject was trained to detect the presence or absence of a hollow aluminium cylinder 12.7 cm long with an outer diameter of 37.85 mm and a wall thickness of 6.35 mm [the ‘standard’ target from Kloepper et al. (2010b)]. When submerged, the cylinder filled with water. At the start of and between trials, the subject stationed horizontally at the water surface by placing the tip of her rostrum on a vertically placed pad on the side of the experimental pen near the trainer. When cued via a hand signal, the whale submerged and swam to the opposite side of the experimental pen, positioning herself in the underwater hoop up to her pectoral fins (thus positioning her head inside the target pen) and remained stationary for the trial. During the whale positioning time a target was placed into the water at 1 m depth for the target present ‘go’ trials. At this point in time, acoustic access to the target was blocked via the acoustically opaque screen and the animal produced bubbles that would help mask any potential target splashing sounds. After the target was lowered into the water, the acoustically opaque screen was moved to reveal the target. The subject ensonified the target pen and determined whether a target was present (a ‘go’) or absent (a ‘no-go’). If the target was present, the subject backed out of the hoop and touched a response paddle with her rostrum. If the target was absent, the subject remained in the hoop until signaled out by the trainer. The subject was rewarded with fish for correct responses. Incorrect responses resulted in no fish reward. Thus, the general form of the procedure was a go/no go paradigm (Schusterman, 1980).

Echolocation signals were recorded in February 2011 using the same setup as described above, with the animal detecting the presence or absence of a target located at 8 m. Eleven Reson 4013 (Reson, Slangerup, Denmark) hydrophones were positioned on a straight line from the head to the target at distances of 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0 and 7.0 m. The blowhole was taken as the zero point of the distance scale as a convenient mark located in close vicinity to the air sacks and melon, the head structures commonly considered as the sonar click generator and focusing device (Cranford et al., 1996). When the whale ensonified the target, each of her sonar clicks was recorded by these hydrophones. Each hydrophone was amplified by 20 dB using a custom-built amplifier and sampled at a rate of 1 MHz using a NI DAQmx-PCI 6133 analog to digital (A/D) board (National Instruments, Austin, TX, USA) and custom-written LABVIEW software (National Instruments). Peak-to-peak voltage measurements were used to calculate the SPL for each hydrophone; 614 clicks from 30 click trains (trials) were recorded and averaged. The distance at which the near field transitioned to the far field was characterized as the distance where the acoustic pressure decreased by approximately the inverse of the distance (Au et al., 1978).

This experiment was conducted in February 2013. The experiment consisted of three sessions of 50 trials each. For each session, the target was presented at the same distance with 25 present trials and 25 absent trials. Thus, this was considered a ‘predictable’ task for the animal (Kloepper et al., 2014). Echolocation signals were recorded with three linear arrays of five Reson 4013 hydrophones, each positioned at 1 m depth and 2, 4 and 7 m distance (close, medium and distant; Fig. 7C). Each array was composed of a polyvinyl chloride (PVC) framework in the shape of an upside-down American football field goal and supported across the middle of the target pen by a large wooden support beam (Fig. 7D). Individual hydrophones were fixed in position with silicone adhesive to a monofilament strung between the open ends of the PVC framework. Inter-sensor spacing of the arrays was chosen to maintain consistent angular spacing with respect to the animal. The hydrophones were positioned 0.125, 0.25 and 0.4 m apart for the 2, 4 and 7 m distance arrays, respectively. This resulted in azimuthal spaced sampling of approximately 3.5 deg between hydrophone elements (Fig. 7C). Each hydrophone occupied an independent channel and was amplified by 20 dB using a custom-built 16-channel pre-amplifier. Signals were digitized using two National Instruments DAQmx-PCI 6133 A/D boards at a sample rate of 250 kHz.

Prior to experimentation, the hydrophone arrays were ground truthed via a two-step procedure. First, each hydrophone was individually calibrated using a 45 kHz pure tone signal and a synthetic broadband click centered at 60 kHz, both using a custom-designed ultrasonic broadband transducer (Whitlow Au, Marine Mammal Research Program) with a half-power beamwidth of 14.5 deg at 60 kHz. The receiving Reson 4013 hydrophones have a flat frequency response between 5 and 170 kHz. The receive voltage sensitivity (RVS) of each hydrophone varied by less than 1 dB re. 1 V μPa⁻¹. Second, the hydrophone arrays were fixed in position and 30 synthetic clicks centered at 60 kHz were projected towards the center array elements. Time series data were recorded for all hydrophone elements on the three arrays using the same equipment as in the animal experiments. After resampling and computing the peak-to-peak click energy, the measured beam pattern was interpolated using a cubic spline for each of the three arrays using MATLAB (MathWorks, Natick, MA, USA). Using the calibrated hydrophone RVS, data were then converted from voltage units to sound pressure level (dB SPL re. 1 μPa) and compensated for spherical spreading losses (dB SPL re. 1 μPa at 1 m). Once the calibration was complete, the arrays remained in their fixed position for the duration of the experiment. The experiment was completed over a 36 h time period of calm weather, which ensured no perturbations in the setup of our arrays.

For each echolocation signal, the on-axis hydrophone was identified as the hydrophone of each array with the highest amplitude signal. Clicks in which the on-axis signal were on the peripheral hydrophones, or in which the on-axis hydrophone was not the same for all three arrays were omitted from analysis. These criteria were used to ensure the −3 dB beam was correctly captured on all three arrays. This resulted in an analysis set of 1121 out of 1373 clicks for the three sessions. Because of variation in echolocation parameters across clicks within a trial (Kloepper et al., 2012, 2014), we chose five sequential clicks (clicks 5–10, which represent the peak emission within a pulse train) for further analysis. Using these clicks, the peak-to-peak voltage and center frequency (as defined in Au, 1993) were calculated for each click on each array distance (2, 4 and 7 m). The voltages of the on-axis signal were normalized relative to the expected transmission losses based on the calibration values; that is, if signals followed spherical spreading transmission losses, we would expect a constant voltage across all three arrays. Thus, we are comparing a normalized voltage value. The center frequency values were compared to ensure that changes in the beamwidth or normalized voltage were not artifacts of frequency-dependent attenuation altering the signal spectrum during propagation. The −3 dB beamwidth was calculated by cubically interpolating voltage values across the dimensions of each linear array and then determining the angular coordinates at which the echolocation signal crosses −3 dB, or half power, the peak of the signal using a MATLAB program (see supplementary material Fig. S1).

To test whether the beam is focused with convergent propagation, we analyzed the beamwidths measured at each array as multivariate data using multivariate T² statistics (Anderson, 2003) testing against a known hypothesis of constant beamwidth over distance. For each click recorded on axis, the beamwidths measured at the three arrays were combined into a multivariate measurement (3×1 vector). The most direct test that the beam is focused is a multivariate T²-test against the known hypothesis that the angular beamwidth was constant across the three arrays (Anderson, 2003). This test is the multivariate analog of the basic t-test for scalar data against a known mean value.

To test whether the beam is focused adaptively on target distance and presence, we used a MANOVA in SPSS (v. 22, IBM, Armonk, NY, USA) with target distance, target presence and click number as fixed factors, and the three parameters (beamwidth, normalized voltage and center frequency) at each of the three array distances as dependent multivariate observations.

This project would not have been possible without the efforts of the staff of the Marine Mammal Research Program, particularly trainers Marlee Breese, Christopher Quintos and Stephanie Vlachos.