Dolphin echo-delay resolution measured with a jittered-echo paradigm

Dolphins and microchiropteran bats utilize sophisticated biosonars to detect and classify objects. The operating principle presumably involves comparing a replica of the emitted sound pulse to returning echoes. Large-scale echo delays reveal target range, and fine scale echo-delay differences reveal spatial properties of the target (Au, 1993). Therefore, an animal must be able to resolve small differences in echo delay to perceive and discriminate fine-scale spatial features resulting from changes in the range of a single reflector or multiple closely spaced reflectors (Simmons et al., 1990b). Knowledge of an animal's echo-delay resolution therefore gives insight into the underlying spatial resolution of the biosonar mental representation; i.e., the biosonar “image.” In auditory science the term “image” is sometimes used to refer to neural activity patterns from the cochlea (e.g., auditory image model, Patterson et al., 1995) or the mental representation of object shape (Herman et al., 1998). Here, “image” is defined as a representation that preserves the spatial (geometric) structure of an object.

Echo-delay resolution in bats and dolphins has been measured using two broad classes of psychophysical tasks. In the first, animals are trained to discriminate between echoes that differ in delay. The echoes may consist of reflections from identical physical targets (located at different azimuthal angles) ensonified by the animal (see Simmons and Vernon, 1971; Murchison, 1980; Simmons and Grinnell, 1988), or electronic (“phantom”) echoes produced by capturing outgoing echolocation pulses and broadcasting delayed replicas back to the animal (Simmons, 1973; Masters and Jacobs, 1989). These studies have generally revealed echo-delay resolution on the order of ∼60–240 μs in bats (see Simmons and Grinnell, 1988; Masters and Jacobs, 1989) and ∼12–40 μs in dolphins (Murchison, 1980).

In the second class of experiments, animals are trained to discriminate between electronic echoes with a fixed echo delay and those whose echo delay alternates, or “jitters,” from one echo to the next (Simmons, 1979; Menne et al., 1989; Moss and Schnitzler, 1989; Simmons et al., 1990a; Moss and Simmons, 1993; Masters et al., 1997; Simmons et al., 1998; Simmons et al., 2003; Simmons et al., 2004; Finneran et al., 2019). The jittered-echo paradigm was developed as a way of avoiding the interfering effects of head movement while measuring echo-delay resolution under the assumption that head movement between successive pulse emissions is negligible (Simmons et al., 1990a). Several studies have measured jitter delay acuity in big brown bats (Eptesicus fuscus, see Simmons, 1979; Menne et al., 1989; Moss and Schnitzler, 1989; Simmons et al., 1990a; Moss and Simmons, 1993; Simmons et al., 1998; Simmons et al., 2003; Simmons et al., 2004). All of the bat studies reported jitter delay acuity thresholds below 1 μs. Simmons et al. (1990a) and Simmons et al. (2004) also tested jitter delays below 0.4 μs and found fine jitter delay acuity on the order of 10 ns; however, this finding remains controversial (Beedholm, 2006). Potential explanations for the 10-ns jitter delay resolution (other than delay)—such as spectral artifacts caused by overlap between vocalizations, stimulus echoes, and extraneous sounds (Pollak, 1993), or signal distortion from impedance mismatches in the delay generating apparatus (Beedholm and Mohl, 1998)—have been proposed (and rebutted, see Simmons, 1993; Simmons et al., 2003), yet the studies of Simmons et al. (1990a) and Simmons et al. (2004) have not been truly replicated.

Several studies have also suggested that the big brown bat's sonar receiver is sensitive to changes in echo phase, despite the lack of evidence for reliable encoding of phase information above 10–20 kHz (see Köppl, 1997): Simmons (1979), Simmons et al. (1990a), and Moss and Simmons (1993) found local increases in errors at jitter delays greater than those near the main error peak about 0 μs. The jitter delays of these additional error peaks corresponded to time lags of secondary peaks in the biosonar pulse autocorrelation function (ACF). Simmons et al. (1990a) and Moss and Simmons (1993) found that bats reliably discriminated non-jittering echoes from those that jittered only in polarity (180° phase shift). Menne et al. (1989) reported that bats could discriminate non-jittering echoes from those that jittered by ±45° without an accompanying shift in overall echo delay.

Jitter delay resolution has also been recently measured in bottlenose dolphins (Finneran et al., 2019). This study utilized an echo-change detection paradigm, where dolphins reported when phantom echoes changed from non-jittering to jittering. The results showed jittered echo-delay thresholds at 1–2 μs, the hardware limit, and peaks in the error function roughly corresponded with time lags of secondary peaks in the click ACF. Error functions were well within the envelope of the ACF, and matched the ACF near zero jitter delay, suggesting the use of phase information as opposed to only the envelope of the echo. When one of the two alternating jittered echoes was inverted in polarity, both dolphins reliably discriminated echoes at all tested delays, including 0 μs (i.e., only jittering in polarity, not delay). However, unlike some bat data (Simmons et al., 1990a; Moss and Simmons, 1993), secondary peaks in the error functions were not observed when polarity was jittered.

The present paper describes the results of a study to further examine echo delay resolution in dolphins using the jittered-echo paradigm. As in Finneran et al. (2019), an echo-change detection paradigm was utilized. Unlike the previous study, where click emissions from the dolphins were recorded using a contact hydrophone placed on the melon, in the present study clicks were measured using a hydrophone located in the farfield along the main biosonar transmit axis. In addition, a fractional delay technique was used to improve jitter delay resolution below the hardware digital sampling interval. Finally, a pilot study was conducted where dolphins discriminated between jittering and non-jittering signals during passive listening, i.e., no biosonar clicks were produced. The goal was to examine if dolphins could discriminate between non-jittering signals and those that jittered in timing and polarity when a reference signal related to the dolphin's outgoing click was not available.

Four bottlenose dolphins (Tursiops truncatus) participated in the biosonar task: APR (female, 34 years), COM (male, 4 years), MKO (female, 36 years), and SPO (male, 3 years). Upper-frequency limits for their hearing, defined as the frequency at which electrophysiological auditory steady-state response thresholds reached a sound pressure level (SPL) of 120 dB re 1 μPa (see ANSI, 2018), were approximately 100 kHz for APR, 140 kHz for COM, 120 kHz for MKO, and 150 kHz for SPO (Strahan et al., 2020). These data indicate full hearing bandwidth for COM and SPO and limited high-frequency loss for APR and MKO.

Tests were conducted within a 9 m × 9 m floating, netted enclosure at the US Navy Marine Mammal Program facility in San Diego Bay, CA. During each trial, the dolphin positioned itself on an underwater “biteplate” supported at a depth of 0.9 m by vertical posts spaced 1.8 m apart (Fig. 1). The biteplate was oriented so the dolphin faced San Diego Bay through an enclosure gate opening containing a netted frame. Two piezoelectric transducers (TC4013, Reson Inc., Slangerup, Denmark) were positioned ∼0.75 m in front of the biteplate: one functioned as the click receiver and the other as the echo projector. The nearest land mass in the direction of the dolphin's biosonar transmissions was ∼1.1 km distant. Mean water depth was ∼7 m. Background ambient noise at the test site was dominated by contributions from snapping shrimp and other dolphins, with occasional contributions from passing vessels and aircraft. Median ambient noise pressure spectral density levels were approximately 70 dB re 1 μPa²/Hz at 10 kHz and decreased linearly with the logarithm of frequency to ∼53 dB re 1 μPa²/Hz at 150 kHz.

The dolphins' task was identical to that described by Finneran et al. (2019). The dolphin was required to produce echolocation clicks, listen to returning phantom echoes, and produce a conditioned acoustic response (APR, COM, SPO = whistle; MKO = burst pulse) when the echoes changed from “non-jittering” (Echo A) to “jittering” (Echo B). For non-jittering echoes, echo delay and echo polarity were constant. For jittering echoes, echo delay varied on alternate echoes (Experiment 1), or both echo delay and echo polarity varied on alternate echoes (Experiment 2). Mean echo delay was fixed at ∼13.2 ms (∼10 m simulated target range) for both experiments. Echo delay was jittered symmetrically about the mean value, for jitter delay values from 20 μs (i.e., ±10 μs relative to mean delay) down to 0.5 μs in experiment (Exp.) 1 or 0 μs in Exp. 2.

Experimental sessions consisted of 60–120 trials, with more trials per session for the older dolphins (APR and MKO). Sessions were divided into 10-trial blocks with constant jitter delay within each block. After each block, jitter delay was reduced for the next block. Approximately 80% of the trials were echo change trials, where the echoes changed from non-jittering to jittering after 4–10 s (uniform distribution). The echo change was followed by a 1-s response interval. The remaining trials were control trials, where non-jittering echoes were presented for the entire 5- to 11-s trial. If the dolphin responded during the response interval after an echo change (a hit), or withheld the response for an entire control trial (a correct rejection), it was rewarded with one fish. Failure to respond during an echo change trial was a miss. A response during a control trial was a false alarm. If the dolphin responded during an echo change trial before the echoes changed from Echo A to B, the trial was re-classified as a control trial and the response scored as a false alarm. The dolphin was recalled with no fish reward after a false alarm or miss. At least 100 trials were conducted for each value of jitter delay for each dolphin, resulting in a total of 2010–2669 trials for each dolphin, depending on the experiment.

Biosonar echoes were created using a phantom echo generator (PEG, Fig. 2(a); see Finneran et al., 2019) based on a TMS320C6713 floating point digital signal processor (Texas Instruments, Dallas, TX) with an analog input/output (I/O) daughtercard (AED109, Signalware Corp., Colorado Springs, CO). Clicks emitted by the dolphin were captured by the click receiver, amplified and filtered (5–200 kHz bandwidth: VP-1000, and 3 C module, Krohn-Hite Corporation, Brockton, MA), then digitized by the AED109 with 1-MHz sampling rate and 12-bit resolution. If the digitized hydrophone signal exceeded an amplitude threshold, the click waveform was extracted and convolved with a target impulse response function (see below) to create the echo waveform. The echo was then scaled in amplitude, delayed, and converted to analog (AED109). The analog echo waveform was then filtered (5–200 kHz, 3 C module), amplified (M7600, Krohn-Hite Corp.), and used to drive the echo transmitter. Echo energy flux density levels were approximately –80 dB relative to the received click (20–30 dB above the dolphins' echo-detection thresholds). Dolphin clicks were also digitized at 2 MHz and 16-bit resolution by an NI PXIe 6368 multifunction data acquisition device (National Instruments, Austin, TX) and stored for later analysis.

Mean echo delay was accomplished by changing the position of the echo waveform in the digital-to-analog converter output buffer. Jitter delay was accomplished by changing the target impulse response from one echo to the next using a fractional delay technique (Välimäki and Laakso, 2000). The target impulse response was defined as

where h(n) is the impulse response, n is the sample index, Δt is the sampling interval, sinc(x) = sin(πx)/(πx), and d is the echo delay. Figure 3 shows examples of the impulse responses and (electronic) echo waveforms for non-jittering echoes and jittering echoes with jitter delay = 0.5 μs.

Operation of the PEG was verified before each session by replacing the dolphin click signal input to the PEG analog-to-digital (A/D) converter with a representative recording of an on-axis dolphin click and inspecting the resulting electronic echo waveforms using a digital oscilloscope [see Fig. 2(c)]. Calibrations were also periodically performed by broadcasting the analog echo waveforms using the echo projector and recording the acoustic echoes (without the dolphin present) using a TC4013 hydrophone positioned at the midpoint between the dolphin's lower jaws when on the biteplate (hereafter designated as “the listening position”). The hydrophone signal was amplified and filtered (5–200 kHz, VP1000 and Krohn-Hite 3 C module), then digitized along with the electronic click waveform at a rate of 100 MHz using a T3DSO1104 high-speed digital oscilloscope. To measure echo delay, the digitized click and echo waveforms were cross-correlated, and echo delay was defined as the time index of the cross-correlation function (XCF) peak.

Dolphin performance in the echolocation task was quantified using the hit rate (HR, number of hits divided by the number of echo-change trials), false alarm rate (FAR, number of false alarms divided by the number of control trials), proportion correct P_C (number of hits + number of correct rejections, divided by total trials), and the error rate (E = 1 – P_C). The error rate is used here to facilitate comparison with bat jittered echo delay results obtained with a two-alternative forced choice paradigm (e.g., Simmons, 1979). When combining data across multiple subjects, only the last 72 echo-change trials and 15 control trials for each subject (the minimum number available for all subjects and jitter delays) were used to compute the error rate. Confidence intervals for binomial variables were calculated using the Clopper-Pearson method (Mathworks, 2019).

Biosonar click parameters were quantified by extracting individual clicks from the digitized click receiver hydrophone signal and computing the peak-to-peak (p-p) SPL, energy flux density level, energy spectrum, center frequency, and (centralized) root-mean-square (rms) bandwidth (Menne and Hackbarth, 1986; Au, 1993; Simmons et al., 2004). Clicks within the first 4 s of each trial (less than the minimum time for the echo change) were not analyzed. From pairs of successive clicks within a trial, the inter-click interval (ICI) and click-to-click change in ICI and p-p SPL were also calculated. Mean values of the click SPL and energy spectrum, and distributions for the remaining quantities, were computed for each subject/experiment. Representative echoes for each dolphin were obtained by replacing the dolphin click input to the PEG with the mean click waveform measured for each dolphin, then broadcasting the resulting analog echo and measuring the echo sound pressure at the listening position [as in Fig. 2(c)]. Coherent averaging was used to extract the broadcast echoes from the background ambient noise.

To examine potential auditory cues available to the dolphins when comparing echoes that jittered in polarity, representative echoes with normal and inverted polarity were input to a model of the dolphin auditory periphery (Branstetter et al., 2007). A complete description of the model can be found in Branstetter et al. (2007); only a brief summary is provided here. The model has three primary stages: (1) a gammatone filter bank (Slaney, 1993) simulating peripheral auditory filters derived from bottlenose dolphin notched-noise masking data (Lemonds, 1999); (2) a non-linear, half-wave rectifier simulating inner hair cell response; and (3) a low-pass (LP) filter with a time-domain, exponential-decay function corresponding to the dolphin integration time of ∼264 μs (Moore et al., 1984), simulating the relative sluggishness of the VIII nerve and other auditory neurons with refractory periods. The output of the model is a two-dimensional matrix, similar to a spectrogram; however, the frequency spacing of the model is based on equal overlap of auditory filters and the spectral and temporal resolution is frequency dependent. From the spectrogram representation, post-processing can be used to compute quantities such as the spectral profile (obtained by summing within each frequency channel across time) and temporal envelope (summing across each frequency channel).

Finally, the four dolphins utilized a variety of click patterns during the experimental trials. A detailed analysis of the click train patterns was beyond the scope of the present paper; however, some simple analyses were conducted to illustrate the differences across individuals. To this end, the occurrence of two features was quantified for each trial: (1) a temporal gap in the click train, defined by an ICI >150 ms, and (2) a local maximum in ICI, defined when a zero-crossing occurred in the first derivative of the ICI (as a function of click number) and the second derivative of the ICI was < –2 ms/click². Specific numeric values for these parameters were defined after trial-and-error adjustment during the preliminary examination of click trains.

The listening task was conducted in a floating netted enclosure in San Diego Bay, using two of the dolphins (COM, SPO) that participated in the biosonar task. The test apparatus [Fig. 4(a)] was similar to that used in the biosonar task, but was constructed of extruded aluminum. The biteplate was at a depth of 1.0 m, with two piezoelectric transducers (TC4013) positioned ∼0.75 m in front of the dolphin's blowhole. One transducer was used to monitor ambient noise and any sounds produced by the dolphin. The second transducer acted as the simulated-echo transmitter.

The listening task was a simulated-echo change-detection task, similar to the biosonar task except the dolphins did not produce biosonar clicks. Instead, a representative click for each dolphin, based on its mean click waveform from Task 1, was input to the PEG [Fig. 2(a)] and the resulting analog “echo” signal broadcast to the dolphin [Fig. 4(b)] with a mean inter-stimulus interval (ISI) of 30 ms (similar to ICIs utilized during Exps. 1 and 2). During each trial, the dolphin remained on the biteplate as the acoustic stimuli were presented. The dolphin's task was to produce a whistle if it detected a change in the signals. Eighty-percent of the trials were change trials, where the signals changed from non-jittering to jittering after 1–5 s. The remainder were control trials, where non-jittering signals were presented for the entire trial duration. Hits and correct rejections were rewarded with one fish. False alarms and misses were not rewarded. The dolphins' performances were quantified using the proportion correct.

Signal polarity, ISI, and amplitude were fixed for non-jittering signals. The goal was to determine if the dolphins could discriminate between non-jittering signals and those that jittered in ISI and polarity (as in Exp. 2). Therefore, for jittering signals, the ISI was jittered by 20 μs (±10 μs; value selected based on performance in Exps. 1 and 2) and the signal polarity alternated on successive presentations. However, to provide an additional cue for training the dolphins to discriminate between jittering and non-jittering signals, jittered signal amplitude was also alternated on successive presentations. Over successive trial blocks, the amount of amplitude jitter was gradually reduced, with the goal of eventually eliminating the amplitude jitter cue entirely. Testing began with amplitude jitter of 12 dB (±6 dB). After each block of five trials, amplitude jitter was changed based on the dolphin's performance during the block: amplitude jitter was reduced if P_C ≥ 0.8, increased if P_C ≤ 0.4, or remained constant for P_C = 0.6. Amplitude jitter was adjusted in 4 dB (±2 dB) steps from 12 dB down to 4 dB (COM) or 8 dB (SPO), then adjusted in 2 dB steps.

Preliminary examination showed no systematic changes in dolphin clicks with experiment or jitter delay; therefore, all clicks from each dolphin were grouped for analysis. This resulted in 3.8 × 10⁵ to 5.7 × 10⁵ individual clicks for analysis, depending on the subject. The resulting mean click waveforms and spectra [Fig. 5(a)] were typical for dolphins and similar to each other. Broadcast echoes [Fig. 5(b)] were similar to clicks, but had longer effective duration, less low-frequency content (below ∼80 kHz), and more symmetric waveform amplitude profiles as a result of the echo projector transmitting response. Despite differences between the click and echo waveforms, the click ACFs were generally similar to the XCFs between mean clicks and representative echoes [Fig. 5(c)]. Examination of all individual click ACFs showed that the locations of the first minimum and (non-zero) maximum varied from 3.8 to 4.6 μs and 7.5 to 9 μs, respectively. LP filtering of the clicks (e.g., to simulate high-frequency hearing loss), caused the central lobe of the ACF to broaden and the time lags for the local minima/maxima to increase [Fig. 5(d)].

The auditory model predictions for representative normal and inverted echoes are shown in Fig. 6. Although the temporal envelope (not shown) and spectral profile [Fig. 6(g)] for the normal and inverted echoes are identical, there are subtle differences in the spectrogram representations [Figs. 6(c)–6(f), 6(h)]. These differences are related to the timing of the rarefaction phases of the echoes and result in the inverted echo spectrogram representation resembling the normal echo spectrogram shifted in time by ∼5 μs.

Click p-p SPLs (Fig. 7) ranged from ∼195 to 220 dB re 1 μPa, with mean values for APR, COM, and SPO near 210 dB re 1 μPa, but MKO's mean p-p SPL lower (204 dB re 1 μPa). Center frequencies ranged from ∼90 to 120 kHz, with relatively high mean values: 106 to 110 kHz. Centralized rms bandwidths were generally between 25 and 37 kHz, with similar means across dolphins (∼31 kHz). ICI distributions for APR, COM, and MKO were unimodal, with means between 26 and 29 ms and almost all ICIs > mean echo delay (13.2 ms); however, ICIs for SPO were bimodal, with one peak at 29 ms and the other at 10 ms (less than the echo delay). Changes in p-p SPL and ICI from one click to the next were small: SPL changes were almost always within ± 1 dB and ICI changes within ± 1.5 ms. These slight differences between successive clicks indicate that within a single trial click, parameters tended to change on a relatively slow time scale.

All four dolphins typically utilized ICIs larger than the mean echo delay. For APR, COM, and MKO, more than 99% of ICIs were larger than mean echo delay. For SPO, only 77% of ICIs were larger than the mean echo delay. There were also substantial differences in the temporal patterns of click emissions across dolphins (Fig. 8). The older dolphins typically clicked continuously during the trials with relatively consistent ICIs and infrequent local maxima in the ICI (i.e., click rate decreased, then increased): for APR and MKO, the mean (± standard deviation, SD) number of temporal gaps per trial was 0.029 ± 0.18 and 0.031 ± 0.22, respectively, and the mean (±SD) number of local maxima per trial was 0.05 ± 0.27 and 0.28 ± 0.78, respectively. The younger dolphins (COM and SPO) exhibited more variable patterns and often had temporal gaps in clicking. For COM and SPO, there were on average 0.51 ± 1.0 and 0.31 ± 0.64 temporal gaps per trial and 2.7 ± 3.3 and 2.0 ± 2.5 local maxima per trial, respectively. On average, the younger dolphins had ∼14× more gaps and local maxima per trial compared to the older dolphins.

The potential error and inherent jitter in echo delay were assessed by repeatedly measuring the acoustic echo delay [as in Fig. 2(c)] and examining the distribution of the resulting values. Figure 9 shows acoustic echo delay distributions measured during calibration, for non-jittering echoes and jittering echoes with jitter delay of 0.5 μs. The data were fit well (0.968 < R² < 0.985) with normal distributions having standard deviations of ∼50 ns, thus 95% of the echo delay values were within ±100 ns of the desired value; i.e., errors in acoustic echo delay were approximately ±100 ns.

Temporal overlap between the dolphin's click emissions (and their reflections) and jittered echoes could provide an unintended cue for discriminating jittering and non-jittering echoes. To assess the potential for temporal overlap between reflections of the dolphin's emitted click and the returning echoes, dolphin clicks recorded by the click receiver were coherently averaged over an entire session. Figure 10 provides a representative example of the mean sound pressure at the click receiver. Low-level reverberation from the dolphin's click can be seen extending out to 6–7 ms relative to click emission, well under the 13.2 ms mean echo delay. Therefore, no significant temporal overlap existed between click reflections and the broadcast echoes.

Figures 11 and 12 show the performance of each dolphin during Exp. 1 (jittered delay only) and Exp. 2 (jittered delay and polarity), respectively. For all dolphins in both experiments, FARs were typically <0.2 and did not show any systematic relationship to jitter delay. For Exp. 1, HR was near 1.0 from 3 to 10 μs, but systematically declined below 3 μs, down to values near zero at 0.5 μs. HRs in all dolphins also decreased for at least some values of jitter delay between 10 and 15 us; however, the extent of the decrease varied substantially across dolphins. In APR, HR dropped by 25% at 11–12 μs, while the other dolphins showed only small decreases (7–8%) in HR. Jitter delay thresholds, defined as the jitter delay for an error rate of 0.5, were 1.2, 1.2, 1.3, and 1.5 μs for APR, COM, MKO, and SPO, respectively (mean = 1.3 μs, SD = 0.14 μs). For Exp. 2, HRs were near 1.0 except around 5 μs, where HR significantly decreased in all dolphins. For jitter delay of zero (jittered echo polarity only), HR was >0.96 and the FAR was ≤0.10 in all dolphins.

Figure 13 shows error rates from Exps. 1 and 2 computed from the data for all four dolphins. The composite error function (Simmons et al., 1990a), defined as the maximum amplitude at each jitter delay value (based on error rates from Exp. 1 plotted upward and those from Exp. 2 plotted downward), is also shown. The composite error curve matches the ACF near zero jitter delay, and overall has a shape that is suggestive of the ACF function; however, the specific error function peak locations do not necessarily match the peaks in the ACF function.

Figure 14 shows P_C for COM and SPO measured during Exp. 3 (passive listening task), where ISI was jittered 20 μs (±10 μs), the signal polarity alternated on successive presentations, and amplitude jitter manipulated. With 12-dB amplitude jitter, P_C was greater than 0.9 for both dolphins. As amplitude jitter decreased, P_C declined, with the P_C = 0.5 threshold equal to 1.5 and 2.1 dB of amplitude jitter for COM and SPO, respectively. Decreases in amplitude jitter below 1–2 dB were not attempted based on the dolphins' performance. These values are similar to measurements of dolphin amplitude-discrimination thresholds for pulsed sounds (1–2 dB, Vel'min et al., 1975; as cited by Bullock and Gurevich, 1979), and estimates of dolphin just-noticeable amplitude differences for pure tones (1–2 dB, Johnson, 1971; Johnson, 1986). The listening task data therefore suggest that the dolphins were not capable of perceiving the stimulus change once the amplitude change in the jittering echoes was no longer perceptible; i.e., they were not capable of detecting changes in stimulus polarity or ISI.

One of the primary goals of the present study was to re-examine jitter delay thresholds in dolphins while eliminating some potential confounds, increasing sample size, and improving echo delay resolution compared to a previous study (Finneran et al., 2019). Specifically, the present study was conducted in a different acoustic environment, utilized a farfield hydrophone for capturing the dolphins' emitted clicks, and used a fractional delay technique to allow jitter delay values below the hardware sampling interval. The resulting jitter delay performance for Exp. 1 (Fig. 11) was similar to that reported by Finneran et al. (2019), suggesting that the contact hydrophone and specific environment/hardware apparatus did not substantially affect the previous data. The mean jitter delay threshold in the present study was 1.3 μs, almost an order of magnitude larger than the errors in acoustic delay measured during calibrations (Fig. 9). Therefore, it does not appear that these jitter delay acuity thresholds (or those from the Finneran et al., 2019, which used the same PEG) were limited by the experimental hardware and likely represent the actual jitter delay acuity for the dolphins. It is possible that movement of the dolphins relative to the echo projector could have caused changes in echo delay not captured by the calibration procedures. However, such movement would have been limited since the acoustic transducers were mounted on the same apparatus as the biteplate and would have occurred on a relatively slow time scale compared to the changes in echo delay from one jittering echo to the next.

The mean jitter delay threshold of 1.3 μs is noteworthy considering the mean echo delay was ∼13 ms, median ICIs were ∼25–30 ms, and changes in ICI from one click to the next were on the order of 1 ms. The dolphins were therefore able to detect echo delay jitter about 10 000× smaller than the mean echo delay and 1000× smaller than the change in absolute timing from one echo to the next. To detect such small changes in jittered-echo delay, dolphins must be capable of registering the time onset of returning echoes with high precision and comparing time onsets of successive echoes. The exact mechanisms underlying this capability are not known. Simmons et al. (1990a) showed that jitter-delay acuity in Eptesicus is sensitive to intensity-latency trading effects—i.e., the perceived delay of jittering echoes is affected by their amplitude. This implies that echo delay is represented by the time of arrival of neural discharges rather than spectral cues (Simmons et al., 1990a; Simmons et al., 1990b). The distribution of frequency-tuned delay receptors across populations of neurons may enable the high delay resolution observed in dolphins and bats (Simmons et al., 2014; Simmons, 2017).

The extent to which jitter detection thresholds vary with mean echo delay is also not known: measurements of jitter-delay acuity in Eptesicus have used similar echo delays (∼3–3.7 ms) and individual studies have kept mean delay constant (Simmons, 1979; Menne et al., 1989; Moss and Schnitzler, 1989; Simmons et al., 1990a; Moss and Simmons, 1993; Simmons et al., 2004). The only previous study of jittered echo delay resolution in dolphins utilized similar mean echo delay as the present study (∼13 ms, Finneran et al., 2019). Dolphin behavior during long-range (>50–75 m) biosonar tasks suggests that there is an upper limit to an animal's ability to resolve echo delay; i.e., there is some upper time limit after which returning echoes can no longer be compared to the emitted click (Finneran, 2013). If jitter detection depends on the animal's ability to compare successive estimates of echo delay (i.e., target range), then jitter delay acuity would decline with mean echo delay itself.

Altes (1989) suggested that error rates (as functions of jitter delay) measured with the jitter paradigm could be used to reveal the perceptual image of an acoustic point target along the range axis; i.e., the compound error curve (Fig. 13) approximates the point-spread function along the range axis (Altes, 1989; Simmons et al., 1990a), which describes the “smear” of the target representation along the range-axis. In the present study, error functions showed a central peak near zero jitter delay, with increases in errors between 10 and 15 μs in Exp. 1 (jittered delay only) and between 5 and 6 μs in Exp. 2 (jittered delay and polarity). These patterns were qualitatively similar to previous bat data that showed secondary peaks in error functions (Simmons, 1979; Simmons et al., 1990a; Moss and Simmons, 1993) and the ability to detect echoes that jittered only in phase (Menne et al., 1989; Simmons et al., 1990a; Moss and Simmons, 1993). For Exp. 1, the increase in errors between 10 and 15 μs matched the previous dolphin data (Finneran et al., 2019), but did not match the time lag for the first peak in the click ACF in the present study (∼8–9 μs). For Exp. 2, error functions peaked at 5–6 μs, a result not seen in the previous dolphin study. This discrepancy was likely caused by the relatively coarse jitter delay spacing utilized in the prior study; i.e., the error function peak was likely missed because of the relatively large separation between jitter delay values.

The reason for the discrepancy between the error function peak at 10–15 μs and the farfield click ACF peak at 8–9 μs is not known; however, it is not clear how much agreement should be expected between the farfield click ACF and the error functions. The extent to which the acoustic farfield biosonar click represents the dolphin's internal click “template” is questionable. It is noteworthy that auditory evoked potential measurements indicate differences in cochlear excitation patterns between a dolphin's own emitted (i.e., “self-heard”) click and a farfield click presented from an external source (Finneran et al., 2017). The effect of pre-existing high-frequency hearing loss on the dolphin's point-spread function is also unknown. Hearing loss would effectively act as a LP filter to a full-bandwidth echo. LP filtering of dolphin clicks increases the time lags for the ACF local minima/maxima and broadens the primary peak of the ACF [Fig. 5(d)]. With a LP filter cutoff of 100 kHz (matching APR's upper cutoff of hearing), time lags for the ACF first minimum/maximum increased to approximately 6 and 12 μs, respectively, which match the jitter delays of error peaks in APR. However, COM, MKO, and SPO had higher upper-frequency limits, thus pre-existing hearing loss cannot fully explain the discrepancy between their ACFs and error functions.

Overall, the similarities between the error functions and the ACF are suggestive, but not conclusive proof that dolphin biosonar includes a process analogous to a cross-correlation receiver. Differences in error functions between Exps. 1 and 2 do indicate that the dolphin biosonar range estimator is sensitive to manipulations of echo phase (Altes, 1981). Simmons et al. (1990a) and Moss and Simmons (1993) show similar results for the big brown bat. This does not mean that the dolphin can perceive echo phase information directly, but that cues related to echo phase are present and were utilized during echo-ranging in this task. Results of the auditory model (Fig. 6) suggest that there are likely differences in the auditory system representation of echoes that differ only in phase. The error function pattern for the inverted echo resembles that of the normal echo shifted by ∼5 μs, which matches the jitter delay of the error peak in Exp. 2. Of course, the model is relatively simple and its predictions should be treated with caution. It is not known if the subtle differences predicted by the model would be perceptible to dolphins—the listening task data suggest that they are not perceptible without the emitted click as a reference/template. However, the main point is that a simple peripheral auditory system model for dolphins that lacks the ability to reliably encode the phase of the high-frequency content of biosonar signals, predicts differences between normal and inverted (180° phase-shifted) echoes.

Finally, we note the apparent discrepancy between results of the present study (as well as Finneran et al., 2019) with those of Ibsen et al. (2013). In this study, a dolphin participated in a go/no-go procedure where the “go” target was a simulated echo from a solid steel sphere and the “no-go” targets were filtered versions of that echo. Full-spectrum target echoes with 180° phase shift were also tested. The dolphin responded correctly to 100% of the standard targets and many of the filtered targets, but only to 40% of the 180° phase shift targets. From these data, the authors concluded that the dolphin was not sensitive to the phase of the echo. However, the dolphin's intermediate performance to the phase-shifted echoes (i.e., between the standard and filtered echoes) could instead indicate that the dolphin was able to detect differences between standard and phase-shifted echoes, but could not reliably classify the phase-shifted echoes (i.e., as either standard or filtered echoes). In this case, the present results would not necessarily contradict those from the earlier study. It is also possible that the echo-delay resolution required for detection of the polarity change was not available due to the experimental design of the Ibsen et al. (2013) study; i.e., it was not a jittered echo paradigm (Altes, 1989). The dolphin tested by Ibsen et al. (2013) also had profound high-frequency hearing loss and utilized only echo frequency content from 29 to 42 kHz when making biosonar discriminations. Simmons et al. (2004) have shown that reducing echo bandwidth lowers echo delay acuity; whether this would affect an animal's ability to discriminate normal and phase-shifted echoes is not known.

As in previous studies, the dolphins used a variety of click emission temporal patterns while performing the task. Unlike the previous jitter study of Finneran et al. (2019), where the dolphin SAY had the most experience and displayed unique click patterns, here the two younger dolphins exhibited highly variable click patterns. The older dolphins utilized stereotypical click trains with limited temporal gaps, infrequent ICI local maxima, and ICIs greater than the mean echo delay. In contrast, the younger dolphins utilized click trains with numerous temporal gaps and local maxima in ICIs. Local maxima in the ICI, where the ICI briefly increased, suggest that the animals may have been using their biosonar to examine distances beyond the 10-m simulated target range. It is possible that the younger, less experienced dolphins were more concerned than the older dolphins with monitoring their surroundings and utilized changing ICIs as a way of attending to the echoes at a simulated range of 10 m while maintaining awareness at distances beyond the enclosure.

The listening task data of Exp. 3 suggested the dolphins were incapable of detecting signals that jittered only in ISI or polarity (i.e., when amplitude jitter approached the threshold of discrimination). In other words, without the emitted click as a timing reference, the dolphins did not appear able to detect changes in echo timing and polarity that were easily detected in Exps. 1 and 2. However, it is possible that during training the dolphins attended to the jittered amplitude cue and when that cue diminished, they failed to transfer to the jittered polarity or ISI cues, despite those cues being perceivable. Therefore, the ability for dolphins to passively detect signals that jitter in ISI or polarity cannot be ruled out. Detection of jittered pulse sequences has been demonstrated in human listeners, with detection thresholds at short ISIs (∼1 ms) in the microsecond range (Pollack, 1968). Thus, it seems likely that under some combinations of jitter delay and ISI, the dolphins would be able to perform the listening task. To conclusively determine whether dolphins can passively detect small amounts of ISI jitter, future testing could first utilize combinations of jitter delay/ISI that elicited a response. The amount of ISI jitter could then be titrated down to map the range of values over which dolphins could still perceive the jittered signals. A passive listening experiment in which a simulated click precedes the jittering echo would also be informative. This experiment could shed light on whether the act of signal production plays a role in jitter detection, or if simply having a non-jittering timing reference is sufficient.

Dolphins have a high-resolution biosonar system including a range-estimator that is sensitive to changes in echo phase. Error functions obtained when jittering echoes in delay and polarity are consistent with but not proof of a biosonar range estimation system that operates with a cross-correlation like process.

The authors thank R. Dear, M. Wilson, H. Bateman, K. Christman, L. Crafton, L. Curtis, R. Echon, C. Espinoza, G. Goya, M. Graves, J. Haynesworth, D. Ram, R. Simmons, T. Wu, and the animal care, training staff, and interns at the Navy Marine Mammal Program. The authors thank Dr. John Buck for suggesting the fractional delay technique. The study followed a protocol approved by the Institutional Animal Care and Use Committee at the Naval Information Warfare Center Pacific and the Navy Bureau of Medicine and Surgery and followed all applicable U.S. Department of Defense guidelines. Financial support was provided by the Office of Naval Research Code 32 (Mine Countermeasures, Acoustics Phenomenology & Modeling Group). Portions of these data were presented at the 176th Meeting of the Acoustical Society of America.