Biosonar interpulse intervals and pulse-echo ambiguity in four species of echolocating bats

Echolocating bats emit trains of intense biosonar pulses to perceive objects in the surrounding scene from echoes that return to their ears (Fenton et al., 2016; Griffin, 1958; Neuweiler, 2000; Surlykke et al., 2014). Each biosonar broadcast is a probe into the scene that yields echoes at different delays according to distances to objects (∼6 ms m⁻¹ of target range; Chiu et al., 2009; Moss and Surlykke, 2010; Wohlgemuth et al., 2016). In practice, small, insect-sized targets are detectable out to no more than 5–10 m, for echo delays of 30–60 ms, while larger background objects would be detectable out to approximately 20–40 m (Stilz and Schnitzler, 2012). The depth of realistic scenes thus potentially encompasses several tens of meters, for echo delays up to at least 100–200 ms. The most elemental problem for the bat to solve is when to transmit individual echolocation sounds (i.e. at what interpulse intervals, or IPIs), particularly in relation to the returning streams of echoes (Kothari et al., 2014).

The experiments reported here examined the biosonar sound emission patterns of four bat species flying in a complex sonar scene – a room containing rows of vertically hanging plastic chains with a 1-m-wide corridor for the bat to fly along (Fig. 1A; Barchi et al., 2013; Petrites et al., 2009; Wheeler et al., 2016). As each of the bat's emitted pulses propagates along the room (Fig. 1B), it reflects off successive rows of the chains (Fig. 1C). The echoes returning to the bat during the epoch of time immediately following the broadcast represent the distances to the different objects. In the simplest case, in Fig. 1D, the bat waits until all of the echoes from one broadcast have returned before emitting the next broadcast (IPI>T, where T is the maximum delay). This keeps echoes in the epoch of one broadcast from mingling with echoes in the epoch of the next broadcast. However, bats frequently fly in acoustically distinctive and often highly cluttered surroundings, such as vegetation (Grunwald et al., 2004; Ming et al., 2017; Müller, 2003; Müller and Kuc, 2000; Yovel et al., 2008, 2009), where some of the objects are in close proximity while others extend farther away. Prompt responses are necessary to avoid collisions, which requires emitting broadcasts at short intervals to keep up with rapidly evolving conditions. Nevertheless, other objects still are present at longer ranges, and their echoes necessarily reach the bat at longer delays. If a new broadcast is emitted while echoes of the previous broadcast are still traveling through the air, the echo-stream epochs of the two broadcasts will overlap (IPI<T; Fig. 1E). The long-delayed echoes of the first broadcast are liable to be judged as having shorter delays relative to the most immediate broadcast, not the correct, longer delays relative to the earlier broadcast. To the bat, phantom objects might suddenly appear at close range and will have to be avoided as hazards to flight even though no such objects actually are present. Misattribution of echoes to the most recent broadcast represents ‘pulse-echo’ or ‘range’ ambiguity, a major problem for radar or sonar systems operating in surroundings in which objects are distributed in depth (Skolnik, 1980; Stimson, 1998).

In principle, there are three ways to mitigate pulse-echo ambiguity. The first solution is to emit sounds at IPIs long enough to accommodate all of the returning echoes before the next broadcast (IPI>T; see Fig. 1D). This entails accepting the risk that nearby obstacles will have to be avoided using information acquired at the slower update rate necessitated by waiting until all echoes have returned. The second solution is to alternate between long and short IPIs. Each long IPI probes the whole scene out to its maximum depth (IPI>T), whereas each short IPI probes for nearby objects that need rapid action for guidance (IPI<T; Fig. 1E). In this solution, ambiguous echoes do arrive after the short IPIs, but, by keeping track of apparent echo delays that occur after both long and short IPIs, the spurious delays that follow the short IPIs can be identified and disregarded (Skolnik, 1980). The third solution is to transmit pulses that alternate in some identifiable acoustic feature, usually frequency or phase. So-called ‘frequency hopping’ (Markley and Antheil, 1942) is a method for coping with ambiguity and is a staple for communications security. Each broadcast ‘tags’ its echoes as distinct from the other broadcast's echoes. Echoes are assigned only to the broadcast having the corresponding frequency (Skolnik, 1980). By any of these three solutions, effective segregation of echo streams is achievable, but the underlying receiver mechanisms will be different.

Biosonar broadcasts have been examined specifically with regard to the pattern of IPIs related to overlap of pulse-echo epochs and emergence of ambiguous echoes (Melcón et al., 2011; Petrites et al., 2009; Barchi et al., 2013; Falk et al., 2014; Kothari et al., 2014; Sändig et al., 2014; Knowles et al., 2015; Wheeler et al., 2016; Accomando et al., 2018). In addition, the strategy of frequency hopping from one pulse to the next is used by some bat species in situations in which ambiguity is likely to occur (Mora et al., 2004; Guillén-Servent and Ibáñez, 2007; Hiryu et al., 2010). These previous studies have developed tools for analyzing IPIs to address the problem of pulse-echo ambiguity. Here, those tools are used to compare four different species of echolocating bats performing the same task.

Individuals of four species of adult, wild-caught bats were tested in flights through arrays of vertically hanging plastic chains that served as a complex biosonar scene for assessing guidance by echolocation. The task challenged their ability to follow a straight corridor from a release point to the far end of the array while receiving echoes from chains at all points in the array (Fig. 1A; Petrites et al., 2009). The challenge to the bats comes from both the presence of multiple near obstacles to be avoided and the long extent of the scene, which delivers echoes over a wide span of delays from as little as 3 ms to as much as 30–35 ms. Big brown bats [Eptesicus fuscus (Palisot de Beauvais 1796)] were flown in tests conducted at Brown University in Providence, Rhode Island, USA. They were captured from house colonies in Rhode Island under a state scientific collection permit. Japanese house bats [Pipistrellus abramus (Temminck 1840)], bent-winged bats (Miniopterus fuliginosus Hodgson 1835) and greater horseshoe bats (Rhinolophus ferrumequinum nippon Temminck 1835) were flown in tests conducted at Doshisha University in Kyotanabe, Japan. Pipistrellus abramus were captured in Kyoto Prefecture; M. fuliginosus and R. f. nippon were captured in Hyogo Prefecture. The bats were maintained in individual cages or a larger colony room in temperature- and humidity-controlled colony rooms (22–24°C and 40–60% relative humidity) that were kept on a reverse light:dark cycle with 12 h:12 h dark:light. Experiments were conducted during the bats' subjective night. All bats were fed live mealworms (larval Tenebrio molitor), with daily rations adjusted to keep individual body mass in a healthy range between 5 and 30 g depending on the species. All of the animals had free access to vitamin-enriched water. For E. fuscus, husbandry and experimental procedures complied with Principles of Animal Care, publication #86-23 (1985) of the US National Institutes of Health (NIH), and were approved by the Brown University Institutional Animal Care and Use Committee. For the other three species, procedures complied with the same NIH document, and current Japanese laws, approved by the Animal Experiment Committee at Doshisha University.

Experiments took place in two custom-built flight rooms. The facility at Brown University was 8.5 m long, 3.3 m wide and 2.4 m high, and insulated acoustically and electrically from external noise, including commercial FM radio signals. To accommodate recording equipment, a net across the width of the room restricted the effective flight space from the release point to the far wall to be 6 m long. The walls and ceiling of the room were entirely covered in fireproof and anechoic acoustic foam (SONEX^®, Pinta Acoustic, Minneapolis, MN, USA) that dampened any residual wall reflections by 20–25 dB, and the floor was carpeted to minimize reverberation. During flights, the only illumination was from low-level red LEDs distributed around the room's walls (Barchi et al., 2013). The facility at Doshisha University was an experimental chamber 8 m long, 3 m wide and 2 m high. Considering the release point for each flight, the useful flight space was approximately 6 m long. This chamber was constructed of steel plates bolted together to minimize interference from external electromagnetic noise, particularly commercial FM radio stations. During experiments, long-wavelength lighting that filtered out wavelengths below 650 nm was used to prevent the bat from using visual information.

Each flight room contained multiple rows of closely spaced plastic chains suspended vertically from ceiling to floor for 1.8–2.0 m. They were arranged to leave a 1-m wide corridor along which the bats could fly (Fig. 1B). This basic chain configuration, but with either straight or curved corridors of varying widths, has been used previously to examine echolocation during flight (Petrites et al., 2009; Knowles et al., 2015; Wheeler et al., 2016). Because the task is a useful laboratory model for guidance in clutter, it also has been used to assess the effects of intense sound exposure on bats (Hom et al., 2016; Simmons et al., 2018). In the Brown University flight room, individual links in the chains measured 4.0 cm wide, 7.5 cm long and 1.0 cm thick. At Doshisha University, the chain links were 4.0 cm wide, 7.0 cm long and 0.8 cm thick. The vertically extended chains are strong reflectors of the bat's incident emissions, returning echoes that decline only slightly with increasing distance owing to their extended shape. Tests with artificial bat sounds to measure echoes from chains at distances from 30 cm to 5 m yielded echoes 11 to 16 dB weaker over that span of distances (Knowles et al., 2015). Longer distances would eventually encounter large losses from atmospheric absorption, but within the confines of the flight space, all of the rows of chains in the array returned easily detected echoes for individual bat sounds, thus posing a problem of pulse-echo ambiguity. Fig. 1A,B illustrates the series of echoes recorded from a series of broadcasts emitted during a representative flight by one species (M. fuliginosus). The indicated broadcast was followed by a long train of echoes that extended over 25 ms, culminating in an echo from the wall at 30 ms delay. The chains were spaced 30 cm apart left to right in each row, and successive rows were separated by 40 cm (Fig. 1B). This configuration creates a complex acoustic echo scene combining proximity, density and spatial extent. It challenges the bat's biosonar capabilities for flight guidance (Barchi et al., 2013). The 1-m corridor width was chosen for these experiments because it is sufficiently more cluttered than an open room to evoke changes in broadcast patterns by E. fuscus (Knowles et al., 2015; Petrites et al., 2009; Wheeler et al., 2016).

During each flight, the trains of pulses emitted by each bat were recorded with several different ultrasonic microphones positioned in the scene to acquire the bat's emitted pulses (Telemike on bat or Knowles microphone on wall in Fig. 1A; FG-3325 or SMG-0291 Knowles Electronics, Itasca, IL, USA) or the echoes from the chains (Anabat microphone in Fig. 1A; Titley Scientific, Brendale, QLD, Australia). The microphones were positioned so that they could record all of the bat's pulses from the time of release until the time of landing on the back wall of the flight room. The microphone on the wall was used to register the broadcasts for calculating IPI values during all flights. The Telemike was used for recording the CF-FM sounds emitted by R. f. nippon because the presence of CF components interspersed between FM signals was a special concern for understanding how the FM components were separated in time. The large Anabat microphone was positioned behind the bat as it flew into the array of chains to document the occurrence of a long sequence of echoes reflected back to the bat after each broadcast. The recorded sounds were digitized at 192 kHz (Model 702T, Sound Devices recorder, Reedsburg, WI, USA) and saved as stereo .wav files. Each recording was manually started by one experimenter before the release of the bat from the other experimenter's hand, and then manually stopped once the bat had landed on the wall. Off-line analyses of the recorded sounds were performed using custom-written MATLAB procedures (R2014a; MathWorks, Natick, MA, USA). For each flight, the recordings were first digitally high-pass filtered at 15 kHz to remove ambient noise. ‘Audio trials’ representing the duration of each flight down the corridor towards the wall were selected in the following manner. The stereo sound file containing the recording from the end point of the flight was defined by the onset of a burst of rapidly emitted pulses characteristic of the landing maneuver (‘landing buzz’; Petrites et al., 2009; Wheeler et al., 2016). Moving backward in time from the first pulse in the landing buzz, a time interval of 1–2 s was selected for analysis. This interval covers the time for a bat to fly down to the end of the corridor after being released, but does not include any pulses emitted by the bat prior to being released, or the landing buzz itself. In each audio trial, the time of each individual pulse was marked as the point at which its envelope reached its maximum amplitude. In some cases, the bat flew several times along the corridor, turning back at the far wall, returning, and then again flying along the corridor towards the far wall. The flight segments when the bat flew away from the Anabat microphone and towards the far wall were identified from the echoes that the Anabat microphone recorded from the chains, which only appeared during the bat's movement away from the Anabat microphone.

IPIs were calculated as the time intervals between the amplitude maxima of successive pulses. This yielded a series of IPIs for a given flight. Then, for each individual pulse, IPIs were labeled as ‘pre-IPI’ (the IPI before the pulse) and ‘post-IPI’ (the IPI after that pulse). This pair of intervals was determined for all but the first (no pre-IPI) and last (no post-IPI) pulses in the entire audio trial. The patterning of IPIs in each audio trial was analyzed using three metrics: (1) the distribution of IPIs for all flights of a given species (plotted as a histogram); (2) the contingency distribution of pre-IPI and post-IPI values for each pulse (plotted as a two-dimensional dot distribution); and (3) the distribution of post-IPI/pre-IPI values for each sound (Wheeler et al., 2016). This ratio metric treats successive IPIs as proportions so that if the bat were to change the absolute size of the IPIs, this metric would still capture their proportional relationship. It allows analysis of how intervals before and after each pulse are related to one another and does not rely on a particular definition of a ‘sonar sound group’ or ‘strobe group’ (Moss et al., 2006; Petrites et al., 2009; Kothari et al., 2014), which are groups of pulses with short, stable IPIs surrounded by longer IPIs.

Bats of all four species successfully made multiple flights along the corridor through the array of chains. Data were analyzed for a minimum of two each of M. fuliginosus, P. abramus, E. fuscus and R. f. nippon. To facilitate direct comparison of the four species, IPIs extracted from the recordings are presented in the same format: first, representative spectrograms from one flight, then a series of plots that summarize IPIs from all of the flights.

Fig. 2A shows spectrograms for a series of FM broadcasts emitted by M. fuliginosus during one flight along the corridor through the chain array to land on the far wall. These sounds were recorded with the Anabat microphone (Fig. 1A), which emphasizes the sequence of echoes reflected back to the bat. Each sound in A appears blurred because it is followed by a stream of echoes from all of the chains situated in front of the bat. The flight terminates in a landing buzz of multiple, closely-spaced sounds that shift down to half of the frequencies contained in the FM sounds emitted along the flight path leading up to the landing. Fig. 2B zooms in two successive broadcasts (FM pulses 1 and 2, delineated by two vertical dashed lines in Fig. 2A), each followed by a long stream of echoes from the chains. Fig. 2A indicates the two IPI metrics extracted from the recordings: the interval before each sound (pre-IPI) and the interval after each sound (post-IPI). In Fig. 2B, the IPI between pulse 1 and pulse 2 is 34 ms, while the IPI from pulse 2 to the next pulse is 27 ms. Fig. 3A shows the IPIs from a series of broadcasts recorded during a 1.5-s segment of one flight by M. fuliginosus. The trace shifts up and down slowly across time, marking the relative consistency of IPIs between successive broadcasts. Fig. 3B shows a histogram of IPIs from all flights. Mean IPI is approximately 50.0 ms with only a slight skew to shorter IPIs. The smoothness of the IPI sequences in the example in Fig. 3A is fully captured in Fig. 3C, a contingency plot of post-IPIs relative to pre-IPIs for each sound in the dataset. The diagonal line in Fig. 3C traces where post IPIs equal pre-IPIs. The data points cluster along the diagonal line, indicating that the IPI after each sound is approximately the same length as the IPI preceding that sound. The distribution of the ratio of post-IPIs to pre-IPIs (Fig. 3D) is narrow and symmetric. The mean ratio is approximately 1.

Fig. 4A shows spectrograms for a series of FM broadcasts emitted by P. abramus during one flight along the corridor through the chain array, which culminates in a turn back into the corridor. They also were recorded with the Anabat microphone (Fig. 1A) to emphasize the sequence of echoes reflected back to the bat. Here, the bat does not land, and the sound sequence does not end with a landing buzz. Fig. 4B zooms in on seven successive broadcasts (segment delineated by two vertical dashed lines in Fig. 4A). Each pulse is followed by a long stream of echoes from the chains. The rhythm of IPIs used by P. abramus is irregular, with long and short IPIs intermingled. The IPI after pulse 1 is 62 ms, while the IPI after pulse 2 is only 24 ms, and after pulse 3 it is 47 ms. In this instance, the interval between pulse 2 and pulse 3 is shorter than the epoch of echo arrivals, as explained in Fig. 1E, indicating that some pulse-echo ambiguity occurs. Fig. 5A shows alternation between long and short IPIs in a series of pulses recorded during a 1.5-s segment of one flight. These alternations reveal sound (strobe) group doublets, with a few triplets marked by adjacent short IPIs. The histogram of IPIs from all flights has a mean of approximately 40 ms, but the distribution is distinctly bimodal, with a narrow peak at 25 ms and broad peak at 30–60 ms (Fig. 5B). The contingency plot of post-IPIs relative to pre-IPIs (Fig. 5C) reflects the bimodal distribution for IPIs less than 60 ms. This part of the plot has two clusters for alternating intervals: short pre-IPIs followed by long post-IPIs, and long pre-IPIs followed by short post-IPIs. For pre-IPIs longer than 60 ms, however, post-IPIs are similar (Fig. 5C). The histogram of post-IPI/pre-IPI ratios (Fig. 5D) is strongly bimodal, with one peak at 0.7 and a second peak at 1.2. A lower, broader region of ratios also extends to 2.0.

Fig. 6A shows spectrograms for a series of FM broadcasts emitted by E. fuscus during one flight prior to landing on the end wall – again, recorded with the Anabat microphone. Fig. 6B zooms in on five successive broadcasts (segment delineated by two vertical dashed lines in Fig. 8A). In this example, the pulses were recorded with the electret microphone on the wall (Fig. 1A) to register broadcasts without their echoes. Like P. abramus in Fig. 4A, the rhythm of IPIs used by E. fuscus is staggered, with long and short IPIs intermingled. Fig. 6B shows a doublet sound (strobe) group followed by a triplet. Fig. 7A shows a series of IPIs used by E. fuscus during one flight segment with strongly alternating long and short IPIs. Some sound (strobe) groups are doublets, some are triplets. The distribution of all IPIs is notably trimodal, with a peak around 30 ms for IPIs within triplets, a peak around 60 ms for IPIs within doublets, and a peak around 100 ms for the longer intervals between sound groups (Fig. 7B). Intervals shorter than approximately 30 ms expose the bat to pulse-echo ambiguity at the beginning of flights when the bat is presented with full depth of the chain array. The contingency plot of post-IPIs to pre-IPIs (Fig. 7C) reveals a bifurcated distribution where short IPIs are followed by long IPIs, reflecting the alternation from within to between sound groups. Sometimes the shortest IPIs are followed by similarly short IPIs, which indicates the triplets. The histogram of post- to pre-IPI ratios (Fig. 7D) has two peaks: one at approximately 0.7, the other at approximately 1.8, which is dominated by IPIs within versus between sound groups.

Fig. 8A shows spectrograms for a series of CF/FM broadcasts emitted by R. f. nippon during one flight prior to turning away from the end wall. These sounds were recorded with the Anabat microphone located behind the flying bat to emphasize the stream of echoes after each pulse. Each sound in A appears blurred because it is followed by a stream of echoes from all of the chains situated in front of the bat. Fig. 8B zooms in on seven successive broadcasts – a quadruplet followed by a triplet (segment delineated by two vertical dashed lines in A). Each pulse is followed by a long stream of echoes from the chains and then from the far wall. Like P. abramus in Fig. 4A and E. fuscus in Fig. 6A, the rhythm of IPIs used by R. f. nippon in Fig. 8A is irregular, with several short-IPI pulses grouped together and the groups separated by a longer IPI. Fig. 8C shows spectrograms of the same sounds recorded by the Telemike carried on the bat to pick up broadcasts without echoes from the chains as in Fig. 8A. The grouping of several broadcasts is more evident with the echoes removed. Fig. 8D shows the same seven broadcasts as in Fig. 8B but recorded by the Telemike without the echoes. The closely spaced pulses in Fig. 8D are shown as intermingled with echoes in Fig. 8B. Overlap of echoes streams occurs for the closely spaced pulses comprising the quadruplet and triplet, so pulse-echo ambiguity occurs often. Staggering of several short IPIs followed by a long IPI separates the overlapping echo streams, but only intermittently. The sample sequence of IPIs in Fig. 9A shows regular alternation between several short IPIs and one long IPI, creating groups of sounds that make up the whole sequence. In Fig. 9B, the distribution of IPIs is strongly skewed to short intervals, with a sharp peak around 25 ms between members of sound (strobe) groups. For inter-group intervals, the distribution spreads to 40–60 ms. From Fig. 8, IPIs shorter than approximately 30 ms regularly expose the bat to overlapping echo streams and consequent pulse-echo ambiguity. The dot pattern for the contingency plot of post- and pre-IPIs (Fig. 9C) has two widely separated clusters lying above and below the diagonal line, signifying the alternation from long IPIs between sound groups to short IPIs within groups. Short IPIs often repeat, signifying the presence of triplets and quadruplets in the sound groups. The histogram for the distribution of post- to pre-IPI ratios is markedly trimodal, with peaks at 0.5, 1.1 and 2.5 (Fig. 9D).

Four species of echolocating bats were tested in flight experiments that exposed each species to the same task (Fig. 1), with presumably substantially the same degree of difficulty. All four species successfully flew along the corridor past multiple rows of vertically-suspended chains, in a corridor 1 m wide between the closest chains on the bat's left and right. In previous flight tests with E. fuscus, the corridor width of 1 m is narrow enough to begin imposing enough difficulty on orientation that bats shift from using relatively long IPIs to pulse timing patterns that intersperse short and long intervals (Knowles et al., 2015; Petrites et al., 2009; Wheeler et al., 2016; Accomando et al., 2018). In the tests described here, E. fuscus again conformed to alternating short and long IPIs.

The broadcast patterns of the four species varied from the simplest IPI distribution to more complex patterns (Figs 3, 5, 7 and 9). These consist of (1) a succession of relatively stable time intervals (M. fuliginosus), (2) increasingly complex sequences that contain groups of sounds (strobe groups) with two or three sounds each (P. abramus and E. fuscus), and (3) three or four closely spaced sounds in each group (R. f. nippon). When viewed in light of the extended echo streams from multiple rows of chains, especially near the start of each flight pass when the entire depth of the chain array faced the bat (Fig. 1A), these differences can be considered as distinct strategies for coping with the potential interference caused by overlap of echo streams. This particular kind of interference is called pulse-echo ambiguity (Skolnik, 1980). Miniopterus fuliginosus largely avoids pulse-echo ambiguity by keeping intervals between sounds longer than the echo streams that follow individual sounds. How M. fuliginosus deals with demands on rapid maneuvering is an open question, but the behavior of E. fuscus, a similar-sized bat, suggests that the task is sufficiently difficult that ambiguity and maneuvering capability both pose challenges on the bats. The alternating short and long IPIs used by P. abramus and E. fuscus seem designed to probe into the entire scene, out to the longest delays in the room, while next looking closely to nearby objects to facilitate rapid guidance reactions. Miniopterus fuliginosus uses FM sounds similar to those recorded in flights here to hunt for flying insects (Hu et al., 2011), and they change the terminal frequency of their FM sweeps when flying in each other's company to avoid mutual jamming (Hase et al., 2018). For R. f. nippon, whose reliance on the long CF components for Doppler-shift perception, there is a different factor to consider: the FM components may be constrained to be far enough apart to accommodate the minimum adequate duration for the intervening CF component. This species uses an exaggerated timing pattern of several closely spaced FM signals to form triplets or quadruplets, followed by long intervals between these grouped sounds. However, the intervening time intervals still are filled by the CF components. It seems likely that the added information supplied by the CF echoes, presumably from Doppler shifts in the echoes returned by the nearest chains in each row, is important for guidance – a feature of the system used by R. f. nippon that is not shared by the other bat species.

The ordering of species from M. fuliginosus to P. abramus to E. fuscus to R. f. nippon that seems reasonable from visual inspection of the IPI histograms and the IPI ratio histograms in Figs 3B,D, 5B,D, 7B,D and 9B,D is supported statistically by the probabilities assigned to the pairwise comparisons of these two distributions using the Kolmogorov–Smirnov tests in Table 1. Miniopterus fuliginosus uses a timing pattern at one end of a continuum and R. f. nippon at the other end, with statistical similarity among the three FM species and statistical difference for R. f. nippon.

Pulse-echo ambiguity is one of the largest problems for sonar and radar, and several technical solutions are typically employed to cope with it. The diversity of IPI patterns shows that bats have evolved implementations of two known solutions that involve intervals. (The third, frequency hopping, is known in bats that emit CF search signals, and in FM bats that are flown in the densest clutter.) We observed that P. abramus and E. fuscus use one of the classical solutions of alternating long and short intervals to ‘look’ far and then near. Rhinolophus f. nippon also alternates intervals, but the pattern is more complex, possibly because of the presence of CF components that have a minimum duration of approximately 5 ms. The presence of these CF components fills the time between successive FM components and may be a factor in the horseshoe bat's use of groups of three or four closely spaced FM signals with CF components filling much of the intervening times. The duty cycle is very high – roughly 90% compared with the roughly 5% used by any of the FM bats.

We thank R. A. Simmons for assistance with statistics.