Subjects and study site

The subject of this study was P. abramus, which is a member of the family Vespertilionidae and has a wingspan of 10–15 cm and a bodyweight of 5–8 g. During natural foraging, P. abramus emits relatively long (9–11 ms), shallow-swept frequency-modulated (FM) pulses, with the energy concentrated in the terminal frequency of the fundamental component at around 40 kHz [3,22]. The bats are regularly observed in large open areas during the evening from early summer to fall. Here, the study site was a large open area over a river with the width of approximately 20 m, near the campus of Doshisha University in southern Kyoto Prefecture, Japan, where only P. abramus regularly appears to forage for airborne insects. Our field studies did not involve endangered or protected species. No specific permissions were required for these locations/activities because the study site was not protected by the regulatory body concerned with the protection of wildlife. The target prey of P. abramus are mainly small hemipterans and dipterans [23]. The flight speed of the common chironomid midge Chironomus plumosus ranges from 0.25 to 1.1 m/s [24], and we visually observed that swarming dipteran midges took several seconds to fly across an area of a few tens of centimeters. From our observation, we concluded that these prey are roughly ten times slower than P. abramus (which has an average speed of 5 m/s) and therefore assumed that the movement of the prey, at this study site, was negligible during the brief period of approach and capture (< 3 s) in each flight sequence examined in this study [17].

When a bat successfully captures an insect, a brief burst of sounds (feeding buzz) occurs, followed by a silent interval (post-buzz pause) [25–27]. Based on our previous recording, P. abramus emits a feeding buzz approximately 0.2 s before capture [3,5], at a distance of a few tens of centimeters (approximately 30 cm) from the prey point. Since the movement of prey can be negligible within this brief period of time, we simply defined the bat’s 3D position at the end of the feeding buzz as the location of the prey at the capture in this study [3,5,17].

It is difficult to draw definitive conclusions about whether a bat has successfully captured prey based only on information about the post-buzz pause [17,27]. However, we confirmed that the distances between successful prey positions were too large for the prey (small midges) to move during the observed inter-capture intervals for the flights analyzed in this study. Therefore, if the bats failed to capture prey, it is highly unlikely that they attacked the same prey again in the second capture trial just after the first unsuccessful capture. Although it is still an assumption, we assumed that the bats attacked different prey sequentially, at least in the case of two successive target captures with short time intervals (< 1.5 s) in this study. We thus categorized two successive target captures with long time intervals (> 3.0 s) as long-interval capture and those with short time intervals (< 1.5 s) as short-interval capture.

Large-scale 3D microphone-array system

The recordings were carried out on 5 separate days (October 14, 2013; July 15, September 30, October 7, and October 16, 2014) for approximately one hour before and after sunset. Recording was conducted for 5–10 min each session and the total number of recording sessions was 32 for 5 days (total recording time: 225 min). To reconstruct the flight paths of the bats and identify the capture points accurately, we selected prey-capture flights where the amplitude of the sonar sounds was sufficiently high with a good signal-to-noise ratio, even at the end of the terminal buzz. At the same time, to ensure measurement accuracy, we selected only flights where the bat approached the targets while flying toward the L-shaped array inside of the U-shaped array. Thus, the vertical and horizontal pulse directions and beam widths could be measured accurately. We analyzed a total of 2,680 pulses from 37 captures in 20 measured flight paths. That is, flight paths with three successive captures were split into two flight paths with two successive captures each. (See Results.)

Echolocation pulses emitted from the bats were recorded using a custom-built 44-ch 3D microphone-array (Fig 1A). We previously reconstructed the horizontal pulse direction along with 3D flight paths using a horizontal U-shaped 32-ch microphone-array system [5]. In this study, we newly built a vertical 12-ch L-shaped microphone-array unit so that the vertical pulse direction could be measured. The data shown here are from measurements using two different configurations with 32 microphones in 2013 (vertical L-shaped 10-ch and horizontal U-shaped 22-ch), and 44 microphones in 2014 (vertical L-shaped 12-ch and horizontal U-shaped 32-ch).

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Fig 1. Large-scale 3D microphone-array system.

(A) Photograph of study site and microphone-array system with 44 microphones consisting of U-shaped 32-ch microphone-array and L-shaped 12-ch microphone-array in 2014. Four Y-shaped arrays (green dots) are part of the U-shaped array. Total of 24 microphones distributed over the entire U-shaped array at the same horizontal level were used to measure horizontal pulse direction, whereas L-shaped array units (orange dots) measured vertical pulse direction. Y-shaped array was used to reconstruct 3D flight paths of the bats. (B) A schematic diagram of the Y-shaped array unit. (C) Side view of the L-shaped array unit. The vertical pulse direction (blue arrow) was determined from the peak of a Gaussian curve (light blue curve), based on the sound pressure vectors (red arrows) across all 12 microphones. The horizontal pulse direction was also determined by the same procedure using the horizontal U-shaped microphone-array. (D) Definitions of the positional relationship between the bat and the target. The gaze angle φ_gaze (or θ_gaze) was the pulse direction (blue arrow) relative to the flight direction (yellow arrow) of the bat. The directions of the capture positions (prey position) φ_fp (or θ_fp) and φ_pp (or θ_pp) were the prey direction (magenta arrow) relative to the flight direction and the pulse direction of the bat, respectively. Here, φ is the horizontal angle and θ is the vertical angle. (See S1 Table).

https://doi.org/10.1371/journal.pone.0169995.g001

The microphone-array units were arranged to cover the entire foraging area over the stream, as shown in Fig 1A. We reconstructed the 3D flight paths using four Y-shaped array units using omnidirectional electret condenser microphones (models FG-23329-C05 and FG-23629-P16; Knowles, Itasca, IL, USA). The emitted echolocation pulses were recorded and amplified using a custom-built electronic circuit via a 10–250 kHz band-pass filter, and were digitized with 16-bit accuracy at a sampling rate of 500 kHz using high-speed data acquisition cards (PXIe-6358; National Instruments, Tokyo, Japan). The output signals were synchronously stored using a personal computer via a custom program using LabVIEW 2011 (National Instruments).

Reconstruction of 3D flight paths and pulse directions

The 3D locations of the bats were obtained using the difference in arrival times between a central and three other microphones separated by 1.3 ± 0.01 m in the Y-shaped array (Fig 1B). The arrival-time differences were calculated from cross-correlation functions using a Matlab routine (Math Works, Natick, MA, USA), and the analytical procedure was the same as in our previous studies [3,5,17]. We combined 3D sound coordinates calculated by each of four Y-shaped array units so that the flight trajectory could be reconstructed within the foraging area, which was enclosed by the microphone-arrays. The maximum range error of the microphone-array system was less than 10 cm for sound sources within 5 m of the Y-shaped array unit [3].

The horizontal pulse direction was calculated based on the sound pressure difference, namely, the differences in peak power in the spectrogram of a sonar sound across 24 microphones that were distributed over the entire array at the same horizontal level. The vertical pulse direction was also measured by the L-shaped array unit by the same method (Fig 1C). The sound pressure levels of the pulses were corrected for the propagation loss of sounds in the air between the bat and each microphone and the sensitivity differences between the microphones in the array. Sound absorption was calculated from measured absorption coefficients that were determined for the average frequencies at the peak energy in the FM pulse of P. abramus (1.2 dB/m at 45 kHz). The sensitivity of the microphone-array elements was measured by sending a 10-ms burst at 45 kHz to each microphone of the array using an ultrasonic loudspeaker (PT-R7, Pioneer, Tokyo, Japan). This allowed the recorded sounds to be calibrated according to sensitivity differences between the microphones. The directivity pattern of the sonar beam was reconstructed by curve fitting using a Gaussian function, and the direction at the peak value of the reconstructed directivity pattern was determined as the pulse direction. The beam width was defined by –6 dB off-axis angles in the reconstructed directivity pattern from the pulse direction. In our previous studies, we calibrated the measurement accuracy of the pulse direction and beam width for a U-shaped array. The error of the pulse direction was less than ±5°, and that of the beam width was less than ±7°, in the horizontal plane when the sonar beam was directed toward the U-shaped horizontal microphone-array [5,17]. In the present study, prior to the experiments, we arranged the L-shaped arrays in the field following the actual recording setup to measure the error of the vertical pulse direction and the beam width by using artificial FM sounds emitted from a loudspeaker (PT-R7; Pioneer, Tokyo, Japan). As a result, when the bat’s sonar beam was directed to the inside of the L-shaped array (as shown in Fig 1C), the errors for both the vertical pulse direction and the beam width were less than ±5°. The amount of error in this study corresponded to that of our previous studies [5,17], which was an acceptable amount of error to investigate the acoustical behavior of bats at the study site. To ensure measurement accuracy, we measured the horizontal beam width only when the vertical pulse direction was within ±45° from the horizontal plane of the U-shaped horizontal microphone-array. Therefore, when the bats emitted a pulse toward the exterior of the microphone-array (i.e., the positive direction in the X-axis in Fig 1A), we did not use the data for calculating beam width, but rather used only that for pulse direction to ensure the measurement accuracy of the beam width because it was unclear whether the vertical pulse direction was directed within ±45° from the horizontal plane. The vertical pulse direction was reconstructed only when the horizontal pulse direction was toward the inside of the U-shaped microphone-array. The vertical beam width was also calculated only when the horizontal pulses were directed within ±45° from negative direction of X-axis (Fig 1A) to ensure measurement accuracy.

In a strict sense, because auditory perception depends on the level of the returning echo and the hearing threshold of the bat [28], we should consider not only the beam width but also the angular range, combined with the transfer function of the outer ear, to define the acoustical field of view [29,30]. In this study, however, we adopted the −6 dB point of the beam width as a simple index of the acoustical field of view during echolocation following the approach used in recent studies [31,32].

We defined the positional relationship between the bat and the prey position, as shown in Fig 1D. The variables φ and θ represent the horizontal and vertical angles, respectively. The bat’s horizontal (vertical) gaze angle φ_gaze (θ_gaze) was defined as the pulse direction relative to the flight direction. When the bat captured multiple successive targets, we used suffixes to represent the order of the captures. φ_fp (or θ_fp) was defined as the direction of the prey position relative to the flight direction of the bat, while φ_pp (or θ_pp) indicates the direction of the prey position relative to the pulse direction. (See S1 Table.)

Acoustic analysis

The analytical procedure was also the same as that used in our previous studies [3,5]. The acoustic characteristics, including IPI and pulse duration, were analyzed from echolocation sounds recorded by the central microphone of the Y-shaped array unit that was spatially closest to the sound source (the bat) and thus received the strongest version of each broadcast using an additional custom program in Matlab. IPI was determined as the time between the amplitude envelope peaks of successively emitted echolocation pulses on oscillograms. The pulse duration was determined from a spectrogram of the first harmonic component of an extracted individual pulse (1024 points fast Fourier transform with a Hanning window, 97% overlap) at −25 dB relative to the peak intensity of the pulse. The foraging behavior of the bats was categorized into three phases based on the characteristics of the sonar sound; namely, a search phase, an approach phase, and a terminal phase [33]. The terminal phase of pipistrelles is usually divided into two signals: buzz I and buzz II [26]. Buzz II signals have lower bandwidth and frequency than buzz I signals [33]. Since the start of the approach phase of wild P. abramus was characterized by the appearance of a slight increase in the pulse duration [3,5], we used this as a simple index for identifying the timing of the beginning of the approach phase in this study.

For statistical comparisons, a t–test and Mardia–Watson–Wheeler test were used, when appropriate, to test for significant differences in beam width and angular variables between data sets.

Methods for the numerical simulation

We numerically simulated the flight trajectory of a bat when approaching two prey successively, so that the relationships between the acoustical field of view and the direction of each prey could be investigated quantitatively. In this framework, the bat dynamically changes its flight direction depending on the directions of the two prey, using the mathematical model proposed in our previous study [17]. Briefly, the modeled flight dynamics in the horizontal and vertical planes can be described as follows: (1) (2) where δ represents positive weighting factors and α is the minimization of the angular difference between the bat’s own flight direction [φ_b(t), θ_b(t)] and the direction to prey 1 [φ_bp1(t), θ_bp1(t)] (similar for β to prey 2). To simplify the numerical simulation, we constrain the parameters as follows: (3) (4)

Therefore, parameters α_h and β_h (α_v and β_v) are described as α_h = sinγ_h and β_h = cosγ_h (α_v = sinγ_v and β_v = cosγ_v). To examine the ratio of the flight attention between the two prey, the arctangent of parameters α and β is defined by γ: namely, γ_h and γ_v represent the arctangents in the horizontal and vertical planes, respectively.

The flight path was numerically simulated for a situation in which two prey are distributed inside the bat’s 3D sonar beam, which was modeled as a circular piston oscillating in an infinite baffle [11]. A simulation trial began when the bat started its approach phase to capture prey 1. The calculation conditions for a parameter set (γ_h and γ_v) are the same as those in our previous study [17], and the beam widths of the sonar beam in the horizontal and vertical planes were defined as ±59° and ±25°, respectively, which were derived from the experimental results of this study. Three trials were performed for each parameter set of γ_h and γ_v, ranging from −π to π, respectively, with 0.01π steps, and 201 × 201 pairs. All variables in this model were calculated by using the fourth-order Runge–Kutta method, with a time step of 0.01 s (the flight speed of the model bat was taken to be 5 m/s based on the experimental data). Pulses to obtain the target positions were emitted at every step. We examined the relationships between the acoustical field of view and the direction of each prey, in cases of both success and failure of the prey-capture trials, using this mathematical model. A parameter set was defined as a success when the bat captured (close in within 10 cm) the immediate prey (prey 1) and then the subsequent prey (prey 2) in sequence (capturing both prey), without losing the location of the prey which the bat intend to capture (i.e., prey 1 before the capture of prey 1 and prey 2 after the capture of prey 1). A simulation trial was defined as a failure when prey 2 was located outside the sonar beam after the capture of prey 1 (capturing only prey 1) (note that cases in which both prey 1 and prey 2 were missed were not considered in the investigation). We categorized the numerical simulation results of all trials into cases of success and failure and then analyzed the relationships between the acoustical field of view and prey directions while approaching prey 1 and prey 2 sequentially. Initial positions of prey 1 and prey 2 were randomly determined in horizontal and vertical space in every trial.

3D flight paths and pulse directions of bats attacking multiple targets in the field

Fig 2A–2C show representative data of the 3D flight paths with pulse directions of P. abramus when the bat captured four insects (Targets 1–4) consecutively in 12 s. The pulse directions did not always coincide with the flight direction, especially in the horizontal plane. The bat changed its flight direction and pulse direction dynamically on either the right or the left side from its flight direction or shifted between different directions. On the other hand, 82% of all pulses whose vertical pulse direction could be measured in this flight case (shown as a blue arrow in Fig 2A–2C) were emitted downward (< 0°), whereas only 18% of the pulses were emitted upward (≥ 0°). This suggests that the bat emitted most of its pulses downward from the horizontal plane in the vertical plane.

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Fig 2. Typical example of multiple consecutive capture flight of Pipistrellus abramus in the field.

(A–C) Top (top panels) and side (bottom panels) views of the 3D flight path and pulse directions of the bat attacking four successive targets. The observed 3D flight path of the bat was separated into three sections according to the timing of each consecutive target capture; namely, Captures 1–2 (A), Captures 2–3 (B), and Captures 3–4 (C). The black curved arrows indicate the initial flight direction of the bat. The blue arrows indicate the directions of pulse emission by the bat. The asterisks show the position where the bat started the approach phase. The gray arrows indicate the pulse emitted toward the out of the U-shaped microphone-array in the horizontal plane. Only pulses emitted before the bat captures its immediate prey are shown in the figure. (D–F) Time series data of IPIs (D), gaze angles (φ_gaze and θ_gaze), and directions of prey positions in the horizontal (E) and vertical planes (F) during this flight. The beam width of the sonar beam is equivalent to the length of gray vertical lines on the gray plots. φ_fp (or θ_fp) indicates the direction of the prey position relative to the flight direction of the bat. (See S1 Table.)

https://doi.org/10.1371/journal.pone.0169995.g002

Fig 2D shows time series data of IPI during the flight shown in Fig 2A–2C. When the bat started the approach to capture an insect, the IPI was decreased from approximately 100 to 5 ms. In this flight case, the time intervals between successive captures (Captures 2–3 and 3–4) were both 1.1 s, whereas the time interval for the first two successive captures (Captures 1–2) was 5.4 s. Throughout this flight period, the horizontal gaze angle, φ_gaze, was widely distributed from approximately −130° to 80° (Fig 2E). In contrast, in the vertical plane, the gaze angle θ_gaze had a narrower range from about −60° to about 40° (Fig 2F), indicating that the bat changed the horizontal acoustical field of view more dynamically than the vertical one during foraging.

Fig 2E and 2F show that φ_gaze and θ_gaze often corresponded to the directions of some of the subsequent prey positions; that is, not only the prey position of the immediate target but also subsequent target prey positions corresponded to the center of the acoustical field of view. In addition, both the immediate and subsequent prey positions were simultaneously within the −6 dB beam width of the sonar beam (gray vertical lines). In particular, Fig 2E shows that the pulse direction corresponded to the positions of Captures 3 and 4, approximately 4 s before Capture 2 occurred. (See from 1.5 s to 3.5 s on the horizontal axis.)

Future prey positions were covered by acoustical field of view

Fig 3A–3C show time series data of target directions before capture of the immediate target (0.5 s) and we could define the capture points of subsequent targets as the positions of the prey themselves in the case of short-interval capture. Fig 3A shows that in the case of long-interval capture, the subsequent prey (φ_pp2 and θ_pp2) were outside the acoustical field of view during the approach period of the immediate target. This suggests that the bat acoustically focused only on the immediate prey during long-interval capture. On the other hand, during short-interval capture, the subsequent target prey positions were within the beam width of the bat’s emissions during the whole or part of this period in both horizontal and vertical planes (Fig 3B and 3C). These results suggest that the bats can detect the positions of both their immediate prey and subsequent ones at the same time by keeping them within their acoustical field of view before capturing the immediate one during a short-interval capture. Fig 3A also shows that the immediate target directions (φ_pp1 and θ_pp1) were not always maintained at the center of the acoustical field of view, but were within the bat’s −6 dB beam width, in both horizontal and vertical planes, in the case of long-interval capture.

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Fig 3. Relationship between target positions and bat sonar beam while approaching targets.

(A–C) Time series data of φ_pp (top panels) and θ_pp (bottom panels) during the approach and terminal phases in long- (A) and short-interval captures (B, C) shown in Fig 2A–2C. φ_pp (or θ_pp) indicates the direction of the prey position relative to the pulse direction. (See S1 Table.) The light blue areas show the range of the −6 dB beam width of the bat’s sonar beam relative to the bat’s pulse direction. The vertical dashed lines show the timing of transition from the approach phase to the terminal phase.

https://doi.org/10.1371/journal.pone.0169995.g003

Fig 4A–4D show the relationship between the target direction and −6 dB beam width during the approach phase and buzz I in terminal phase for all recorded flight data (20 flights). The time of the measured flight paths ranged from 2 to 18 s, with an average of 7.5 s. In the long-interval captures (10 flights), the horizontal and vertical mean −6 dB beam widths of the pulses were ±51 ± 13° (N = 150 pulses) and ±27 ± 14° (N = 95 pulses), respectively. On the other hand, in the short-interval captures (10 flights), the horizontal and vertical mean −6 dB beam widths of the pulses were ±59 ± 12° (N = 131 pulses) and ±25 ± 8° (N = 85 pulses), respectively. Namely, the horizontal mean beam widths were significantly wider than the vertical ones for both short- (the t–test, t(214) = 25.1, P < 0.001) and long-interval capture cases (the t–test, t(195) = 13.7, P < 0.001). In addition, the short-interval capture case showed a slightly but significantly wider horizontal beam width than the long-interval capture case (the t–test, t(279) = 5.2, P < 0.001), whereas the vertical ones were not significantly different between short- and long-interval capture cases (the t–test, t(153) = 1.06, P = 0.146).

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Fig 4. Relationship between the prey direction relative to pulse direction and the directivity patterns of the sonar beam as bats converge on immediate prey in short- and long-interval captures.

Circular histograms show the directions of the immediate (horizontal, φ_ppi; vertical, θ_ppi) and subsequent (horizontal, φ_pps; vertical, θ_pps) prey relative to the bat’s pulse direction. Data were obtained from the recording sounds while the bat converged immediate prey (except for buzz II) for 10 flights each of (A, C) long- and (B, D) short-interval captures. The open light-blue circles indicate the amplitude measured at each microphone, showing the directivity patterns of the sonar beam. We defined 0 dB as the peak value of the curve-fitted directivity pattern of each sound. The vertical (A, B) and horizontal (C, D) axes for the circular histogram show the proportion relative to each number of pulses. Note that the sample sizes in the circular histogram differ from those in the directivity patterns. This is because the beam width data were analyzed only for pulses whose horizontal and vertical pulse directions could be appropriately measured at the same time. (See Materials and Methods).

https://doi.org/10.1371/journal.pone.0169995.g004

Fig 4A–4D also show the directions of the immediate and subsequent prey relative to the bat’s pulse direction accompanying beam patterns while approaching the immediate prey. We found that in the cases of long-interval captures, only 30% (59/196 pulses) of pulses covered the subsequent prey within the mean beam width (i.e., ±51 ± 13°), whereas the immediate prey was covered by 98% (193/196 pulses) of pulses in the horizontal plane (Fig 4A). On the other hand, most of the pulses emitted while approaching the immediate prey in the case of short-interval captures (90%, 167/186 pulses) covered the directions of both immediate and subsequent prey within the mean beam width in the horizontal plane (i.e., ±59 ± 12°) (Fig 4B). In the vertical plane, the immediate and subsequent prey directions, θ_ppi and θ_pps, were covered within the vertical mean beam width (i.e., ±27 ± 14°) by 94% (164/175 pulses) and 93% (162/175 pulses) of pulses, respectively for long-interval captures (Fig 4C). In the case of short-interval captures (Fig 4D), 81% (140/172 pulses) of pulses in the subsequent prey direction, θ_pcs, were observed within the vertical mean beam width (i.e., ±25° ± 8°). The horizontal mean directions of the subsequent prey φ_pps in the cases of long- and short-interval captures were −106° (long-interval captures) and 9° (short-interval captures), respectively, which were significantly different (the Mardia–Watson–Wheeler test, B(2) = 165.1, P < 0.001). In addition, those in the vertical plane were also significantly different (the Mardia–Watson–Wheeler test, B(2) = 32.1, P < 0.001), whereas those were 8° and 7°, respectively. This shows that the bats maintained the subsequent prey within their 3D acoustical field of view in the short-interval captures; this supports the acoustical field hypothesis.

Simultaneous coverage of both immediate and subsequent prey within the acoustical field of view is supposed to be suitable for planning of the bats’ future path to ensure capture of both prey. To test this, we conducted a numerical simulation (Fig 5). The numbers of simulation trials of failure and success were and 4,841 (229,706 pulses) and 1,665 (68,466 pulses), respectively. In the case of failure (only prey 1 was captured), only 39% (89,323/229,706 pulses from 4,841 trials) of pulses covered the subsequent prey within the beam width in the horizontal plane (Fig 5A, φ_pps). On the other hand, in the success cases, 62% (42,418/68,466 pulses from 1,665 trials) of pulses covered the subsequent prey (prey 2) within the beam width before the capture of the immediate prey (prey 1) in the horizontal plane (Fig 5B, φ_pps). This also suggests that the bat could potentially succeed in capturing both prey without invariably keeping the subsequent prey within the beam width in the horizontal plane; that is, the bat could occasionally lose the location of prey 2 just after the start of the simulation trial but could find it while changing the flight direction to capture the prey 1 because the pulse direction was equal to flight direction in the numerical simulation. In the vertical plane, 66% (151,655/229,706 pulses) of pulses in the failure cases and 87% (59,253/68,466 pulses) of pulses in the success cases covered both prey 1 and prey 2 (Fig 5C and 5D). These results suggest that acoustically viewing both the immediate and the subsequent prey simultaneously increases the success rate for the bats to capture both prey.

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Fig 5. Numerical simulation of relationship between prey direction relative to pulse direction and directivity patterns of sonar beam as bats converge on immediate prey during failure and success cases.

Circular histograms show the directions of the immediate (horizontal, φ_ppi; vertical, θ_ppi) and subsequent (horizontal, φ_pps; vertical, θ_pps) prey relative to the bat’s pulse direction calculated based on the simulation results. A simulation starts when the bats start to converge on immediate prey, and pulses to obtain the target positions were emitted at every step. A parameter set was defined as a success when the bat captured (close in within 10 cm) the immediate prey (prey 1) and then the subsequent prey (prey 2) in sequence (capturing both prey), without losing the location of the prey which the bat intend to capture. The simulation was assumed for the phase in which the bat converge immediate prey. Data were taken from 4,841 trials of failure (A, C) and 1,665 trials of success cases (B, D). The light blue lines show the directivity patterns of the sonar beam used in the numerical simulation.

https://doi.org/10.1371/journal.pone.0169995.g005

Relationship between acoustic sensing and bat flight

In this study, we found that, in the case of short-interval capture, the bats simultaneously maintained both their immediate and subsequent prey within the horizontal and vertical beam width of the emitted pulse. In addition, the numerical simulations in this study demonstrated that keeping both targets within the beam width increased the success rate of consecutive prey captures. This is considered to be a basic axis of efficient route planning for consecutive-capture flights. These findings suggest that the bats control their pulse direction to cover multiple targets simultaneously within their acoustical field of view. This supports the acoustical field hypothesis derived from our previous studies [5,17].

One of our previous studies showed that, in the case of capturing multiple prey within a short time interval, the sonar beam of P. abramus during foraging shifted directions predictably between the current target and the next target [5]. Based on the measurement results for the 3D beam width in the present study, we found that the bats actually encompassed both prey in their acoustical field of view. This suggested that when attacking two successive targets, the bats can focus their acoustic attention on a subsequent target before capturing the immediate one. This observed acoustic behavior can account for the flight dynamics for the flight attention of bats. That is, the bat distributes its flight attention between the immediate and subsequent prey so that it can plan its future flight path for a high success rate of consecutive prey captures [17].

Interestingly, our experimental data show that the bats did not always maintain their immediate prey at the center of the beam width (e.g., Fig 3A and 3B). Instead, they kept the targets within the beam width including the peripheral part, using their wide directional beam effectively to distribute their acoustic attention among multiple targets. Such practical operation of wide directional beam scanning employed by the bats is different from the design concepts of existing sensing methods, namely, ultrasonography and radar, which employ high-speed spatial scanning of a narrow directional beam to maintain the spatial resolution of echoes.

Because the movement speed of the prey was insignificant when compared to that of the bats during aerial-feeding flights, at least for a brief period (< 3 s), we set the capture point as the target position during the approach and terminal phases. (See Materials and Methods.) On the other hand, we often see the target prey of P. abramus (i.e., mainly small hemipterans and dipterans) [23] swarming at the same position for several tens of seconds, implying that P. abramus in our study site may use information on patch locations of insect swarming for consecutive captures. For example, Fig 2E shows that the pulse direction corresponded to the positions of Captures 3 and 4, approximately 4 s before Capture 2 occurred. (See from 1.5 s to 3.5 s, in the horizontal axis.) It is still difficult to conclude, however, that the coincidence of the pulse direction with the future prey positions implies that the bat might obtain information on the subsequent prey in advance beyond our expectations. There is another possibility: other prey might be incidentally covered by the acoustic beam before the bat captures its immediate prey during flight. That is, the bat’s sonar beam could incidentally cover multiple prey while it forages in an area where the prey density is high. Therefore, at the beginning of approaching the consecutive prey, this would be less of a strategy than a coincidence with respect to keeping multiple prey within the bat’s acoustical field of view.

Our previous numerical simulation, however, revealed that a bat’s active utilization of positional information on subsequent prey is effective for planning future flight paths during short-interval captures [17]. Furthermore, the modeling results in the present study support the idea that maintaining multiple targets within one sonar beam is an effective strategy for consecutive capture. Based on all of these findings, we suggest that the bat’s wide sonar beam incidentally covers multiple prey, and then the bat keeps future targets within its acoustical field of view by actively controlling its acoustical field of view for effective foraging. Mathematical modeling allows us to analyze animal behavior quantitatively, while also suggesting new insights and implementations of cause and effect [e.g., 34, 35]. Further experimental and mathematical investigations into how capable bats are at prediction, and the utilization of the gathered information, will be helpful to clarify the collaborative control of the acoustical field of view and flight path planning employed by bats, in the context of effective adaptation of foraging behavior.

Acoustic sensing in the horizontal and vertical planes

The experimental results demonstrated that the scanning behavior of P. abramus differed in the horizontal and vertical planes. We found that the vertical scanning range and the sonar beams were narrower than the horizontal ones in both long- and short-interval capture flights. (See Fig 4A–4D.) The bat changed the horizontal acoustical field of view more dynamically than the vertical one, sampling spatial information preferentially in the horizontal plane. In addition, the vertical flight range of the bats (variation of flight height) was also narrower by over five times than the horizontal one. (See Fig 2A–2C.) Namely, the bats modify their flight attention on the horizontal plane for prey that are incidentally on the same vertical plane. Prey insects are usually limited to a certain height above the water. The bats at our study site must avoid bumping into the riverbank during their acrobatic flight maneuvers. Hence, the physical restrictions of the study site may dictate that bats mostly scan their environment horizontally.

On the other hand, the experimental results show that the acoustical coverage rate of subsequent prey in the vertical plane (93% of pulses, Fig 4C) was higher than that in the horizontal plane in the case of long-interval capture (30%, Fig 4A), which is consistent with the numerical simulations of failure cases (capturing only prey 1) (Fig 5A vs. 5C). Experimental and mathematical results suggest that the bats tend to search for target prey distributed within a certain altitude range, which results to narrow down the vertical scanning and flight ranges. Foraging P. abramus often emits pulses downward (see Results) and attacks insect prey in descending flights [3]. Simplifying sensing and flight control in the vertical plane may be effective for complex aerial-feeding flight in 3D space.