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 φgaze (or θgaze) was the pulse direction (blue arrow) relative to the flight direction (yellow arrow) of the bat. The directions of the capture positions (prey position) φfp (or θfp) and φpp (or θpp) 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).
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 (φgaze and θgaze), 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. φfp (or θfp) indicates the direction of the prey position relative to the flight direction of the bat. (See S1 Table.)
Fig 3.
Relationship between target positions and bat sonar beam while approaching targets.
(A–C) Time series data of φpp (top panels) and θpp (bottom panels) during the approach and terminal phases in long- (A) and short-interval captures (B, C) shown in Fig 2A–2C. φpp (or θpp) 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.
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, φppi; vertical, θppi) and subsequent (horizontal, φpps; vertical, θpps) 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).
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, φppi; vertical, θppi) and subsequent (horizontal, φpps; vertical, θpps) 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.