Energy compensation and received echo level dynamics in constant-frequency bats during active target approaches

Echolocating bats navigate and catch prey by auditory processing of the highly dynamic echoes returning from objects they have ensonified with powerful ultrasonic calls. To manage the complexity of such an actively generated acoustic scene, bats control the sensory flow by adjusting both the transmitting and receiving parts of their biosonar system. On the transmission side, bats can actively adjust the repetition rate (Wheeler et al., 2016; Wilson and Moss, 2004), duration (Britton et al., 1997), intensity (Brinkløv et al., 2009; Waters and Jones, 1995), gaze (Ghose and Moss, 2003), directionality and bandwidth of their vocalizations to the task at hand (Fujioka et al., 2014; Kalko and Schnitzler, 1993). When approaching airborne prey, insectivorous bats follow a stereotyped search, approach and buzz phase strategy (Griffin et al., 1960). In the search phase, bats emit powerful and relatively invariant calls to detect prey. The approach phase is characterized by gradual reductions of call duration and source level (SL), as well as inter-call interval. Just before capturing prey, bats transition into a buzz consisting of a short train of calls with short duration, low SL and an extremely high repetition rate.

Range-dependent reductions in SLs have been ascribed to the need for echo levels (ELs) to return in a dynamic range matched to the hearing system of bats, i.e. with sufficient energy for detection and processing without exceeding comfortable levels (Denzinger and Schnitzler, 1998) – a phenomenon that has often been coined ‘echo intensity compensation’ or ‘intensity compensation’ (Budenz et al., 2018; Hartley, 1992a; Koblitz et al., 2011). Here, we use the term ‘energy compensation’ for SL adjustments during approach of a target, as the mammalian ear integrates intensity over time to detect energy (Green and Swets, 1966; Surlykke and Bojesen, 1996).

If bats did not perform energy compensation, the returning ELs for a given target would increase by up to ∼70 dB during an approach. This is illustrated in Fig. 1 for a bat emitting a constant-frequency call (call frequency of 68 kHz; hereafter, ‘CF bat’) approaching a point target (target strength, TS=−15 dB at 0.1 m) using different output level strategies. For a constant output level (Fig. 1, dark blue line), the sound will return to the bat with at least a 40log₁₀(R) (where R is target range in units of the reference distance of 10 cm) loss of sound energy due to 20log₁₀R geometrical spreading of sound in both the outward and return trip from a point target (Fig. 1, grey dashed line). In addition to this geometrical spreading loss, sound energy is also lost by acoustic absorption (i.e. friction between air molecules) (Griffin, 1971); this absorption increases linearly with range and in a more complex way with frequency. For example, in a CF bat species with 68 kHz calls (e.g. Hipposideros armiger), absorption adds 15 dB in transmission loss (TL) to the 59 dB of geometric spreading for a target at 3 m range (Fig. 1, grey shaded area). Thus, if the same bat closes in on a point target while emitting calls of constant SL, the ELs increase by up to 74 dB over an approach from 3 m to 0.1 m, greatly superseding the preferred dynamic range of the hearing system of some 40 dB (Denzinger and Schnitzler, 1998) (Fig. 1, light blue line). Varying target size will further add 20–30 dB to the overall dynamic range of ELs that bats receive over time. Probably to solve this dynamic range problem, bats have been shown to partially adjust both their receiving sensitivity and their output levels as functions of echo delay and therefore target range. Receiving sensitivity is reduced just before each call emission by a contraction of the middle ear muscles – a phenomenon termed ‘automatic gain control’ by a few studies showing an increase in sensitivity following roughly a 6 dB per doubling of range lasting up to 1 m in front of the bat (Hartley, 1992a; Patheiger, 1998).

Output level adjustments in bats have been investigated in several experiments using different methods, recording equipment and species (Koblitz et al., 2011). Most studies have used logarithmic models to describe the lowering of call SLs with decreasing target range, but have reached substantially different conclusions as to whether bats partially (Budenz et al., 2018; Hartley et al., 1989; Saillant et al., 2007; Lewanzik and Goerlitz, 2018) or fully (Hiryu et al., 2007; Kobler et al., 1985; Koblitz et al., 2011; Melcón et al., 2007) compensate for the reduced TL, and/or whether they rely on EL or just echo delay to inform the evoked SL changes (Boonman and Jones, 2002). For bats using frequency-modulated calls (hereafter, ‘FM bats’), such studies have shown that they decrease their output levels by between 4 and 9 dB per halving of range when approaching both mirror targets (Hiryu et al., 2007; Koblitz et al., 2011; Melcón et al., 2007) and point targets (Boonman and Jones, 2002; Hartley, 1992b; Melcón et al., 2007). For CF–FM bats using Doppler-shift compensation, SL reduction towards mirror targets has shown similar reductions in output levels of approximately 6 dB per distance halved (Hiryu et al., 2008; Kobler et al., 1985; Tian and Schnitzler, 1997). Thus, the SL compensation when CF–FM and FM bats approach both mirror and point targets appears to be around 6 dB per distance halved (dB/dh). This results in a roughly constant received EL for mirror targets, but an increase of 3–8 dB per halving of range when approaching point targets (Fig. 1, light blue dotted line). It has been proposed that the combined effect of transmitting and receiving side adjustments renders fairly constant perceived ELs for point targets (Hartley, 1992b). In an extreme version of such a scenario in which the perceived EL is maintained strictly constant, bats would only know something about the size of the ensonified target by keeping track of the call-by-call compensatory changes in SLs and auditory sensitivity. While such rapid feedback is used to adjust call frequency in Doppler-compensating CF bats to gauge prey movements (Schnitzler, 1973), there is little evidence to suggest that bats evoke a similar closed loop feedback on ELs (Budenz et al., 2018). Rather, Budenz and co-workers (2018) have argued that the low output levels emitted when bats are close to objects would perhaps not result in a contraction of the middle ear muscles large enough to affect the sensitivity to the following echoes. Instead, they argue that FM bats use the differences in EL development during target approach to differentiate between point and mirror targets.

Even though many studies of SL adjustments with range interpret their data as evidence for an overall 6 dB/dh or 20log₁₀R reduction, there are often large deviations from these predictions and a substantial spread between studies. This might be ascribed to differences in experimental design (stationary versus free-flying bats, point targets versus mirror targets, simple versus complex echoic scenes, or field versus captive studies), the species chosen (CF versus FM species) as well as a low number of repetitions per animal (typically between 3 and 10 flights). In addition, there may be wide variations in the clutter level in these studies [e.g. from recording equipment directly behind a target (Budenz et al., 2018; Hartley et al., 1989; Saillant et al., 2007) or from nearby structures in the flight room such as walls and ceiling], potentially influencing the energy compensation strategy used by bats.

Given these large variations, it may be speculated that biosonar output dynamics as a function of range are not entirely explained by control models based only on geometric spreading losses (Norum et al., 2012). Most energy compensation studies have used either species that emit low-frequency pulses or an experimental setup with short operating distances. In both situations, acoustic absorption has often been neglected as the effect is fairly small under these circumstances. However, for species using vocalizations with higher frequency, e.g. 68 kHz in Fig. 1, differences in absorption at longer versus shorter ranges will lead to developments in ELs during target approaches that cannot be compensated for by adjusting the SL in an xlog₁₀R fashion (Fig. 1, light blue and green lines).

Thus, the call frequency of the species in question and the experimental setup are predicted to have an effect on the relationship between output levels and range, and hence on the echo energy available to the animals. This will affect how we understand the bats' adjustments of their emitted energy and therefore how they may organize echo information perceptually. In this study, we sought to understand how CF bats that are subject to significant acoustic absorption perform range-dependent adjustments in call output for different target sizes. Specifically, we hypothesized that as a result of absorption, these bats would delay the onset of SL adjustment so as to increase the possibility of detecting echoes at long ranges, but would then reduce call output levels with decreasing range by more than what has been measured in lower-frequency species under similar experimental settings. We further hypothesized that bats would not compensate their output levels for target size and so would receive useful information on target movement and size based on relative changes in ELs.

We tested these hypotheses by conducting a target approach experiment using two CF species, the great roundleaf bat (Hipposideros armiger) and Pratt's roundleaf bat (Hipposideros pratti), approaching four different target sizes. We show that such CF bats using higher frequency vocalizations do not use a logarithmic decrease in output levels with range. Instead, they maintain the returning ELs within a dynamic range of around 34 dB by emitting calls with a nearly constant output level at long distances and dramatically decreasing their output levels close to the target.

This work was carried out under Institutional Animal Care and Use Committee Permit No. 15-067. Two Hipposideros pratti Thomas 1891 (73 and 93 g) and one Hipposideros armiger (Hodgson 1835) (63 g) were used for the study. The bats were trained to fly diagonally across a flight room (4×3.5×3.5 m; Shandong University, China) and land on target spheres of different sizes. Four plastic spheres (diameter: 0.30, 0.20, 0.12, 0.07 m; TS: −3, −6, −10, −15 dB) were wrapped with thin cloth to facilitate landing and placed in a corner of the flight room at 2 m height. A star-shaped array of six Knowles microphones (FG-3329, 2.6 mm diameter) spaced at 0.25 and 0.5 m were placed behind the target spheres and completely embedded in 30 cm deep pyramidal acoustic foam (Fig. 2). The surfaces of the room were covered with 5 cm deep acoustic foam and the room was kept dark during the experiments except for dim computer light used for running the set-up and for handling of the bats (Fig. 2).

The six Knowles microphones were connected through a custom-built 30 dB amplifier and filter box (a 1-pole 1 kHz high-pass filter and a 4-pole 100 kHz anti-alias filter) to an A/D converter (USB-6356, National Instruments, Houston, TX, USA) and sampled synchronously at a rate of 250 kHz per channel, with 16-bit resolution and with a clipping level of 106 dB re. 20 µPa pk. The echolocation calls were recorded by the array when manually triggered, and stored in 5 s files for each landing. An archival sound recording tag (Stidsholt et al., 2018) was attached to the back of the bats with Velcro and glue (Ökonorm Pro) during trials to continuously record the echolocation pulses and echoes. The tag measured 14×33×6 mm and weighed 2.6 g. The tag audio data were recorded at a sampling rate of 187.5 kHz, with 16 bit resolution and a clipping level of 121 dB re. 20 µPa pk. The tag included a 10 kHz 1-pole high-pass filter and an 80 kHz 4-pole anti-aliasing filter. The frequency responses of the Knowles microphones (FG-3329) both in the array and on the tag were corrected prior to analysis by convolving the recorded signals with the predetermined impulse response of the recording system (Stidsholt et al., 2018).

Each bat was instrumented with the tag for approximately 4 h in total over four experimental days (maximum duration of 60 min per session). As the tag weighed 2.6 g, the loading did not exceed 5% of the mass of any of the bats (63–93 g). The tag did not appear to adversely influence the flight performance over the short flight paths studied here and the bats were carefully observed during the flights for any sign of fatigue. The three bats completed between 20 and 45 landings on each target (354 flights analysed; Table 1). Because of the time required to change targets, a single target size was used per day. When a bat landed on a target, a synchronization sound unique for each trial (400 ms and frequency content between 1 and 8 kHz) was emitted by a small speaker embedded in the array. This sound was recorded on both the array and the tag, thus facilitating synchronization. The emission of the synchronization sound also served as a bridge signal, indicating a successful trial, and the bat was subsequently fed a mealworm.

The tag and array data were synchronized within an error of a few milliseconds by cross-correlating with the unique synchronization sound recorded on both the array and tag for each trial. All calls were automatically detected by a custom-written call detector. Only the second and strongest harmonic of the calls and echoes were extracted for analysis by digitally filtering the data with an 8-pole band-pass Butterworth filter with low-frequency cut off at 50 kHz and 47 kHz, and high-frequency cut off at 70 kHz and 65 kHz, respectively, for H. armiger and H. pratti.

The location of the bat was determined by acoustic localization using time of arrival differences between the array microphones for each recorded call. Time of arrival differences were found by cross-correlating the downward FM sweep of each call. A simplex minimization algorithm (Macaulay et al., 2017; Nelder and Mead, 1965) was used to estimate the location of the bat based on the time delays between calls. A Kalman filter was used to smooth the location estimates across successive calls. The received levels (RLs) at each microphone were calculated and calls with RL 10 dB above the noise floor were chosen for further analysis. The in-band noise floor of the array was 25 dB re. 20 µPa RMS for H. armiger and 24 dB re. 20 µPa for H. pratti. To back-calculate the RL to a SL at 0.1 m, TL was compensated for by assuming spherical spreading loss, i.e. 20log₁₀R, plus a frequency-dependent absorption loss (sensu Jakobsen et al., 2012). The localization and SL estimates were validated by transmitting a broad-band sweep from an Avisoft ultrasonic dynamic speaker (frequency range: 5–120 kHz; sensitivity: −83 dB re. 1 V/20 μPa at 1 m) at distances from 0.5, 1, 2 and 3 m perpendicular to the array and the target. SLs were calculated as energy flux density (EFD), i.e. acoustic energy per unit area, expressed in dB re. 20 µPa² s. The RMS SL, expressed in dB re. 20 µPa² was also calculated for comparison with previous studies. Both EFD and RMS were measured over the −6 dB window of the envelope of each call.

To identify calls where the acoustic beam axis was directed towards the target, calls were only extracted for further analysis if their RLs were highest on any of the three microphones closest to the target.

We extracted echo information from the tag when the bat was within 0.6–1.5 m of the target. At shorter distances, the target echoes overlapped with the emitted call, and at greater distances, the target echoes were masked by echoes from the walls, as verified by visual inspection of call–echo spectrograms and echograms (Stidsholt et al., 2018).

To determine target echo energy, each call–echo pair was separated in time based on the FM downward sweep from the call applied as a matched filter to find the end of the call and the end of the echo. Target echoes with less than 10 dB in-band signal-to-noise ratio were rejected to ensure accurate energy measurement. The in-band noise floor of the tag was predetermined to be 4 dB re. 20 µPa RMS (H. armiger) and 2 dB re. 20 µPa RMS (H. pratti). As the calls in the array and tag recordings were synchronized, the target range could be calculated for each call–echo pair detected on the tag. Thus, for each call, we measured the SL (from the array), the EL (on the tag) and the range to the target (by acoustic localization). SL results for each session were fitted to the logarithm of range, R. To test the hypothesis that bats do not adjust SL in a fixed logarithmic manner throughout target approaches, we fitted xlog10R curves in logarithmically spaced bins (0.6–1, 1–1.6, 1.6–2.5 and 2.5–4 m). If our hypothesis is true and dissimilar slopes occur between the bins, we expect to find the highest slopes when the bat is closest to its target because the ELs rise faster close to the target.

The ELs received by the bat were predicted using the sonar equation based on target range (R), call SL and calculated TS of the spheres (Urick, 1983) and compared with the measured EL recorded by the tag for the largest target. TS of the spheres was not measured by ensonification, but calculated from the equation provided by Urick (1983).

All analyses were performed with custom scripts in Matlab 2018a.

To investigate how SL is reduced during the last 2 m of target approaches, the SLs were first fitted to target range, by linear fit of SL (measured in EFD and RMS) to log₁₀R. xlog₁₀R slopes were estimated for each individual for each target size for comparison with previous studies. Next, all SLs (EFD) were modelled using a generalized linear mixed-effects model (GLME, Matlab function: ‘fitglme’) using log₁₀R and target size as fixed effects and bat ID and individual flight trials as random effects (Table 2). The residuals of the full model were plotted and visually inspected for signs of non-normality and heteroscedasticity.

To investigate whether the bats adjusted SL according to the size of different targets, a three-way ANOVA (Matlab function: ‘anovan’) was performed to test for any changes between the measured ELs from the different targets. Here, we used target size, bat ID and range as explanatory variables and used ELs received between 0.6 and 1.5 m distance to avoid overlap with masking echoes. A model comparison (Matlab function: ‘multcompare’) between the output from the two-way ANOVA was used to determine significant differences between ELs for different target sizes and individual bats.

All SL (both EFD and RMS) and EL measurements were normally distributed (Anderson–Darling test, Matlab function: ‘adtest’).

We recorded the vocalizations and echo returns of three hipposiderid bats approaching targets of four different sizes. For comparison with previous studies, we first fitted SLs to logarithmic curves over the last 2 m of the approaches (Fig. 3, Table 1). When approaching the targets, all bats decreased the SL (Fig. 3D) and duration (Fig. 3C) of their vocalizations. In the last 2 m before landing, the three bats showed energy compensation of 5–11 dB per distance halved with an average of 9 dB per distance halved (29log₁₀R; Table 1) but with considerable variation (16–41log₁₀R; Table 1). Absorption over this 2 m interval did not cause a strong deviation from a logarithmic model. Thus, to test whether there was a non-logarithmic SL adjustment consistent with the greater absorption at longer ranges, we performed fits of measured SL within logarithmically spaced bins from 0.6 to 4 m. The rate of energy compensation increased as the bats approached the targets from approximately 0–20log₁₀R at 2–4 m to approximately 40log₁₀R close to the target, but with large individual differences (Fig. 5).

If bats adjust their SL so as to stabilize ELs, they risk losing information about target size. To test whether EL varied with target size, the ELs from each on-axis call were extracted from the tag recordings (Fig. 4) in the overlap-free zone between 0.6 and 1.5 m distance (Fig. 6). Because of the length of the calls, echoes were masked by the bats' own vocalizations at target ranges closer than 0.6 m, while at distances further than 1.5 m, the echoes were embedded in clutter even though the flight room was covered in acoustic foam (Fig. 6). EL predictions based on the sonar equation using SL, range and TS agreed well with the actual ELs recorded by the tag for the largest target (Fig. 4). The calculated ELs were therefore used for further analysis to avoid interference and clutter and to allow the same method to be used for all targets. The calculated ELs were overall between 0 and 40 dB re. 20 µPa² s (Fig. 7; 95% distribution of ELs between 7 and 36 dB re. 20 µPa² s), but varied widely with individual and target size (95% distribution of ELs for each individual: 11–34, 6–29 and 6–40 dB re. 20 µPa² s). A two-way ANOVA using bat ID and target size as explanatory variables revealed that ELs differed significantly for each bat [F=183, P<0.0001, population means of 19 and 22 dB re. 20 µPa² s (H. pratti) and 25 dB re. 20 µPa² s (H. armiger)]. Target size was also a significant explanatory variable (F=120, P<0.0001). The four targets (30, 20, 12, 7 cm) reflected mean ELs of 22, 26, 25 and 20 dB re. 20 µPa² s, respectively.

Bats actively control the echo information available to them during navigation and prey acquisition by changing the time and frequency pattern of their calls to match the task at hand (Griffin et al., 1960). As part of this dynamic control over echo information, they have been reported to reduce their output levels logarithmically as they approach targets, presumably to maintain ELs in a dynamic range suited for their hearing system and to reduce forward masking of the echoes received milliseconds after emission of calls (Hartley, 1992b; Koblitz et al., 2011). This transmission-level control is joined by a receiving sensitivity control in which the hearing threshold is gradually increased during target approach by contraction of the stapedial muscles. In concert, these two mechanisms have been proposed to render stable perceived ELs for FM bats (Hartley, 1992b) by compensating for the decreasing TL as bats approach targets. However, the TL is the sum of a geometric spreading component which is logarithmic with range and an absorption component that is linear with range (Fig. 2). The contribution of absorption is minor for bats using low frequencies, but the effect is substantial for species such as the hipposiderid bats studied here (Fig. 3A,B). With the inherent limitations of the low sample size in this study, we sought to understand how bats facing high absorption adjust their sonar emissions during active approaches to point targets. We hypothesized that because of the increasing effect of absorption at greater distances, CF bats using higher frequency vocalizations would adjust their SLs less at large distances to ensure a sufficiently high echo-to-noise ratio (ENR), and more at shorter distances where the absorption is less significant.

Previous target approach studies of some species of CF bats have shown that they reduce SLs logarithmically with target range by between 6 and 9 dB per distance halved when approaching large targets (Hiryu et al., 2008; Kobler et al., 1985; Tian and Schnitzler, 1997) and on average 6 dB per distance halved when approaching a meal worm close to the ground (Hartley et al., 1989). Mantani and co-workers (2012) recorded the reduction in the intensity of vocalizations of Rhinolophus ferrumequinum nippon catching fluttering moths using a telemike. A reduction of 35 dB was found during an approach spanning 2.5 s. However, the range to the target and absolute on-axis SL were not measured in that study. Here, we show that three individuals from two species of CF bats (H. armiger and H. pratti) reduce both call duration (Fig. 3C) and SL (Figs 3D and 4) when approaching target spheres. The CF bats used in this study on average halved the duration of their emitted signals during the approach (Fig. 3). For the same amplitude, a halving of the pulse length will result in the same peak–peak and RMS levels for the two pulse lengths. In contrast, the energy level (EL) would decrease by 3 dB, which explains the slightly larger values of EFD adjustment compared with RMS (Table 1). The difference in SL adjustment estimates using RMS pressure versus energy will be larger for some FM species in which call duration may change by an order of magnitude during approach, leading to a 10 dB reduction in energy (but not RMS) from just the change in duration. This assumes that bats are using all the available energy in their calls even if the duration of these exceeds the integration time (Surlykke and Bojesen, 1996). The integration time has been measured in only a few studies, with values of 200–400 µs (Simmons et al., 1989; Wiegrebe and Schmidt, 1996), 2.4 ms (Surlykke and Bojesen, 1996) and 60 ms (Schmidt and Thaller, 1994) for FM bats, suggesting an adaptable integration time matched to the task (Surlykke et al., 2016). To our knowledge, integration time has not been measured in either Hipposideros armiger or H. pratti. However, as these bats exert an impressive dynamic control of the duration of their calls in relation to different tasks, it appears parsimonious to assume a dynamic integration time in keeping with those changes in call duration and hence report levels in energy.

For the bats studied here, the SL reduction resulted in an energy compensation between 5 and 11 dB/dh during the last 2 m before landing (Table 1) with an average of 9 dB/dh, when computed from the RMS. The rates are slightly higher for SL calculated in energy rather than RMS (Table 1), but the effect is most pronounced for the xlog₁₀R values (Table 1). We further show that the energy reduction rate was not constant during the approach (Fig. 5). At more than 2.5 m target range, the bats on average adjusted their SL little to changing range. As the bats closed in on the target, the energy compensation gradually increased to on average around 40log₁₀R at close distances, but with large variations (Fig. 5). These results are consistent with data from eight FM species (Artibeus jamaicensis, Macrophyllum macrophyllum, Myotis daubentonii, Phyllostomus hastatus, Phyllonycteris poeyi, Saccopteryx bilineata, Saccopteryx leptura and Rhynchonycteris naso) showing variable reduction rates far above the established 20log₁₀R relationship with a maximum of 99log₁₀R in one extreme case (i.e. 30 dB/dh), spanning both laboratory settings and in the wild (Jakobsen et al., 2015; Norum et al., 2012). However, the reported reduction rates vary widely between studies from 3 to 99log₁₀R, leading us to posit that logarithmic fitting of SL to target range is not biologically relevant, as also suggested by Norum and colleagues (2012). In contrast to exponential fitting suggested by these authors, we argue that the search for a general control law for SL operable over all target ranges may mask the finer details of how bats adjust their transmitting energy.

Instead, we propose for long target ranges that these bats produce high-intensity calls with little range adjustment to match the high absorption at greater ranges to improve poor ENRs after initial detection. This notion is supported by a weak mean EL of 2 dB re. 20 µPa² s (23 dB re. 20 µPa RMS for a 7 ms echo) for all targets at a distance between 3 and 4 m. This must be assumed to be close to the hearing threshold of bats (Stilz and Schnitzler, 2012), which supports the hypothesis that absorption is an important limiting factor for these species at greater ranges. In contrast, at closer ranges, the relative effect of absorption on the total TL is much lower, which in concert with a greatly reduced geometric spreading loss means that the increase in EL of a point target during a decrease of bat–target range will increase rapidly if no SL adjustment is used. Thus, these bats are reducing their outgoing call levels a lot at close ranges, resulting in received ELs of all targets in a dynamic range between 6 and 40 dB re. 20 µPa² s (Fig. 7).

We initially hypothesized that target size would not affect the output adjustments, meaning that the relative EL differences between targets would correspond to the differences in the actual TS. The four targets (largest to smallest TS: −3, −6, −10, −15 dB) resulted in mean ELs of 22, 26, 25 and 20 dB re. 20 µPa² s, but with large variation. As the differences in mean received ELs are smaller than the relative differences in TS between the spheres and do not even vary monotonically with the TS, the bats must have been partially adjusting for target size, but not in a 1 dB:1 dB fashion. As the largest target did not result in the largest mean EL (22 dB re. 20 µPa² s), estimation of target size by the bats is apparently not informed solely by relative differences in EL distribution between targets during approaches, but rather perhaps by the relationship between the loudness of the outgoing call and the EL for a given echo delay (Denzinger and Schnitzler, 1998). Alternatively, bats might use only the first few call–echo pairs after detection to estimate the size of the target rather than the entire EL distribution of approach calls. Either way, it means that the studied bats do not seek to stabilize perceived ELs. When bats approach targets, they can also use other cues to distinguish the targets, e.g. the angular range in which the echoes return (Heinrich and Wiegrebe, 2013). It may also be that the bats were adjusting SL more steeply in the approach as the target size increases. This notion is supported by the literature showing that bats decrease their output levels at a distance of 2 m before landing on platforms and walls representing large targets (Kobler et al., 1985; Koblitz et al., 2011), whereas smaller target interceptions cause a delayed reduction beginning within the last 1 m of approach (Boonman and Jones, 2002; Hartley, 1992b; Melcón et al., 2007; Saillant et al., 2007). Hence, it seems as if these CF bats defend a fairly narrow received EL dynamic range for all target sizes, which span 6–40 dB re. 20 µPa² s, matching the preferred dynamic range of some 40 dB of non-echolocating mammals, such as humans for speech (Rhebergen et al., 2009). The dynamics of the perceived EL would be further narrowed if the stapedial reflex affects the sensitivity to echoes received just after sound emission, as seen for FM bats (Hartley, 1992b). But, there is no clear evidence of a stapedial reflex affecting perceived echo intensities in CF bats, perhaps because of the Doppler-induced spectral decoupling between outgoing calls and returning echoes by which outgoing calls and incoming echoes will excite different populations of auditory neurons given the sharp tuning curves of CF bats (Tian and Schnitzler, 1997).

Thus, while CF bats use a tight closed-loop echo feedback to provide spectral Doppler compensation, they do not show a closed-loop energy compensation even when they approach a point target. What then guides the onset of the energy compensation? This is an important question not only to help understand the way bats perceive their environment but also because SL adjustment is widely interpreted as marking the beginning of the acoustical approach phase (Griffin et al., 1960).

Previous studies have suggested that the transition into approach phase is guided by target detection (Griffin et al., 1960; Kalko and Schnitzler, 1989) or by a target EL threshold (Budenz et al., 2018). Budenz and co-workers (2018) proposed that the onset of energy reduction was triggered by a certain target EL, which in their study was around 41–42 dB re. 20 µPa² RMS (duration: ∼2 ms resulting in 15 dB re. 20 µPa² s) for Myotis myotis under cluttered conditions. Our bats performed energy compensation in response to echoes below this threshold in 13% of the calls emitted between 0.6 and 1.5 m ranges, which means that for CF bats this is not a valid threshold even under semi-cluttered conditions (Fig. 6). As the mean calculated ELs between 3 and 4 m were around 2 dB re. 20 µPa² s (or 23 dB re. 20 µPa² RMS for a call duration of 7 ms), which is slightly above the estimated hearing threshold of 20 dB re. 20 µPa² RMS (Stilz and Schnitzler, 2012), we argue that bats should just be able to detect the spheres at take-off and during their first few metres of flight, where they do not yet adjust, probably to maximize ENR. Thus, the onset of SL and inter-call interval adjustment to a target is probably not triggered by target detection, or by a specific EL, as the ELs around the time of adjustment vary over a 20 dB range. Our data therefore support the notion that acoustically and behaviourally defined approach phases may differ and that the detection distance cannot be reliably inferred from the acoustically defined approach phase (Boonman and Jones, 2002).

In conclusion, we found that three individuals of two species of Hipposideros reduce their emitted energy during target approach in a non-logarithmic fashion to maximize ENR at long ranges and to avoid high ELs when close to the targets. The effect of this adjustment is that target echoes are maintained in a dynamic range from 6 to 40 dB re. 20 µPa² s over the target distance, which gives non-overlapping target echoes. As the energy compensation is loosely controlled in contrast to the extremely well-regulated spectral Doppler-shift compensation, we posit that the energy compensation should not be seen as an automatic gain control but rather as a dynamic range compression strategy. This may be operated as a hysteretic control whereby bats reduce their emitted intensity gradually when the EL in a sequence of calls increases progressively closer to the presumed upper limit of the comfort zone of the receiving sonar system of approximately 40 dB re. 20 µPa² s (∼60 dB re. 20 µPa RMS for these calls). For species affected by high sound attenuation, and limited at long ranges by a maximum call energy, the rise in EL would begin closer to the target during active approaches compared with that for lower-frequency species for the same output level. Thus, we predict that CF bat species using even higher frequency (e.g. 100–200 kHz; Heller and Helversen, 1989) will start reducing biosonar output (and therefore transition into the acoustically defined approach phase) closer to a target in comparison to a low-frequency species performing the same task and using the same initial output level. To study further how bats perceive the auditory sensory stream from a target, it will be necessary to measure the integration time(s) in CF bats, to understand how the hearing sensitivity changes with varying SL, range and species, and to address how the energy compensation is modulated during capture of moving prey in the wild with natural masking noises and higher SLs.

Yanan Zhao kindly assisted during data collection, and N. U. Kristiansen and J. Svane constructed the recording array. We thank Jamie MacAulay for help with localization routines as well as Michael Ladegaard and two reviewers for helpful feedback of the manuscript.