A spectral jamming avoidance response does not help bats deal with jamming

For decades, researchers have speculated how echolocating bats deal with acoustic interference created by conspecifics when flying in aggregations. It is thus surprising that there has been no attempt to quantify what are the chances of being jammed, or how such jamming would affect a bat’s hunting. To test this, we developed a computer model, simulating numerous bats foraging in proximity. We used a comprehensive sensorimotor model of a hunting bat, taking into consideration the physics of sound propagation and bats’ hearing physiology. We analyzed the instantaneous acoustic signals received by each bat, and were able to tease apart the effects of acoustic interference and of direct resource competition. Specifically, we examined the effectiveness of the spectral Jamming Avoidance Response - a shift in signal frequencies - which has been suggested as a solution for the jamming problem. As expected, we found that hunting performance deteriorates when bats forage near conspecific. However, applying a Jamming Avoidance Response did not improve hunting, and our simulations clearly demonstrate the reason: bats have adequate natural signal variability due to their constant adjustment of echolocation signals to the task. The probability to be jammed is thus small and further shifting the frequencies does not mitigate spectral jamming. Our simulations reveal both negative and positive insight: they show how bats can hunt successfully in a group despite potential sensory interference and they suggest that a Jamming Avoidance Response is not useful.


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Echolocation, a prime example of active sensing, provides bats with the ability to detect and 26 hunt flying insects while avoiding obstacles in total darkness 1 . Echolocating bats emit high-27 frequency sound-signals and process the reflected echoes to sense their surroundings. While 28 hunting in a group, conspecific bats emitting signals with similar frequencies may interfere 29 with the ability of nearby bats to detect and process their own echoes. Understanding how 30 bats avoid this interference, which is referred to as 'jamming' or 'masking', and how they 31 segregate the desired weak echoes from the much louder calls emitted by other bats is one 32 of the most central debates in the field. We define a 'masking signal' as any signal that may 33 interfere with the bat's ability to detect and localize an echo, and a 'jamming signal' as a signal 34 that completely blocks the detection of an echo (see Methods). 35 The question of how bats deal with conspecific masking and whether they perform a spectral 36 Jamming Avoidance Response (JAR) has been widely studied but is still under dispute. Many 37 studies have suggested that bats change their echolocation frequencies when hunting the 38 presence of other bats 2-5 or when exposed to playback partially or fully overlapping signals 6-9 39 2-8, 10,11 . Particularly, in this study, we only deal with spectral JAR (which we will term JAR). In 40 contrast, several recent field-studies and laboratory experiments found no evidence for a use 41 of spectral JAR by bats [12][13][14] . 42 The main goal of our study is to use a mathematical approach in order to deepen the 43 understanding of the masking problem and its impact on bats' hunting, and specifically to 44 examine whether an intentional shift of signal frequencies (i.e., a spectral JAR) can assist bats 45 to mitigate the masking problem. We developed an integrated sensorimotor model of bats 46 pursuing prey. The modeling approach entails several advantages in comparison to studies 47 with real bats. (1) It allows us to assess the exact acoustic input received by each of the hunting 48 bats at every instance. This is currently impossible to do in reality even when a microphone is 49 placed on the bat. (2) Modeling enables manipulation of different parameters and examining 50 their influence on masking including testing hypothetical scenarios that tease apart factors 51 that are coupled in reality. 52 We analyzed the effect of masking under various prey and bat densities and when using 53 different echolocation behaviors. We measured the probability of jamming, the hunting 54 performance and we explicitly examined whether applying a spectral JAR improves hunting 55 performance when hunting with conspecifics. We were able to discriminate between the 56 effect of direct interference resulting from the need to avoid conspecifics and to compete with 57 them over prey, and the effect of sensory masking due to conspecific calling. We show that 58 shifting the emission frequencies (i.e., a JAR) does not assist mitigating masking because bats' 59 signals already differ from each other due to their well-known behavior of adjusting their 60 signals based on the task and the environment. 61

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The model consists of numerous bats searching for and attacking prey in a confined 2D area 63 using echolocation. Each simulated bat transmits sound signals and receives the echoes 64 returning from prey items, as well as the signals emitted by conspecifics, which might mask or 65 jam its own echoes. The prey's movement mimics a moth 21,22 with no ability to hear the bats. 66 Prey echoes are detected and localized based on biological-relevant assumptions which 67 consider sound reflection and propagation, and hearing physiology (see Methods). Based on 68 the incoming acoustic information, the bat decides whether to continue searching, to pursue 69 prey or to avoid obstacles such as other bats. It then adjusts its echolocation and movement 70 according to the vast literature on bat echolocation 1,23 , and the recently published control 71 models of bat flight and hunting 15, 16,[24][25][26][27][28] . For example, the simulated bats emit search signals 72 with a power of 110 dB-SPL (at 0.1m) and they lower their power (and adjust other 73 echolocation parameters) when approaching prey. A successful hunt (i.e. a capture) occurs 74 only when the simulated bat gets within 5cm from the prey. That is, the bats sometimes 75 initiate attacks but miss. 76 We first demonstrate that our simulations behave similarly to bats. The simulated bats 77 managed to detect, pursue and capture prey at high rates both when hunting alone and when 78 hunting in a group (see Figure 1 and Movie S1 for examples of hunting by simulated bats). The 79 movement parameters of the bats in both single and multiple individual scenarios were similar 80 to those of actual bats, suggesting that our model managed to capture the essence of the 81 foraging movement (Fig S 1). 82 83 84 (3) ( (4) panels B1-4. All colors and symbols in B1-4 are the same as in A1-4. Magenta lines depict 98 trajectories of conspecifics. In panel B4 we depict one signal for each bat, illustrating the 99 variations between the signals due to the different behavioral phases of each bat. Note that 100 bat 2 also detects the same prey item and pursues it and thus its signals are 'approach' signals. 101 From detection to capture, bat 1 emitted 64 echolocation signals, 8 of which were jammed. 102 The influence of a spectral JAR: we next compared the detection and localization performance 103 of bats applying a JAR to bats that do not actively react to masking signals. In both groups, 104 the frequencies of the individuals were sampled from a normal distribution with a standard 105 deviation of 4 kHz, as observed in nature 15, 16,29 , and they adjusted their signals according to 106 their task and their distance to object. In some simulations, the bats applied a JAR, namely, 107 whenever their signals were jammed -they shifted their terminal frequency away from the 108 jamming signal in steps of 2kHz and they kept shifting the frequency as long as masking occurs 109 (the signal was shifted either upward or downward in the opposite direction of the jamming 110 frequency, Methods). The entire frequency range of the signals was shifted upward or 111 downward. We tested two different receiver models with different assumptions: 1) the 112 'correlation-detector' which is an optimal receiver and is at least slightly better than the bat's 113 brain 30-35 ; (2) the 'filter-bank receiver' which is considered to represent the mammalian 114 auditory physiology and implements a series of gammatone band-pass filters 34,36-39 (see 115 Methods). 116 The main function of a spectral JAR should be to improve detection by decreasing the overlap 117 between the spectra of the masking signal and the echo. We, therefore, start with examining 118 whether a JAR under different conditions (e.g., different receiver models and different bat 119 densities) achieves this goal. To quantify this, we used four detection-criteria (see Methods): 120 (1) The jamming-probability is defined as the probability that the echo reflected from the 121 closest prey item is totally jammed by a masking signal and is thus not detected. (2) The SNR 122 (Signal to Noise and interference Ratio) is defined as the ratio between the peak intensity of 123 the detected echo, and the peak intensity of all masking signals. (3) The ranging error is the 124 difference between the estimated and the actual distance to prey. (4) The false-alarm rate is 125 the probability of identifying a masking signal as prey by mistake. 126 In all scenarios, and for the two different receiver models, the jamming avoidance response 127 did not decrease spectral masking (see Fig S 2), and did not improve detection performance 128 according to any of the four criteria defined above. See Figure 2 A possible explanation for this seemingly surprising result is the fact that a bat's signals 133 continuously vary depending on its behavioral phase and its distance to the targets. Therefore, 134 at any instance, the signals of two bats will already differ, even if their signal repertoire is 135 identical. Therefore, the influence of additional variability between the signals, achieved by 136 spectral JAR, is insignificant, see Fig S 2. 137 Figure 2: Applying a JAR does not improve detection. Panels A-D depict four detection criteria 138 as a function of bat density for a correlation-receiver (solid black), and a filter-bank receiver 139 (solid blue) with and without a JAR (dashed gray and dashed turquoise respectively). The prey 140 density was constant with 20 prey items per 100m 2 . Error-bars depict standard-errors in all 141 panels. Each data point represents 60-80 simulated bats. (A) Jamming Probability. (B) SNR-142 The SNR is the Signal to Interference Ratio, measured on all detected prey items. (C) Range 143 errors. Note that the range-errors are high because they are calculated for all detected prey. 144 The errors for the pursued prey (i.e. prey items that bats attacked) are substantially lower, 145 since, as the bats approach their targets echoes have higher SNR and the errors decrease. (D) 146 False-alarm rate, which is measured only for the filter-bank model. 147 The effect of masking on hunting: next, we tested the effect of masking on hunting 148 performance (i.e., the prey capture rate) under different scenarios. We started with a 149 hypothetical scenario ('no-masking'), in which bats forage in a group without any masking, i.e. 150 they detect and pursue prey regardless of any sensory interference, but they still have to avoid 151 other bats and sometimes lose prey due to competition. This null-hypothesis scenario enabled 152 us to estimate the non-sensory effects of group hunting, which would be very difficult to do 153 in an experiment with real bats. Ultimately, it allowed us to isolate the effect of sensory 154 interference only. Hunting performance was measured in different bat-densities (from 1 to 20 155 bats per 100m 2 ) and different prey densities (3, 10, 20 moths per 100m 2 ), see Figure 3. 156 Even without any sensory interference (i.e., in the 'no-masking' condition), hunting 157 performance significantly degraded as bat density increased due to competition over prey and 158 due to the need to avoid conspecifics (Figure 3A-C; see Green lines). The reduction in 159 performance was significant in all prey densities and resulted in a maximum decrease of 36%, 160 57% and 67% in performance when the bats' density increased (from 1 to 20) at three prey 161 To deepen our understanding of why a JAR does not improve performance, we analyzed the 178 jamming-probability in different behavioral phases. We found that jamming mostly occurred 179 during the search phase while, as the bats shifted from the search to the approach phase, the 180 probability of jamming decreased significantly because the prey's echoes become louder 181 ( Figure 3 A3-B3-C3, ANCOVA, for the comparison between search and approach at any bat 182 and prey density: F1, 8527 =2784, p<0.0001, panels B3-C3 show that less than 15% of the prey 183 echoes are jammed during the approach phase). Notably, if a potential prey echo is jammed 184 in the search-phase, the bat is likely to detect the prey with one of its following emissions, so 185 jamming during the search phase is less detrimental for foraging. The low probability of 186 jamming during the approach is probably the main reason for the relatively small effect of 187 sensory masking on performance. 188 We also analyzed the causes of unsuccessful attacks when bats initiated an attack but failed 189 to capture prey. There were four reasons for failed attacks: avoiding a nearby conspecific, 190 losing the prey to a conspecific, avoiding an obstacle (the borders of the arena) and missing 191 the prey due to an insufficient maneuver or due to sensory error (resulting for example from 192 jamming). We analyzed the proportion of these different sources of failure with and without 193 sensory masking (see Fig S4 ). With 20 bats and 10 prey items per 100m 2 , without masking, 194 34%±2% of the capture attempts were successful (mean±SE). The unsuccessful attempts were 195 due to conspecifics avoidance: 27%±2%; lost prey to conspecifics: 17%±1.5%; obstacle 196 avoidance: 7%±2% and misses: 15%±2%. When sensory masking was added, the proportion 197 of successful captures significantly decreased to 26%±2% (One-way ANOVA, F1, 198=4.59, 198 p=0.033), and misses became the most substantial cause for failure, significantly increasing to 199 38%±3.5% (One-way ANOVA: F1, 198=68  items. Line colors and styles depict the performance of different receiver models: green -no-206 masking; solid black -correlation-detector with random signal variability; dashed dark gray -207 correlation-detector with JAR response; dash-sotted light gray -correlation-detector without 208 signal variability. Panels (A1-C1) depict the performance as a function of bat density; a green 209 circle shows the performance of a single bat. The regression slopes of no masking condition 210 (green lines) are (mean± SD): 0.06± 0.0065 0.08± 0.0084, 0.079± 0.013 captures per bat per 211 ten seconds, at the prey densities above, respectively (ANCOVA: F1, 564 = 84.3, p<0.0001; F1, 679 212 = 90.4, p<0.0001; F1, 431 = 37.8, p<0.0001). There was no significant difference in performance 213 when applying or not applying spectral JAR -see main text and compare gray and black lines.
214 Panels (A2-C2) show the masking-effect on hunting, i.e., the relative decrease in hunting 215 relative to the 'no-masking' condition. (A3-C3) The probability of jamming at different 216 behavioral phases: search (turquoise marker), approach (magenta marker) and buzz (red 217 markers). Jamming probabilities during the search were significantly lower by at most 4.5% 218 when using a JAR (ANCOVA, F1, 2422=23.42, p<0.0001). However, in the approach and buzz 219 phases (which are more critical for foraging), there was no significant difference between the 220 two models (ANCOVA, F1,2388=0.11, p=0.74; F1, 2347 = 0.11, p=0.73, respectively). Error-bars 221 show means and standard-errors for 70-120 simulated bats in each data-point. 222 The effect of prey density on group hunting: Finding and catching prey is easier when prey is 223 abundant, and as excepted, the hunting rate significantly increased as a function of prey 224 density in all bat densities see Figure 4A. The regression slopes for the correlation-detector 225 indicates an improvement of 0.09±0.001, 0.011±0.001, 0.086±0.001, 0.08±0.001 captures per 226 additional prey item per 10 seconds, for 1, 5, 10 and 20 bats per 100 m 2 , respectively; mean± 227 SD are reported. The masking effect did not change significantly as a function of prey density, 228 see Figure 4B, Pearson Regression: F2, 48 = 1.2, p=0.28. Assuming that a bat arriving at a 229 foraging site can roughly estimate the density of prey and the density of bats in the area, we 230 examined how the ratio of these two densities affects performance. Hunting performance 231 drops rapidly with an increase in the bat to prey density ratio, but that it levels out once the 232 bat to prey ratio increases above '1'. In general, the same pattern was observed for different 233 bat densities ( Figure 4C), but for a given bat to prey ratio, the performance was better when 234 there were more bats (and more prey). The improvement in performance as a function of bat 235 density, when the bat-to-prey ratio was below 1, was significant in scenarios with masking 236 ( The effect of the echolocation signal design and the detection threshold on hunting in a 251 group: after observing that spectral changes do not assist mitigating jamming, we tested 252 whether other adjustments to echolocation or physiological parameters could improve bats' 253 performance when hunting in a group. We tested the effect of two prominent signal 254 parameters: power and duration, and we also examined the influence of the detection 255 threshold, which is a function of the auditory system (for all parameters, we used a range of 256 values suggested in the bat literature). For each of these parameters, we first examined its 257 effect on the overall hunting success when foraging in a group (i.e., including both direct 258 competition and sensory interference), and we then examined the parameter's effect 259 specifically on the masking. 260 Increasing the signal's power improved hunting performance, but only up to power of ca. 110-261 120 dB-SPL, (at 0.1m) above which the improvement was negligible and insignificant (Figure 262 5 A1, shows that performance increased significantly when signal power increased from 90 to 263 110 dB: ANCOVA, slope=0.06 captures/dB, F4, 3815=386, p<0.001; performance did not change 264 when signal power increased from 120 to 150dB: F4, 4795=0.1, p=0.98). Interestingly, the power 265 of the signal had no effect on the masking effect (i.e., the reduction in performance beyond 266 the no-masking condition), suggesting that increasing the emission power assists hunting in 267 general (through increasing the detection range) and does not assist overcoming the masking 268 problem specifically ( Figure  The jamming problem is one of the most fundamental problems raised by researchers of 296 echolocation, but to our best knowledge, nobody ever estimated what are the chances of 297 being jammed by another bat and how such jamming would actually affect hunting 298 performance. This is very difficult to do with real bats as even if a microphone is placed on the 299 bat, it is typically not as sensitive as the bat itself and it is not placed inside the ear. The 300 substantial body of literature that has accumulated on bat echolocation and sensorimotor 301 control now allows simulating natural scenarios where bats are foraging in aggregations. Using 302 Detection threshold (dB-SPL) this approach, we show that even in very high bat-densities, bats can probably capture insects 303 at high rates. Because we always underestimated the bats' performance (see Methods), this 304 result probably reflects reality too. Notably, we did not fit any of the model's parameters -305 we used parameters that are based on our measurements on real bats or published results. 306 Similarly, we used a simple control strategy to steer the bat to the prey. For example, we do 307 not assume any memory of the position of the target while real bats probably use memory to 308 overcome temporal miss-detections caused by momentary jamming. The ability of real bats 309 to catch prey and avoid obstacles under severe masking was corroborated by several 310 behavioral studies 10,13,23,31,40 . 311 Furthermore, our analysis is based on relative measurements between different scenarios, 312 therefore, even if the exact rates of prey-capture that we estimated are biased somehow, the 313 principles which we observed are likely correct, providing insight to the jamming problem. The 314 two most important results are: (1) Much of the interference that bats suffer from when 315 foraging in a group results from competition over prey and from the need to avoid 316 conspecifics, and not from acoustic masking. One of the main reasons for this is that jamming 317 mostly occurs when the bat is still searching for prey, while once it has detected prey and is 318 closing in on it, prey echoes become loud and the chances of jamming substantially decrease. 319 Masking during search might sound problematic, but even if a prey's echo is completely 320 jammed, another echo from the same prey will likely be detected with one of the following 321 echolocation signals.
(2) Using a spectral JAR, which has been suggested by many previous 322 researchers, is ineffective for solving the jamming problem or even reducing it. The reason for 323 this is that bats constantly change their signals according to behavioral phase and distance to 324 nearby objects. Even if two bats have the same signal repertoire, at any moment in time, their 325 signals are different due to the different behavioral phase they are in and because they are 326 likely to have objects at different distances. Moreover, we only used the bats' first harmonic. 327 Simulating the second harmonic too, thus using signals with more than twice as much 328 bandwidth, would have probably made the jamming avoidance response even more 329 irrelevant, because the differences between the signals of different bats would be naturally 330 larger at any moment (even without a JAR). In theory, in bats that emit narrow bandwidth 331 signals, such as bats with shallow FM calls 41 , jamming might be more influential and a spectral 332 JAR might be more beneficial. However, most shallow FM bats increase bandwidth 333 considerably when pursuing prey, and thus spectral JAR is probably not substantial for those 334 bats too, at least during the pursuit. Indeed, in a previous study, we did not observe a spectral 335 JAR in a bat that uses shallow FM calls (R. microphyllum) 12 . 336 Both of the receiver models that we tested revealed the same results regarding the 337 inefficiency of a JAR. One of the models (the correlation-receiver) is considered optimal in 338 terms of its detection abilities and probably over-estimates bats' abilities. The fact that such 339 a detector, which is extremely sensitive to the specific spectro-temporal pattern of the desired 340 signal, did not show better performance when a JAR was applied, strongly suggests that the 341 JAR is not helpful for real bats too, as their ability to use the differences induced by a JAR are 342 lesser, compared to this receiver. 343 As expected, the correlation-receiver outperforms the filter-bank in all scenarios; it has higher 344 SNR, it detects more objects (see Fig S 5 ), and it has a lower probability to be jammed by 345 masking signals (see Figure 2 a,b). Consequently, the total hunting performance is better 346 (compare Figure 3 A1-A3 with Fig S 3 A1-A3). The range-errors of the filter-bank seem lower 347 (Figure 2c), but this is only because the correlation-receiver detects farther objects than the 348 filter-bank receiver and these objects have lower SNR and thus higher range errors. 349 Apparently, this larger error has a little effect on the performance, as the bats get closer to 350 targets, the SNR improves and the errors decrease. 351 Another interesting result of the simulations was revealed when testing which of the 352 echolocation parameters would allow bats to perform best when hunting in aggregations. We 353 found that the emission power actually used by real bats when hunting in a group (ca. 110-354 120 dB-SPL 24,42,43 ) gave the best performance in the simulation. Increasing the emission power 355 mainly helped increasing prey detection range and not overcoming masking -the masking 356 effect was the same independently of the emission power. Moreover, increasing emission 357 power beyond this level did not further improve hunting probably because when hunting in 358 aggregations there is no benefit in detecting prey beyond a certain distance. Prey that is 359 farther than this distance is very likely to be detected and caught by a closer bat. This result 360 demonstrates how everyone can call louder and still benefit up to a certain degree, 361 corroborating our and others' previous observations 2,13,44 . It would have been difficult to 362 explain the benefit of everyone calling louder without a simulation (note that we did not 363 consider the caloric cost of increasing the emission power which might further reduce actual 364 calling power in reality). 365 Changing the signal's duration did not affect the performance. A possible explanation is the 366 fact that all simulated bats increased their signal duration. Therefore, the benefit of own 367 longer signals is apparently balanced with the greater probability of overlapping with 368 conspecific signals. Note that we are not saying that signal duration irrelevant for hunting in 369 general, but only that it does not affect the ability to mitigate masking and does not improve 370 hunting in a group. 371 Our simulations also provide insight on bats' behavioral ecology. An analysis of the effect of 372 the bat-to-prey density on hunting performance indicates that performance drops rapidly 373 when the bat-to-prey density ratio increases above '1', but that the effect then levels out. On 374 the one hand, this implies that in most cases (when the ratio is below 1) a bat should join an 375 aggregation of bats because such an aggregation usually implies the presence of food. On the 376 other hand, when there are very few bats in an insect-patch, it might be beneficial for these 377 bats to exhibit a patch defense behavior. Indeed, most cases of patch defense described in 378 the bat literature discuss a situation when a single bat deters conspecifics arriving at its 379 patch 14,45,46 . 380 Several previous studies reported that bats change their emission frequencies in response to 381 actual nearby conspecifics 2-5 or to the playback of interfering signals 6-10 . Researchers have 382 interpreted this behavior as a spectral jamming avoidance response. Explaining all previous 383 studies would require much more than a short discussion. We will thus suggest two alternative 384 hypotheses that could explain these findings and should be further pursued. Except for a few 385 exceptions, the great majority of previous studies reported an upward frequency shift, i.e., 386 bats always elevated their frequency. Such a response could be part of the clutter response 387 that is typical for bats when flying in the vicinity of nearby objects. The function of the clutter 388 response 19 is to improve localization of nearby objects; in this case other bats. A clutter 389 response is characterized by higher signal frequencies and by additional signal adjustments 390 such as a decrease in signal duration, as several of these studies reported 5 . Some of the 391 previous studies where playback experiments 6-9 , in which additional bats were not present. 392 In these experiments the clutter should not have increased and thus should not have caused 393 a frequency shift. One possibility is that bats approach the playback speaker (as many bats 394 do 47-49 ) and thus clutter actually did increase in these experiments. Another possible 395 explanation is based on the Lombard effect, i.e. raising emission intensity in the presence of 396 noise, which is well documented in many mammalian species 44,50-53 , including bats 2,13 . It is 397 documented that increasing the signal frequencies could be a by-product of the increase in 398 signal amplitude 54-56 . In both hypotheses, the change in frequency does not aim to decrease 399 spectral overlap and thus cannot be considered a spectral jamming avoidance response. 400 Importantly, the great majority of these studies found an increase in frequency in the 401 presence of conspecifics independently of the frequencies of the two nearby bats. In fact, we 402 also found this in two previous studies 5,12 . We suggest that such an increase can be explained 403 by the well-documented echolocation response of bats to nearby objects (in this case other 404 bats). We used our simulations to test this hypothesis by reproducing the analysis performed 405 in these previous studies. That is, we analyzed the frequencies used by bats when flying alone 406 and when flying with nearby conspecifics (as was done in previous studies). Indeed, our 407 simulations show that bats' average frequency in the presence of conspecifics would rise by 408 as much as 400 Hz in comparison to when flying alone, as reported in previous studies, 409 although they are not performing a jamming avoidance response (see Fig S 6). Our results thus 410 explain the findings of most of the previous studies that reported a JAR. 411 Our work demonstrates the power of simulations to reveal new insight into complex biological 412 systems that are difficult to examine and analyze otherwise. Our model shows both positively 413 and negatively that jamming is less of a problem than previously suggested. On the positive 414 side, it proves that bats can successfully hunt in the presence of other bats without applying 415 any JAR, while on the negative side, it shows that applying a JAR has no significant impact on 416 prey detection or SNR. Similar (modified) simulations can be used in the future to examine 417 many additional fundamental questions in echolocation and to provide insight that may allow 418 us to interpret previous behavioral results and to design better behavioral studies. 419

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General 421 The The echolocation behavior and flight-control of the simulated bats are illustrated in Fig S 7. At 453 the beginning of a simulation, each bat starts foraging in a random position and transmits 454 echolocation signals with 'search' phase parameters (Table 1). 455 After emitting an echolocation signal, the bat processes all of the sensory inputs (echoes and 456 masking sounds) and decides its next step. The rules of the decision making are as follows: (1) 457 If the bat's flight-path comes too close to another bat (less than 20 cm) or to the borders of 458 the area, it avoids them and changes its flight direction and velocity.
(2) If one or more prey 459 items are detected, the bat chooses the closest one and executes a hunting maneuver. (3) 460 Else, the bat continues searching. According to its decision, the bat adjusts its flight control 461 and echolocation behavior. This decision process is executed every inter-pulse-interval (i.e., 462 between the emissions of two echolocation signals). 463 464

2) Echolocation behavior 465
The echolocating behavior of the simulated bats was modeled based on a rich body of 466 literature 15,25,43,58 . The foraging behavior of insectivorous bats is divided into three main 467 phases: 'Search', 'Approach' and 'Buzz' 23 . Each phase is characterized by a different set of 468 echolocation parameters. Our model follows the echolocation and hunting behavior of 469 Pipistrellus kuhlii based on field studies 15,24 and on lab recordings of eight P. kuhli bats trained 470 to search for and land on a static target in a flight room (4.5x5.5x2.5m 3   Once prey is detected, the hunting phase is defined by the distance to the target. Based on 478 the literature, 'Search' switches to 'Approach' at 1.2 m from the target and 'Approach' 479 switches to Buzz' at 0.4 m. 'Terminal Buzz 1' changes to 'Terminal Buzz 2' at 0.2 m. During 480 each behavioral phase, the IPI, pulse duration, bandwidth, and pulse power (in dB) are 481 reduced linearly between the start and end values (Table 1). 482 Alternative JAR models 483 Bats emit linear frequency modulated (FM) down-sweeps. We tested three versions of the 484 model: (1) All bats have the same baseline signal, meaning that if two bats are in the same 485 phase and equal distances to targets, their signals will be identical. (2) Each of the simulated 486 bats emits a slightly different echolocation signal; differing by randomly selecting the terminal 487 frequency from a normal distribution, with a mean set to 39 kHz, and a standard deviation of 488 4 kHz in the 'Search' phase. The bandwidth of the signals is constant between bats, so the 489 entire frequency range shifts according to the terminal frequency. This frequency range is in 490 line with the variance of the terminal frequencies reported in the field for this species 15 . (3) 491 To examine the effect of JAR in the third version of the model, bats used active JAR. They 492 evaluated whether their echoes were jammed (e.g. the masking signal blocks the detection of 493 the prey) by conspecifics' signals. In such cases, they shifted their terminal frequency upward 494 or downward in steps of 2 kHz, in the opposite direction of the masker (i.e. if the masker's 495 frequency was lower than their own, they would raise their frequency). These frequency-shifts 496 are in line with the findings of studies reporting evidence of JAR 5,6 . The bats kept transmitting 497 the modified signal for five consecutive signals, and if during that period another echo was 498 jammed, the bats would shift their frequency again in the proper direction. The terminal 499 frequencies were bounded between 35 and 43 kHz (i.e., there was no shift beyond these 500 boundaries). 501

3) Flight Control 502
Before a prey is detected, simulated bats fly according to a 'correlated random walk' path, 503 with a constant linear velocity 3.5m/s and a random change of direction, sampled from a 504 normal distribution of angular velocities: 0±1 rad/sec (mean±SD) 27,32,58 . A new angular velocity 505 is sampled before each echolocation emission and the bat turns according to this velocity until 506 the next emission. Once a target is detected the bat turns toward the prey by changing its 507 angular velocity according to its relative direction to the target, using a delayed linear adaptive 508 law described in 27 We neglect head movements; the original model 20,27,59 refers to the gaze angle (i.e., the angle 516 between the head's direction and the target), but for simplicity, we assume that the head and 517 body are aligned. Even though we know the head and body are not always aligned; this 518 assumption does not affect the behaviors tested in this study. To keep its direction aligned 519 with the target, the bat typically slows down when the angle to the target ( ) is large, 520 and accelerates linearly when the target is straight ahead 18,60 . To model this, we implemented 521 a velocity-model suggested by Vanderelst and Peremans to simulate this behavior 27 , 522 described in Equation 5. V phase is the maximal velocity in each behavioral phase (3.5m/s in 523 the approach and search phases, and 2m/s during the buzz phase). Like the direction, the bat 524 adjusts its velocity after each inter-pulse-interval. Indeed, the accelerations and turning rates 525 of the simulated bats correspond well to those reported in the field 18,60 , see Fig S 1. 526 : A successful hunt (capture) is achieved when the bat is less than 5cm from the prey 27 . 528

4) Sensory Processing 529
The simulated bat detects and estimates the range and direction of objects in the environment 530 (prey and obstacles), based on the incoming acoustic input. Echoes will only be processed if 531 they cross the auditory threshold set to 0 dB-SPL based on the literature 42,61-63 (we also tested 532 the influence of that threshold between 0-30 dB-SPL, see results, Figure 5 C). We define such 533 detected echoes as 'Pre-Masking Echoes'. Next, we calculate the effect of masking using two 534 different detection-models: the correlation-receiver which is well-well studied theoretical 535 reference model, and the gammatone filter-bank receiver which represents the temporal 536 reaction of the inner ear to auditory signals. After the preliminary detection, the bat chooses 537 its target again, from the non-jammed echoes. 538 The correlation-receiver is based on a similarity between the bat's own transmitted signals 539 and the received signals 30,64 . The detector calculates two correlations: (i) the self-correlation 540 between the echo and its own transmitted signal. (ii) The cross-correlation between the 541 masking interference signal and its own transmitted signal. For the echo to be detected, the 542 self-correlation peak should be higher than the cross-correlation peak with more than the 543 'forward detection threshold' (set to 5dB) if the cross-correlation peak is within 3ms before 544 the echo, and higher than the masking peak by more than the 'backward detection threshold' 545 (e.g. 0db), if the masking signal arrives within 1ms after the wanted signal (see Fig S 8). The 546 periods and thresholds were defined according to 'the law of first wave-front' 63 ch. 2.4.5, 65 ch. Then, we shift each channel in time to compensate for the delay time between the emission 564 time and the response time of each channel, according to the chirp's slope. Finally, we sum 565 the time-compensated filter-channels and look for peaks in the integrated signal. We define 566 prominent peaks as those that are higher than their surroundings by more than the acoustic 567 noise level. All prominent peaks that are also higher than the detection-threshold, set to 568 0 dB-SPL, are referred to as potentially detected echoes, and their distance from the bat is 569 estimated relative to the peak detection-time, see Fig S 9. Note that these peaks might be a 570 result of desired echoes or masking signals and their amplitude will be determined simply by 571 running them through the filter-bank model. 572 Like with the correlation-receiver, for each transmitted signal, we implemented the filter-bank 573 receiver twice: (a) only on the echoes from the bat's own emitted signal, and (b) on both 574 masking signals and echoes. We compared (a) and (b) detected peaks as described above and 575 then defined the following criteria: a jammed signal is a peak that was detected in (a) but not 576 in (b); the time-estimation error is the difference between the estimated peak-time in (b) and 577 the actual received time of the reflected echo; and false-alarm occurs when a bat decides to 578 pursue a 'target' that was detected only in (b), and therefore is not a prey echo, but a masking 579 signal. 580 Note that 'correlation-receiver' assumes that the bat can differ between desired prey echoes 581 and masking signals and echoes from conspecifics 13,68 . On the other hand, the 'filter-bank 582 receiver', only assumes that bat estimates the times of its own transmitted signal in each 583 channel. 584 The SNR (Signal to Noise and interference Ratio) is calculated for each detector by Equation 585 8. 586 Equation 8: To analyze the effect of signal duration on performance, we modified the model by 588 implementing the correlation-detector in the detection process too, before the masking 589 calculations. Here, the received echo was first correlated with the emitted signal and then it 590 was compared to a detection-threshold. The detection threshold for the correlation was set 591 to 15 dB-SPL, which equals to the maximum of the autocorrelation of an 8ms 'search' signal. 592 After the detection process, the bat estimates the range and the Direction Of Arrival (DOA) of 593 the reflecting object, based on all of the received signals (echoes and masking signals). The 594 range estimation is based on the acoustic two-way time-travel of the signal with an error 595 (Equation 9), comprised of two elements: the bat's accuracy in measuring time, and a noise 596 term which reduces with increasing SINR (Equation 8, calculated using either the Correlation 597 or the Filter-bank model). For simplicity, because all bat signals are FM-chirps, we use an error 598 that is independent of the signal's parameters: the term 1 ⁄ , where 1 is a coefficient 599 set to scale the error to values of ±1cm at SNR of 10dB, based on behavioral studies 30,63,69,70 . 600 The independency of the signal's parameters is reasonable because all bat signals in our 601 simulation were similar. The term (in Equation 9) is sampled from a Gaussian 602 distribution with a mean ± SD of 0±50 microseconds, equivalent to a range error of 0.85 cm, 603 which is a low boundary estimation of bats capabilities to measure distance 54 . 'c' is the speed 604 of sound: 343m/s. 605 In general, our model intentionally underestimates the bats' actual performance, and thus real bats are likely to cope with acoustic interference even better than our simulated bats: (1) we simulated monaural bats, while real bats use two ears with spatial selectivity 31 .
(2) We assumed a low detection threshold (0 dB-SPL), thus the bats were more susceptible to masking (see Figure 5 C2). (3) We chose long backward and forward masking windows (3ms, 1ms), and low jamming thresholds: 0dB for backward masking, 5dB for forward masking (e.g. a masking signal that was received first, even if it is 5dB lower than the desired echo, will totally jam it). (4) The model implied a pulse-by-pulse detection and estimation strategy with no memory, therefore, temporal miss-detections caused by momentary jamming had a very substantial effect on hunting attempts.

Acoustics Calculations 613
The estimated intensities of the reflected echoes based on the sonar/radar equation (  The transmitted power (Pt) of a search signal equals 110 dB-SPL at a distance of 0.1 meters 627 from the source 71 . Pt during the hunt varies according to the distance to the prey (see Table  628 1). The transmission gain of the bat's mouth Gt(ϕ, f) is modeled by a circular piston source 73-629 75 , given in Equation 12. The directivity of the emitted call depends on the ratio between the 630 wavelength of the signal (λ) and the radius of the emitter (mouth), 'a' (set to 3 mm 74 ); J1 is the 631 Bessel function of the first order and k= 2 /λ. G0 of the mouth (at the head direction) is set to 632 1, matching the measurements of intensities of bat's calls from a distance of 0.1m. 633 The original piston model is symmetric: the back-lobe is equal to the front-lobe. In our model, 641 bats receive signals from the back hemisphere too, therefore we modified the piston model 642 for the back hemisphere (for transmission and reception), and it is shaped by the piston model 643 with additional attenuation of 0-20dB, increasing linearly (in dB) from ±90º to ±180º, relative 644 to the bat. The modified piston model for ear and mouth are illustrated in Fig S 12 , the Radar (sonar) Cross-Section (RCS, or 'target strength') of the moth, is modeled as a disc 649 with a radius ('r') equals 2 cm, equally reflecting in all directions. We apply the approximation 650 of the RCS for this type of reflector 77 , given in Equation 15, where A is the geometric area of 651 the disc (A=πr 2 ). 'r' was set to 2cm, simulating a moth's wing-length. This approximation is in 652 line with measurements of the target strength of medium-sized insects 42 [ figure 1h], 43 . In each scenario that we simulated, we tested the effect of the varied parameters on hunting 672 performance using ANCOVA, ANOVA or multiple regression, depending on the type of the 673 parameters (e.g. continuous or categorical) and their number. The Statistics were calculated 674 using Standard Least Squares method with JMP 14 and MATLAB R2018b. 675 For testing the significance of the masking effect, we used a different procedure. Because the 676 masking effect is a ratio (see Equation 1) we had to compute its SD. Thus, for each set of 677 conditions, we estimated the standard deviation of the masking effect, using Equation 19 78 . 678 In order to determine whether the masking effect significantly dependent on the tested 679 parameters, we simulated 100 points in each scenario with the average and SD calculated 680 above, and executed ANCOVA to estimate the F test, for the simulated scenario. We repeated 681 this process 1000 times in each scenario and used the average results of the F tests and p-682 values as the statistics. This process of repetitions was executed only for the statistics of the 683 masking effect. 684

Equation 19
: We also evaluated the 'Jamming Probability' as the proportion of pursued prey echoes (echoes 686 of prey the bat chose to pursue) that are blocked by masking signals (Equation 20). Note, that 687 this ratio is not the proportion of all the jammed echoes to all detected echoes, because for 688 each signal there can be several detected echoes from different prey items, but only one 689 (maximum) is pursued. The effect of JAR behavior can be quantified by examining the similarity between 706 the desired prey echoes and the masking signals. During the search phase, the correlation 707 between the desired echo and the emitted signal is on average ~10dB higher than the 708 correlation between the emitted signal and masking signals produced by bats in other 709 behavioral phases. Additionally, there is no benefit in shifting the frequencies of the emitted 710 signal to cope with masking from those signals. If the masking signal is a search signal (as the 711 emitted one), shifting the frequency by 2kHz has a limited improvement of 2dB at most (A3-712 D3). As a result of this constant spectral variability, applying a spectral JAR to shift the 713 frequencies of the emitted signal does not affect the correlation with the masking signals (E1-714 E3). Panel A1 depicts the spectrogram of a transmitted search signal with a duration of 7ms 715 and bandwidth of 8kHz (Table 1). Panel A2 illustrates the correlation function between the 716 transmitted signal and potential masking signals of bats at different behavioral phases (black 717 -the correlation with another search signal, blue and red-with two different approach signals, 718 and green -with a buzz signal). All signals were received with the same power. The correlation 719 gain is defined as the difference between the peak of the auto-correlation and the maximum 720 of each cross-correlation function (blue arrow-the correlation gain for the search signal 721 relative to the approach1 signal). The correlation gain of the transmitted signal with a search 722 signal is 0dB by definition. To examine the effect of a JAR response, we gradually shifted the 723 terminal frequencies of the masking signals and calculated the correlation gain for each 724 frequency shift. Panel A3 describes the correlation gain as a function of the frequency shift.

C1 B1 A1
Buzz masking; solid blue -filter-bank receiver with random signal variability; dashed turquoise -744 filter-bank receiver with JAR response; dash-dotted magenta-filter-bank receiver without 745 signal variability. Panels (A1-C1) depict the performance as a function of bat density; a green 746 circle shows the performance of a single bat. In the no-masking condition (green lines) there 747 is a significant degradation in performance as the bat's density rises from 1, and it reaches to 748 maxima of ca.: 60%, 43%, 32% where, for 20 bats and 3,10,20 prey items per 100m2, 749 respectively. There was no significant difference in performance when applying or not 750 applying spectral JAR-compare turquoise and blue lines (One -way ANOVA: F2,1007=0.467, 751 p=0.529; F2,1355=0.651, p=0.42; F2,1529=0.207, p=0.645. Panels (A2-C2) show the masking-effect 752 on hunting, i.e., the relative decrease in hunting relative to the 'no-masking' condition. The 753 masking effect for 10 and 20 bats per 100m2 was between 40%, and 60%, respectively. (A3-754 C3) The probability of jamming at different behavioral phases: search (turquoise marker), 755 approach (magenta marker) and buzz (red markers). For prey densities of 10 and 20 prey items 756 per 100m2, there was no significant difference between JAR and no JAR scenarios, in all flight-757 phases (One-way ANOVA). In scenarios including low prey density (i.e., 3 prey items per 758 100m 2 ), the probability of jamming was low, with a maximum of ca. 10%. Pie charts present the proportions of successful 763 and unsuccessful attacks with different failure reasons for groups of 1 to 20 bats, with masking 764 ('correlation-detector') and without masking. Each chart is divided into the following 765 categories: (i) captures -maneuvers that ended with a successful capture; (ii) misses -766 maneuvers in which the bats failed to capture the target because of insufficient maneuvering 767 and/or masking ; (iii) avoid obs (obstacles) -flight paths that came too close to the borders of 768 the arena and the bat seized hunting; (iv) avoid cons (conspecifics) -hunting maneuvers that 769 were ended in order to avoid collision with another bat; (v) lost to cons -hunting attempts 770 that were terminated because the prey was caught by a conspecific. The pie charts present 771 the mean and the standard-errors for 100 simulated bats. Each panel includes 100 simulated 772 bats. The absolute rates for each category are presented near the pie chart. In all bat densities 773 the proportion of missing the prey increased when adding sensory masking (One-way ANOVA: 774 effect-size=3%, F1, 198=3.21, p=0.075; effect-size=11%, F1, 198=20.7, p*<0.0001; effect-size=23%, 775 F1, 198=68.8, p*<0.0001, for 5, 10 and 20 bats per 100m 2 ). Asterisk (*) indicates significant 776 difference. The permutation test was executed as follows: (1) we randomly sampled 150 777 points from each data-set (i.e., the received power of 'JAR' and 'no JAR').
(2) We defined the 778 sampled effect-size as the difference between the medians of the samples. An echo from a target (green) is received 819 by the bat. The reception window (blue) is composed of two periods: the 'forward masking 820 time' starts 3ms before the arrival time of the signal, and the 'backward masking time' starts 821 at the arrival time and lasts 2ms. The 'forward masking threshold' is set to 5dB below the 822 maximum of the received signal during the 'reception window', and the 'backward masking 823 threshold' is equal to the maximum power of the signal. Any signal (even below the two 824 thresholds) that arrives within the reception window will mask the target's echo and will 825 reduce its localization accuracy, as a function of the SINR. If a masking signal's power is above 826 one of the two relevant thresholds, the echo is jammed, and the bat does not detect the 827 target. Panel (B) illustrates an example of a received echo with three potentially masking 828 signals (red). Masker 1 does not affect the detection, because it is outside the 'reception 829 window'. Masker 2 is above the forward masking threshold; thus the echo is jammed and the 830 prey is not detected at all. Masker 3 is received within the reception window, but is below the 831 backward threshold, and as a consequence, the signal is detected but the localization error 832 increases, according to the SINR (Equation 9, Equation 10). Both models of receivers 833 ('correlation-detector' and 'peak-detector') apply the same 'reception window, and 834 thresholds. However, the peak-detector uses the maximum power of the received signals to 835 set the thresholds, whereas the correlation-detector uses the maximum of the correlations 836 between the received and the transmitted signals. 837 , is split to n-838 channels of gammatone filters. In each channel, the signal is filtered by a band-pass filter, with 839 center frequency fck, and input response hk.. The signal goes through a low-pass filter 840 ('envelope detector') that removes phase information. Then, each signal is shifted in time (τk) 841 to compensate for the chirp slope (i.e. τk is equal to the time difference between the start of 842 the transmitted chirp, and the response in each channel). The channels are integrated, and 843 the detector looks for local maxima (i.e. peaks). The receiver estimates the intensities and 844 delays of the detected peaks' that cross the detection threshold (see text). Panel (B) depicts 845 the frequency responses of several gammatone filters (11 out of 80). τk illustrates the signals 846 in several points at the process: (C1) Spectrogram of a reflected echo from prey (S(t)); (C2) 847 The response of three gammatone filters (fc1,fc2,fc3), before the time shift; (C3) The 848 receiver's output (Y(t)) after the integration and peak-detection processes.