Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Public review):
We thank the reviewer for his valuable input and careful assessment, which have significantly improved the clarity and rigor of our manuscript.
Summary:
Mazer & Yovel 2025 dissect the inverse problem of how echolocators in groups manage to navigate their surroundings despite intense jamming using computational simulations.
The authors show that despite the 'noisy' sensory environments that echolocating groups present, agents can still access some amount of echo-related information and use it to navigate their local environment. It is known that echolocating bats have strong small and large-scale spatial memory that plays an important role for individuals. The results from this paper also point to the potential importance of an even lower-level, short-term role of memory in the form of echo 'integration' across multiple calls, despite the unpredictability of echo detection in groups. The paper generates a useful basis to think about the mechanisms in echolocating groups for experimental investigations too.
Strengths:
(1) The paper builds on biologically well-motivated and parametrised 2D acoustics and sensory simulation setup to investigate the various key parameters of interest
(2) The 'null-model' of echolocators not being able to tell apart objects & conspecifics while echolocating still shows agents successfully emerge from groups - even though the probability of emergence drops severely in comparison to cognitively more 'capable' agents. This is nonetheless an important result showing the directionof-arrival of a sound itself is the 'minimum' set of ingredients needed for echolocators navigating their environment.
(3) The results generate an important basis in unraveling how agents may navigate in sensorially noisy environments with a lot of irrelevant and very few relevant cues.
(4) The 2D simulation framework is simple and computationally tractable enough to perform multiple runs to investigate many variables - while also remaining true to the aim of the investigation.
Weaknesses:
There are a few places in the paper that can be misunderstood or don't provide complete details. Here is a selection:
(1) Line 61: '... studies have focused on movement algorithms while overlooking the sensory challenges involved' : This statement does not match the recent state of the literature. While the previous models may have had the assumption that all neighbours can be detected, there are models that specifically study the role of limited interaction arising from a potential inability to track all neighbours due to occlusion, and the effect of responding to only one/few neighbours at a time e.g. Bode et al. 2011 R. Soc. Interface, Rosenthal et al. 2015 PNAS, Jhawar et al. 2020 Nature Physics.
We appreciate the reviewer's comment and the relevant references. We have revised the manuscript accordingly to clarify the distinction between studies that incorporate limited interactions and those that explicitly analyze sensory constraints and interference. We have refined our statement to acknowledge these contributions while maintaining our focus on sensory challenges beyond limited neighbor detection, such as signal degradation, occlusion effects, and multimodal sensory integration (see lines 58-64):
(2) The word 'interference' is used loosely places (Line 89: '...took all interference signals...', Line 319: 'spatial interference') - this is confusing as it is not clear whether the authors refer to interference in the physics/acoustics sense, or broadly speaking as a synonym for reflections and/or jamming.
To improve clarity, we have revised the manuscript to distinguish between different types of interference:
• Acoustic interference (jamming): Overlapping calls that completely obscure echo detection, preventing bats from perceiving necessary environmental cues.
• Acoustic interference (masking): Partial reduction in signal clarity due to competing calls.
• Spatial interference: Physical obstruction by conspecifics affecting movement and navigation.
We have updated the manuscript to use these terms consistently and explicitly define them in relevant sections (see lines 84-85, 119-120). This distinction ensures that the reader can differentiate between interference as an acoustic phenomenon and its broader implications in navigation.
(3) The paper discusses original results without reference to how they were obtained or what was done. The lack of detail here must be considered while interpreting the Discussion e.g. Line 302 ('our model suggests...increasing the call-rate..' - no clear mention of how/where call-rate was varied) & Line 323 '..no benefit beyond a certain level..' - also no clear mention of how/where call-level was manipulated in the simulations.
All tested parameters, including call rate dynamics and call intensity variations, are detailed in the Methods section and Tables 1 and 2. Specifically:
• Call Rate Variation: The Inter-Pulse Interval (IPI) was modeled based on documented echolocation behavior, decreasing from 100 msec during the search phase to 35 msec (~28 calls per second) at the end of the approach phase, and to 5 msec (200 calls per second) during the final buzz (see Table 2). This natural variation in call rate was not manually manipulated in the model but emerged from the simulated bat behavior.
• Call Intensity Variation: The tested call intensity levels (100, 110, 120, 130 dB SPL) are presented in Table 1 under the “Call Level” parameter. The effect of increasing call intensity was analyzed in relation to exit probability, jamming probability, and collision rate. This is now explicitly referenced in the Discussion. We have revised the manuscript to explicitly reference these aspects in the Results and Discussion sections – see lines 346-349, 372-375.
Reviewer #2 (Public review):
We are grateful for the reviewer’s insightful feedback, which has helped us clarify key aspects of our research and strengthen our conclusions.
This manuscript describes a detailed model of bats flying together through a fixed geometry. The model considers elements that are faithful to both bat biosonar production and reception and the acoustics governing how sound moves in the air and interacts with obstacles. The model also incorporates behavioral patterns observed in bats, like one-dimensional feature following and temporal integration of cognitive maps. From a simulation study of the model and comparison of the results with the literature, the authors gain insight into how often bats may experience destructive interference of their acoustic signals and those of their peers, and how much such interference may actually negatively affect the groups' ability to navigate effectively. The authors use generalized linear models to test the significance of the effects they observe.
In terms of its strengths, the work relies on a thoughtful and detailed model that faithfully incorporates salient features, such as acoustic elements like the filter for a biological receiver and temporal aggregation as a kind of memory in the system. At the same time, the authors' abstract features are complicating without being expected to give additional insights, as can be seen in the choice of a twodimensional rather than three-dimensional system. I thought that the level of abstraction in the model was perfect, enough to demonstrate their results without needless details. The results are compelling and interesting, and the authors do a great job discussing them in the context of the biological literature.
The most notable weakness I found in this work was that some aspects of the model were not entirely clear to me.
For example, the directionality of the bat's sonar call in relation to its velocity. Are these the same?
For simplicity, in our model, the head is aligned with the body, therefore the direction of the echolocation beam is the same as the direction of the flight.
Moreover, call directionality (directivity) is not directly influenced by velocity. Instead, directionality is estimated using the piston model, as described in the Methods section. The directionality is based on the emission frequency and is thus primarily linked to the behavioral phases of the bat, with frequency shifts occurring as the bat transitions from search to approach to buzz phases. During the approach phase, the bat emits calls with higher frequencies, resulting in increased directionality. This is supported by the literature (Jakobsen and Surlykke, 2010; Jakobsen, Brinkløv and Surlykke, 2013). This phase is also associated with a natural reduction in flight speed, which is a well-documented behavioral adaptation in echolocating bats(Jakobsen et al., 2024).
To clarify this in the manuscript, we have updated the text to explicitly state that directionality follows phase-dependent frequency changes rather than being a direct function of velocity, see lines 543-545.
If so, what is the difference between phi_target and phi_tx in the model equations?
𝝓<sub>𝒕𝒂𝒓𝒈𝒆𝒕</sub> represents the angle between the bat and the reflected object (target).
𝝓<sub>𝑻𝒙</sub> the angle [rad], between the masking bat and target (from the transmitter’s perspective)
𝝓<sub>𝑻𝒙𝑹𝒙</sub> refers to the angle between the transmitting conspecific and the receiving focal bat, from the transmitter’s point of view.
𝝓<sub>𝑹𝒙𝑻𝒙</sub> represents the angle between the receiving bat and the transmitting bat, from the receiver’s point of view.
These definitions have been explicitly stated in the revised manuscript to prevent any ambiguity (lines 525-530). Additionally, a Supplementary figure demonstrating the geometrical relations has been added to the manuscript.
What is a bat's response to colliding with a conspecific (rather than a wall)?
In nature, minor collisions between bats are common and typically do not result in significant disruptions to flight (Boerma et al., 2019; Roy et al., 2019; Goldshtein et al., 2025). Given this, our model does not explicitly simulate the physical impact of a collision event. Instead, during the collision event the bat keeps decreasing its velocity and changing its flight direction until the distance between bats is above the threshold (0.4 m). We assume that the primary cost of such interactions arises from the effort required to avoid collisions, rather than from the collision itself. This assumption aligns with observations of bat behavior in dense flight environments, where individuals prioritize collision avoidance rather than modeling post-collision dynamics. See lines 479-484.
From the statistical side, it was not clear if replicate simulations were performed. If they were, which I believe is the right way due to stochasticity in the model, how many replicates were used, and are the standard errors referred to throughout the paper between individuals in the same simulation or between independent simulations, or both?
The number of repetitions for each scenario is detailed in Table 1, but we included it in a more prominent location in the text for clarity. Specifically, we now state (Lines 110-111):
"The number of repetitions for each scenario was as follows: 1 bat: 240; 2 bats: 120; 5 bats: 48; 10 bats: 24; 20 bats: 12; 40 bats: 12; 100 bats: 6."
Regarding the reported standard errors, they are calculated across all individuals within each scenario, without distinguishing between different simulation trials.
We clarified in the revised text (Lines 627-628 in Statistical Analysis)
Overall, I found these weaknesses to be superficial and easily remedied by the authors. The authors presented well-reasoned arguments that were supported by their results, and which were used to demonstrate how call interference impacts the collective's roost exit as measured by several variables. As the authors highlight, I think this work is valuable to individuals interested in bat biology and behavior, as well as to applications in engineered multi-agent systems like robotic swarms.
Reviewer #3 (Public review):
We sincerely appreciate the reviewer’s thoughtful comments and the time invested in evaluating our work, which have greatly contributed to refining our study.
We would like to note that in general, our model often simplifies some of the bats’ abilities, under the assumption that if the simulated bats manage to perform this difficult task with simpler mechanisms, real better adapted bats will probably perform even better. This thought strategy will be repeated in several of the s below.
Summary:
The authors describe a model to mimic bat echolocation behavior and flight under high-density conditions and conclude that the problem of acoustic jamming is less severe than previously thought, conflating the success of their simulations (as described in the manuscript) with hard evidence for what real bats are actually doing. The authors base their model on two species of bats that fly at "high densities" (defined by the authors as colony sizes from tens to tens of thousands of individuals and densities of up to 33.3 bats/m2), Pipistrellus kuhli and Rhinopoma microphyllum. This work fits into the broader discussion of bat sensorimotor strategies during collective flight, and simulations are important to try to understand bat behavior, especially given a lack of empirical data. However, I have major concerns about the assumptions of the parameters used for the simulation, which significantly impact both the results of the simulation and the conclusions that can be made from the data. These details are elaborated upon below, along with key recommendations the authors should consider to guide the refinement of the model.
Strengths:
This paper carries out a simulation of bat behavior in dense swarms as a way to explain how jamming does not pose a problem in dense groups. Simulations are important when we lack empirical data. The simulation aims to model two different species with different echolocation signals, which is very important when trying to model echolocation behavior. The analyses are fairly systematic in testing all ranges of parameters used and discussing the differential results.
Weaknesses:
The justification for how the different foraging phase call types were chosen for different object detection distances in the simulation is unclear. Do these distances match those recorded from empirical studies, and if so, are they identical for both species used in the simulation?
The distances at which bats transition between echolocation phases are identical for both species in our model (see Table 2). These distances are based on welldocumented empirical studies of bat hunting and obstacle avoidance behavior (Griffin, Webster and Michael, 1958; Simmons and Kick, 1983; Schnitzler et al., 1987; Kalko, 1995; Hiryu et al., 2008; Vanderelst and Peremans, 2018). These references provide extensive evidence that insectivorous bats systematically adjust their echolocation calls in response to object proximity, following the characteristic phases of search, approach, and buzz.
To improve clarity, we have updated the text to explicitly state that the phase transition distances are empirically grounded and apply equally to both modeled species (lines 499-508).
What reasoning do the authors have for a bat using the same call characteristics to detect a cave wall as they would for detecting a small insect?
In echolocating bats, call parameters are primarily shaped by the target distance and echo strength. Accordingly, there is little difference in call structure between prey capture and obstacles-related maneuvers, aside from intensity adjustments based on target strength (Hagino et al., 2007; Hiryu et al., 2008; Surlykke, Ghose and Moss, 2009; Kothari et al., 2014). In our study, due to the dense cave environment, the bats are found to operate in the approach phase most of the time, which is consistent with natural cave emergence, where they are navigating through a cluttered environment rather than engaging in open-space search. For one of the species (Rhinopoma), we also have empirical recordings of individuals flying under similar conditions (Goldshtein et al., 2025). Our model was designed to remain as simple as possible while relying on conservative assumptions that may underestimate bat performance. If, in reality, bats fine-tune their echolocation calls even earlier or more precisely during navigation than assumed, our model would still conservatively reflect their actual capabilities. See lines 500-508.
The two species modeled have different calls. In particular, the bandwidth varies by a factor of 10, meaning the species' sonars will have different spatial resolutions. Range resolution is about 10x better for PK compared to RM, but the authors appear to use the same thresholds for "correct detection" for both, which doesn't seem appropriate.
The detection process in our model is based on Saillant’s method using a filterbank, as detailed in the paper (Saillant et al., 1993; Neretti et al., 2003; Sanderson et al., 2003). This approach inherently incorporates the advantages of a wider bandwidth, meaning that the differences in range resolution between the species are already accounted for within the signal-processing framework. Thus, there is no need to explicitly adjust the model parameters for bandwidth variations, as these effects emerge from the applied method.
Also, the authors did not mention incorporating/correcting for/exploiting Doppler, which leads me to assume they did not model it.
The reviewer is correct. To maintain model simplicity, we did not incorporate the Doppler effect or its impact on echolocation. The exclusion of Doppler effects was based on the assumption that while Doppler shifts can influence frequency perception, their impact on jamming and overall navigation performance is minor within the modelled context.
The maximal Doppler shifts expected for the bats in this scenario are of ~ 1kHz. These shifts would be applied variably across signals due to the semi-random relative velocities between bats, leading to a mixed effect on frequency changes. This variability would likely result in an overall reduction in jamming rather than exacerbating it, aligning with our previous statement that our model may overestimate the severity of acoustic interference. Such Doppler shifts would result in errors of 2-4 cm in localization (i.e., 200-400 micro-seconds) (Boonman, Parsons and Jones, 2003).
We have now explicitly highlighted this in the revised version (see 548-581).
The success of the simulation may very well be due to variation in the calls of the bats, which ironically enough demonstrates the importance of a jamming avoidance response in dense flight. This explains why the performance of the simulation falls when bats are not able to distinguish their own echoes from other signals. For example, in Figure C2, there are calls that are labeled as conspecific calls and have markedly shorter durations and wider bandwidths than others. These three phases for call types used by the authors may be responsible for some (or most) of the performance of the model since the correlation between different call types is unlikely to exceed the detection threshold. But it turns out this variation in and of itself is what a jamming avoidance response may consist of. So, in essence, the authors are incorporating a jamming avoidance response into their simulation.
We fully agree that the natural variations in call design between the phases contribute significantly to interference reduction (see our discussion in a previous paper in Mazar & Yovel, 2020). However, we emphasize that this cannot be classified as a Jamming Avoidance Response (JAR). In our model, bats respond only to the physical presence of objects and not to the acoustic environment or interference itself. There is no active or adaptive adjustment of call design to minimize jamming beyond the natural phase-dependent variations in call structure. Therefore, while variation in call types does inherently reduce interference, this effect emerges passively from the modeled behavior rather than as an intentional strategy to avoid jamming.
The authors claim that integration over multiple pings (though I was not able to determine the specifics of this integration algorithm) reduces the masking problem. Indeed, it should: if you have two chances at detection, you've effectively increased your SNR by 3dB.
The reviewer is correct. Indeed, integration over multiple calls improves signal-tonoise ratio (SNR), effectively increasing it by approximately 3 dB per doubling of observations. The specifics of the integration algorithm are detailed in the Methods section, where we describe how sensory information is aggregated across multiple time steps to enhance detection reliability.
They also claim - although it is almost an afterthought - that integration dramatically reduces the degradation caused by false echoes. This also makes sense: from one ping to the next, the bat's own echo delays will correlate extremely well with the bat's flight path. Echo delays due to conspecifics will jump around kind of randomly. However, the main concern is regarding the time interval and number of pings of the integration, especially in the context of the bat's flight speed. The authors say that a 1s integration interval (5-10 pings) dramatically reduces jamming probability and echo confusion. This number of pings isn't very high, and it occurs over a time interval during which the bat has moved 5-10m. This distance is large compared to the 0.4m distance-to-obstacle that triggers an evasive maneuver from the bat, so integration should produce a latency in navigation that significantly hinders the ability to avoid obstacles. Can the authors provide statistics that describe this latency, and discussion about why it doesn't seem to be a problem?
As described in the Methods section, the bat’s collision avoidance response does not solely rely on the integration process. Instead, the model incorporates real-time echoes from the last calls, which are used independently of the integration process for immediate obstacle avoidance maneuvers. This ensures that bats can react to nearby obstacles without being hindered by the integration latency. The slower integration on the other hand is used for clustering, outlier removal and estimation wall directions to support the pathfinding process, as illustrated in Supplementary Figure 1.
Additionally, our model assumes that bats store the physical positions of echoes in an allocentric coordinate system (x-y). The integration occurs after transforming these detections from a local relative reference frame to a global spatial representation. This allows for stable environmental mapping while maintaining responsiveness to immediate changes in the bat’s surroundings.
See lines 600-616 in the revised version.
The authors are using a 2D simulation, but this very much simplifies the challenge of a 3D navigation task, and there is an explanation as to why this is appropriate. Bat densities and bat behavior are discussed per unit area when realistically it should be per unit volume. In fact, the authors reference studies to justify the densities used in the simulation, but these studies were done in a 3D world. If the authors have justification for why it is realistic to model a 3D world in a 2D simulation, I encourage them to provide references justifying this approach.
We acknowledge that this is a simplification; however, from an echolocation perspective, a 2D framework represents a worst-case scenario in terms of bat densities and maneuverability:
• Higher Effective Density: A 2D model forces all bats into a single plane rather than distributing them through a 3D volume, increasing the likelihood of overlap in calls and echoes and making jamming more severe. As described in the text: the average distance to the nearest bat in our simulation is 0.27m (with 100 bats), whereas reported distances in very dense colonies are 0.5m (Fujioka et al., 2021), as observed in Myotis grisescens (Sabol and Hudson, 1995) and Tadarida brasiliensis (Theriault et al., no date; Betke et al., 2008; Gillam et al., 2010)
• Reduced Maneuverability: In 3D space, bats can use vertical movement to avoid obstacles and conspecifics. A 2D constraint eliminates this degree of freedom, increasing collision risk and limiting escape options.
Thus, our 2D model provides a conservative difficult test case, ensuring that our findings are valid under conditions where jamming and collision risks are maximized. Additionally, the 2D framework is computationally efficient, allowing us to perform multiple simulation runs to explore a broad parameter space and systematically test the impact of different variables.
To address the reviewer’s concern, we have clarified this justification in the revised text and will provide supporting references where applicable (see Methods lines 450455).
The focus on "masking" (which appears to be just in-band noise), especially relative to the problem of misassigned echoes, is concerning. If the bat calls are all the same waveform (downsweep linear FM of some duration, I assume - it's not clear from the text), false echoes would be a major problem. Masking, as the authors define it, just reduces SNR. This reduction is something like sqrt(N), where N is the number of conspecifics whose echoes are audible to the bat, so this allows the detection threshold to be set lower, increasing the probability that a bat's echo will exceed a detection threshold. False echoes present a very different problem. They do not reduce SNR per se, but rather they cause spurious threshold excursions (N of them!) that the bat cannot help but interpret as obstacle detection. I would argue that in dense groups the mis-assignment problem is much more important than the SNR problem.
There is substantial literature supporting the assumption that bats can recognize their own echoes and distinguish them from conspecific signals (Schnitzler, Bioscience and 2001, no date; Kazial, Burnett and Masters, 2001; Burnett and Masters, 2002; Kazial, Kenny and Burnett, 2008; Chili, Xian and Moss, 2009; Yovel et al., 2009; Beetz and Hechavarría, 2022)). However, we acknowledge that false echoes may present a major challenge in dense groups. To address this, we explicitly tested the impact of the self-echo identification assumption in our study see Results Figure 1: The impact of confusion on performance, and lines 399-404 in the Discussion.
Furthermore, we examined a full confusion scenario, where all reflected echoes from conspecifics were misinterpreted as obstacle reflections (i.e., 100% confusion). Our results show that this significantly degrades navigation performance, supporting the argument that echo misassignment is a critical issue. However, we also explored a simple mitigation strategy based on temporal integration with outlier rejection, which provided some improvement in performance. This suggests that real bats may possess additional mechanisms to enhance self-echo identification and reduce false detections. See lines 411-420 in the manuscript for further discussion.
We actually used logarithmically frequency modulated (FM) chirps, generated using the MATLAB built-in function chirp(t, f0, t1, f1, 'logarithmic'). This method aligns with the nonlinear FM characteristics of Pipistrellus kuhlii (PK) and Rhinopoma microphyllum (RM) and provides a realistic approximation of their echolocation signals. We acknowledge that this was not sufficiently emphasized in the original text, and we have now explicitly highlighted this in the revised version to ensure clarity (see Lines 509-512 in Methods).
The criteria set for flight behavior (lines 393-406) are not justified with any empirical evidence of the flight behavior of wild bats in collective flight. How did the authors determine the avoidance distances? Also, what is the justification for the time limit of 15 seconds to emerge from the opening? Instead of an exit probability, why not instead use a time criterion, similar to "How long does it take X% of bats to exit?" :
While we acknowledge that wild bats may employ more complex behaviors for collision avoidance, we chose to implement a simplified decision-making rule in our model to maintain computational tractability.
The avoidance distances (1.5 m from walls and 0.4 m from other bats) were selected as internal parameters to support stable and realistic flight trajectories while maintaining a reasonable collision rate. These values reflect a trade-off between maneuverability and behavioral coherence under crowding. To address this point, we added a sensitivity analysis to the revised manuscript. Specifically, we tested the effect of varying the conspecific avoidance distance from 0.2 to 1.6 meters at bat densities of 2 to 40 bats/3m². The only statistically significant impact was at the highest density (40 bats/3m²), where exit probability increased slightly from 82% to 88% (p = 0.024, t = 2.25, DF = 958). No significant changes were observed in exit time, collision rate, or jamming probability across other densities or conditions (GLM, see revised Methods). These results suggest that the selected avoidance distances are robust and not a major driver of model performance, see lines 469-47.
The 15-second exit limit was determined as described in the text (Lines 489-491): “A 15-second window was chosen because it is approximately twice the average exit time for 40 bats and allows for a second corrective maneuver if needed.” In other words, it allowed each bat to circle the ‘cave’ twice to exit even in the most crowded environment. This threshold was set to keep simulation time reasonable while allowing sufficient time for most bats to exit successfully.
We acknowledge that the alternative approach suggested by the reviewer— measuring the time taken for a certain percentage of bats to exit—is also valid. However, in our model, some outlier bats fail to exit and continue flying for many minutes, such simulations would lead to excessive simulation times making it difficult to generate repetitions and not teaching us much – they usually resulted from the bat slightly missing the opening (see video S1. Our chosen approach ensures practical runtime constraints while still capturing relevant performance metrics.
What is the empirical justification for the 1-10 calls used for integration?
The "average exit time for 40 bats" is also confusing and not well explained. Was this determined empirically? From the simulation? If the latter, what are the conditions?
Does it include masking, no masking, or which species?
Previous studies have demonstrated that bats integrate acoustic information received sequentially over several echolocation calls (2-15), effectively constructing an auditory scene in complex environments (Ulanovsky and Moss, 2008; Chili, Xian and Moss, 2009; Moss and Surlykke, 2010; Yovel and Ulanovsky, 2017; Salles, Diebold and Moss, 2020). Additionally, bats are known to produce echolocation sound groups when spatiotemporal localization demands are high (Kothari et al., 2014). Studies have documented call sequences ranging from 2 to 15 grouped calls (Moss and Surlykke, 2010), and it has been hypothesized that grouping facilitates echo segregation.
We did not use a single integration window - we tested integration sizes between 1 and 10 calls and presented the results in Figure 3A. This range was chosen based on prior empirical findings and to explore how different levels of temporal aggregation impact navigation performance. Indeed, the results showed that the performance levels between 5-10 calls integration window (Figure 3A)
Regarding the average exit time for 40 bats, this value was determined from our simulations, where it represents the mean time for successful exits under standard conditions with masking. We have revised the text to clarify these details see, lines 489-491.
Reviewer #1 (Recommendations for the authors):
(1) Data Availability:
As it stands now, this reviewer cannot vouch for the uploaded code as it wasn't accessible according to F.A.I.R principles. The link to the code/data points to a private company's file-hosting account that requires logging in or account creation to see its contents, and thus cannot be accessed.
This reviewer urges the authors to consider uploading the code onto an academic data repository from the many on offer (e.g. Dryad, Zenodo, OSF). Some repositories offer an option to share a private link (e.g. Zenodo) to the folder that can then be shared only with reviewers so it is not completely public.
This is a computational paper, and the credibility of the results is based on the code used to generate them.
The code is available at GitHub as required:
https://github.com/omermazar/Colony-Exit-Bat-Simulation
(2) Abstract:
Line 22: 'To explore whether..' - replace 'whether' with 'how'?
The sentence was rephrased as suggested by the reviewer.
(2) Main text:
Line 43: '...which may share...' - correct to '...which share...', as elegantly framed in the authors' previous work - jamming avoidance is unavoidable because all FM bats of a species still share >90% of spectral bandwidth despite a few kHz shift here and there.
The sentence was rephrased as suggested by the reviewer.
Line 49: The authors may wish to additionally cite the work of Fawcett et al. 2015 (J. Comp. Phys A & Biology Open)
Thank you for the suggestion. We have included a citation to the work of Fawcett et al. (2015) in the revised manuscript.
Line 61: This statement does not match the recent state of the literature. While the previous models may have assumed that all neighbours can be detected, there are models that specifically study the role of limited interaction arising from the potential inability to track all neighbours, and the effect of responding to only one/few neighbours at a time e.g. Bode et al. 2011 R. Soc. Interface, Jhawar et al. 2020 Nature Physics.
We have added citations to the important studies suggested by the reviewer, as detailed in the Public Review above.
Line 89: '..took all interference signals into account...' - what is meant by 'interference signals' - are the authors referring to reflections, unclear.
We have revised the sentence and detailed the acoustic signals involved in the process: self-generated echoes, calls from conspecifics, and echoes from cave walls and other bats evoked by those calls, see lines 99-106.
Figure 1A: The colour scheme with overlapping points makes the figure very hard to understand what is happening. The legend has colours from subfigures B-D, adding to the confusion.
What does the yellow colour represent? This is not clear. Also, in general, the color schemes in the simulation trajectories and the legend are not the same, creating some amount of confusion for the reader. It would be good to make the colour schemes consistent and visually separable (e.g. consp. call direct is very similar to consp. echo from consp. call), and perhaps also if possible add a higher resolution simulation visualisation. Maybe it is best to separate out the colour legends for each sub-figure.
The updated figure now includes clearer, more visually separable colors, and consistent color coding across all sub-panels. The yellow trajectory representing the focal bat’s flight path is now explicitly labeled, and we adjusted the color mapping of acoustic signals (e.g., conspecific calls vs. echoes) to improve distinction. We also revised the figure caption accordingly and ensured that the legend is aligned with the updated visuals. These modifications aim to enhance interpretability and reduce ambiguity for the reader.
Figure C3: What is 'FB Channel', this is not explained in the legend.
FB Channel’ stands for ‘Filter Bank Channel’. This clarification has been added to the caption of Figure 1.
Figure 3: Visually noticing that the colour legend is placed only on sub-figure A is tricky and readers may be left searching for the colour legend. Maybe lay out the legend horizontally on top of the entire figure, so it stands out?
We have adjusted the placement of the color legend in Figure 3 to improve visibility and consistency.
Line 141: '..the probability of exiting..' - how is this probability calculated - not clear.
We have clarified in the revised text that the probability of exiting the cave within 15 seconds is defined as the number of bats that exited the cave within that time divided by the total number of bats in each scenario, see lines 159160.
Line 142: What are the sample sizes here - i.e. how many simulation replicates were performed?
We have clarified the number of repetitions in each scenario the revised text, as detailed in the Public Review above.
Line 151: 'The jamming probability,...number of jammed echoes divided by the total number of reflected echoes' - it seems like these are referring to 'own' echoes or first-order reflections, it is important to clarify this.
The reviewer is right. We have clarified it in the revised text, see lines 173175.
Line 153: '..with a maximum difference of ...' - how is this difference calculated? What two quantities are being compared - not clear.
We have revised the text to clarify that the 14.3% value reflects the maximum difference in jamming probability between the RM and PK models, which occurred at a density of 10 bats. The values at each density are shown in Figure 2D, see lines 175-177.
Line 221: '..temporal aggregation helps..' - I'm assuming the authors meant temporal integration? However, I would caution against using the exact term 'temporal integration' as it is used in the field of audition to mean something different. Perhaps something like 'sensory integration' , or 'multi-call integration'
To avoid ambiguity and better reflect the process modeled in our work, we have replaced the term "temporal aggregation" with "multi-call integration" throughout the revised manuscript. This term more accurately conveys the idea of combining information from multiple echolocation calls without conflicting with existing terminology.
(4) Discussion
Lines 302: 'Our model suggests...increasing the call-rate..' - not clear where this is explicitly tested or referred to in this manuscript. Can't see what was done to measure/quantify the effect of this variable in the Methods or anywhere else.
We have rephrased this paragraph as detailed in the Public Review above, see lines 346-349.
Line 319: 'spatial interference' - unclear what this means. This reviewer would strongly caution against creating new terms unless there is an absolute need for it. What is meant by 'interference' in this paper is hard to assess given that the word seems to be used as a synonym for jamming and also for actual physical wave-based interference.
We have rephrased this paragraph as detailed in the Public Review above, see line 119-120, 366-367.
Line 323: '..no benefit beyond a certain level...' - also not clear where this is explicitly tested. It seems like there was a set of simulations run for a variety of parameters but this is not written anywhere explicitly. What type of parameter search was done, was it all possible parameter combinations - or only a subset? This is not clear.
We have rephrased this paragraph as detailed in the Public Review above, see lines 372-375.
Line 324: '..ca. 110 dB-SPL.' - what reference distance?
All call levels were simulated and reported in dB-SPL, referenced at 0.1 meters from the emitting bat. We have clarified it in the revised text in the relevant contexts and specifically in line 529.
(5) Methods
Line 389 : '...over a 2 x 1.5 m2 area..' It took a while to understand this statement and put it in context. Since there is no previous description of the entire L-arena, the reviewer took it to mean the simulations happened over the space of a 2 x 1.5 m2 area. Include a top-down description of the simulation's spatial setup and rephrase this sentence.
To address the confusion, we revised the text to clarify that the full simulation environment represents a corridor-shaped cave measuring 14.5 × 2.5 meters, with a right-angle turn located 5.5 meters before the exit, as shown in Figure 1A. The 2 × 1.5 m area refers specifically to the small zone at the far end of the cave where bats begin their flight. The revised description now includes a clearer spatial overview to prevent ambiguity, see lines 456-460.
Line 398: Replace 'High proximity' with 'Close proximity'
Replaced.
Line 427: 'uniform target strength of -23 dB' - at what distance is this target strength defined? Given the reference distance can vary by echolocation convention (0.1 or 1 m), one can't assess if this is a reasonable value or not.
The reference distance for the reported target strength is 1 meter, in line with standard acoustic conventions. We have revised the text to clarify this explicitly (line 531).
Also, independent of the reference distance, particularly with reference to bats, the target strength is geometry-dependent, based on whether the wings are open or not. Using the entire wingspan of a bat to parametrise the target strength is an overestimate of the available reflective area. The effective reflective area is likely to be somewhere closer to the surface area of the body and a fraction of the wingspan together. This is important to note and/or mention explicitly since the value is not experimentally parametrised.
For comparison, experimentally based measurements used in Goetze et al. 2016 are -40 dB (presumably at 1 m since the source level is also defined at 1 m?), and Beleyur & Goerlitz 2019 show a range between -43 to -34 dB at 1 m.
We agree with the reviewer that target strength in bats is strongly influenced by their geometry, particularly wing posture during flight. In our model, we simplified this aspect by using a constant target strength, as the detailed temporal variation in body and wing geometry is pseudo-random and not explicitly modeled. We acknowledge that this is a simplification, and have now stated this limitation clearly in the revised manuscript. We chose a fixed value of –23 dB at 1 meter to reflect a plausible mid-range estimate, informed by anatomical data and consistent with values reported for similarly sized species (Beleyur and Goerlitz, 2019). To support this, we directly measured the target strength of a 3D-printed RM bat model, obtaining –32dB.
Moreover, a sensitivity analysis across a wide range (–49 to –23 dB) confirmed that performance metrics remain largely stable, indicating that our conclusions are not sensitive to this parameter, and suggesting that our results hold for different-sized bats. See lines 384-390, 533-538, and Supplementary Figures 3 and 4 in the revised article.
Line 434: 'To model the bat's cochlea...'. Bats have two cochleas. This model only describes one, while the agents are also endowed with the ability to detect sound direction - which requires two ears/cochleas.... There is missing information about the steps in between that needs to be provided.
We appreciate the reviewer’s observation. Indeed, our model is monaural, and simulates detection using a single cochlear-like filter bank receiver. We have clarified this in the revised text to avoid confusion. This paragraph specifically describes the detection stage of the auditory processing pipeline. The localization process, which builds on detection and includes directional estimation, is described in the following paragraph (see line 583 onward), as discussed in the next comment and response.
Line 457: 'After detection, the bat estimates the range and Direction of Arrival...' This paragraph describes the overall idea, but not the implementation. What were the inputs and outputs for the range and DOA calculation performed by the agent? Or was this information 'fed' in by the simulation framework? If there was no explicit DOA step that the agent performed, but it was assumed that agents can detect DOA, then this needs to be stated.
In the current simulation, the Direction of Arrival (DOA) was not modeled via an explicit binaural processing mechanism. Instead, based on experimental studies (Simmons et al., 1983; Popper and Fay, 1995). we assumed that bats can estimate the direction of an echo with an angular error that depends on the signal-to-noise ratio (SNR). Accordingly, the inputs to the DOA estimation were the peak level of the desired echo, noise level, and the level of acoustic interference. The output was an estimated direction of arrival that included a random angular error, drawn from a normal distribution whose standard deviation varied with the SNR. We have revised the relevant paragraph (Lines 583-592) to clarify this implementation.
Line 464: 'To evaluate the impact of the assumption...' - the 'self' and 'non-self' echoes can be distinguished perhaps using pragmatic time-delay cues, but also using spectro-temporal differences in individual calls/echoes. Do the agents have individual call structures, or do all the agents have the same call 'shape'? The echolocation parameters for the two modelled species are given, but whether there is call parameter variation implemented in the agents is not mentioned.
In our relatively simple model, all individuals emit the same type of chirp call, with parameters adapted only based on the distance to the nearest detected object. However, individual variation is introduced by assigning each bat a terminal frequency drawn from a normal distribution with a standard deviation of 1 kHz, as described in the revised version -lines 519-520. This small variation is not used explicitly as a spectro-temporal cue for echo discrimination.
In our model, all spectro-temporal variations—whether due to call structure or variations resulting from overlapping echoes from nearby reflectors—are processed through the filter bank, which compares the received echoes to the transmitted call during the detection stage. As such, the detection process itself can act as a discriminative filter, to some extent, based on similarity to the emitted call.
We acknowledge that real bats likely rely on a variety of spectro-temporal features for distinguishing self from non-self-echoes—such as call duration, received level, multi-harmonic structure, or amplitude modulation. In our simulation, we focus on comparing two limiting conditions: full recognition of self-generated echoes versus full confusion. Implementing a more nuanced self-recognition mechanism based on temporal or spectral cues would be a valuable extension for future work.
(6) References
Reference 22: Formatting error - and extra '4' in the reference.
The error has been fixed.
(7) Thoughts/comments
Even without 'recogntion' of walls & conspecifics, bats may be able to avoid obstacles - this is a neat result. Also, using their framework the authors show that successful 'blind' object-agnostic obstacle avoidance can occur only when supported by some sort of memory. In some sense, this is a nice intermediate step showing the role of memory in bat navigation. We know that bats have good long-term and long-spatial scale memory, and here the authors show that short-term spatial memory is important in situations where immediate sensory information is unreliable or unavailable.
We appreciate the reviewer’s thoughtful summary. Indeed, one of the main takeaways of our study is that successful obstacle avoidance can occur even without explicit recognition of walls or conspecifics—provided that a clustered multi-call integration is in place. Our model shows that when immediate sensory information is unreliable, integrating detections over time becomes essential for effective navigation. This supports the broader view that memory, even on short timescales, plays an important role in bat behavior.
(8) Reporting GLM results
The p-value, t-statistic, and degrees of freedom are reported consistently across multiple GLM results. However, the most important part which is the effect size is not consistently reported - and this needs to be included in all results, and even in the table. The effect size provides an indicator of the parameter's magnitude, and thus scientific context.
We agree that the effect size provides essential scientific context. In fact, we already include the effect size explicitly in Table 1, as shown in the “Effect Size” column for each tested parameter. These values describe the magnitude of each parameter’s effect on exit probability, jamming probability, and collision rate. In the main text, effect sizes are presented as concrete changes in performance metrics (e.g., “exit probability increased from 20% to 87%,” or “with a decrease of 3.5%±8% to 5.5%±5% (mean ± s.e.)”), which we believe improves interpretability and scientific relevance.
To further clarify this in the main text, we have reviewed the reported results and ensured that effect sizes are mentioned more consistently wherever GLM outcomes are discussed. Additionally, we have added a brief note in the table caption to emphasize that effect sizes are provided for all tested parameters.
The 'tStat' appears multiple times and seems to be the output of the MATLAB GLM function. This acronym is specific to the MATLAB implementation and needs to be replaced with a conventionally used acronym such as 't', or the full form 't-statistic' too. This step is to keep the results independent of the programming language used.
We have replaced all instances of tStat with the more conventional term ‘t’ throughout the manuscript to maintain consistency with standard reporting practices.
Reviewer #2 (Recommendations for the authors):
In addition to my public review, I had a few minor points that the authors may want to consider when revising their paper.
(1) Figures 2, 3, and 4 may benefit from using different marker styles, in addition to different colors, to show the different cases.
Thank you for the suggestion. In Figures 2–4, the markers represent means with standard error bars. To maintain clarity and consistency across all conditions, we have chosen to keep a standardized marker style – and we clarify this in the legend. We found that varying only the colors is sufficient for distinguishing between conditions without introducing visual clutter.
(2) The text "PK" in the inset for Figure 2A is very difficult to read. I would suggest using grey as with "RM" in the other inset.
We have updated the insert in Figure 2A to improve legibility.
(3) Are the error bars in Figure 3 very small? I wasn't able to see them. If that is the case, the authors may want to mention this in the caption.
You are correct—the error bars are present in all plots but appear very small due to the large number of simulation repetitions and low variability. We have revised the caption to explicitly mention this.
(4) The species name of PK is spelled inconsistently (kuhli, khulli, and kuhlii).
We have corrected the species name throughout the manuscript.
(5) Table 1 is a great condensation of all the results, but the time to exit is missing. It may be helpful if summary statistics on that were here as well.
We have added time-to-exit to the effect size column in Table 1, alongside the other performance metrics, to provide a more complete summary of the simulation results.
(6) I may have missed it, but why are there two values for the exit probability when nominal flight speed is varied?
The exit probability was not monotonic with flight speed, but rather showed a parabolic trend with a clear optimum. Therefore, we reported two values representing the effect before and after the peak. We have clarified this in the revised table and updated the caption accordingly.
(7) Table 2 has an extra header after the page break on page 18.
The extra header in Table 2 after the page break has been removed in the revised manuscript.
(8) The G functions have 2 arguments in their definitions and Equation 1, but only one argument in Equations 2 and 3. I wasn't able to see why.
Thank you for pointing this out. You are correct—this was a typographical error. We have corrected the argument notation in Equations 2 and 3 and explicitly included the frequency dependence of the gain (G) functions in both equations.
(9) D_txrx was not defined but it was used in Equation 2.
The variable D_txrx is defined in the equation notation section as: D<sub>₍ₜₓ</sub>r<sub>ₓ</sub> – the distance [m] between the transmitting conspecific and the receiving focal bat, from the transmitter’s perspective. We have now ensured that this definition is clearly linked to Equation 2 in the revised text. Moreover, we have added a supplementary figure that illustrates the geometric configuration defined by the equations to further support clarity, as described in the Public Review above.
(10) It was hard for me to understand what was meant by phi_rx and phi_tx. These were described as angles between the rx or tx bats and the target, but I couldn't tell what the point defining the angle was. Perhaps a diagram would help, or more precise definitions.
We have revised the caption to provide clearer and more precise definitions Additionally, we have included a geometric diagram as a supplementary figure, as noted in the Public Review above, to visually clarify the spatial relationships and angle definitions used in the equations, see lines 498-499.
(11) Was the hearing threshold the same for both species?
Yes. We have clarified it in the revised version.
(12) Collision avoidance is described as turning to the "opposite direction" in the supplemental figure explaining the model. Is this 90 degrees or 180 degrees? If 90 degrees, how do these turns decide between right and left?
In our model, the bat does not perform a fixed 90° or 180° turn. Instead, the avoidance behavior is implemented by setting the maximum angular velocity in the direction opposite to the detected echo. For example, if the obstacle or conspecific is detected on the bat’s right side, the bat begins turning left, and vice versa.
This turning direction is re-evaluated at each decision step, which occurs after every echolocation pulse. The bat continues turning in the same direction if the obstacle remains in front, otherwise it resumes regular pathfinding. We have clarified this behavior in the updated figure caption and model description, see lines 478-493.
Reviewer #3 (Recommendations for the authors):
(1) Lines 27-31: These sentences mischaracterize the results. This claim appears to equate "the model works" with "this is what bats actually do." Also, the model does not indicate that bats' echolocation strategies are robust enough to mitigate the effects of jamming - this is self-evident from the fact that bats navigate successfully via echolocation in dense groups.
Thank you for the comment. Our aim was not to claim that the model confirms actual bat behavior, but rather to demonstrate that simple and biologically plausible strategies—such as signal redundancy and basic pathfinding—are sufficient to explain how bats might cope with acoustic interference in dense settings. We have revised the wording to better reflect this goal and to avoid overinterpreting the model's implications.
See abstract in the revised version.
(2) Line 37: This number underestimates the number of bats that form some of the largest aggregations of individuals worldwide - the free-tailed bats can form aggregations exceeding several million bats.
We have revised the text to reflect that some bat species, such as free-tailed bats, are known to form colonies of several million individuals, which exceed the typical range. The updated sentence accounts for these extreme cases, see lines 36-37.
(3) The flight densities explained in the introduction and chosen references are not representative of the literature - without providing additional justification for the chosen species, it can be interpreted that the selection of the species for the simulation is somewhat arbitrary. If the goal is to model dense emergence flight, why not use a species that has been studied in terms of acoustic and flight behavior during dense emergence flights---such as Tadarida brasiliensis?
Our goal was to develop a general model applicable to a broad class of FMecholocating bat species. The two species we selected—Pipistrellus kuhlii (PK) and Rhinopoma microphyllum (RM)—span a wide range of signal characteristics: from wideband (PK) to narrowband (RM), providing a representative contrast in call structure.
Although we did not include Tadarida brasiliensis (TB) specifically, its echolocation calls are acoustically similar to RM in terminal frequency and fall between PK and RM in bandwidth. Therefore, we believe our findings are likely to generalize to TB and other FM-bats.
Moreover, as noted in a previous response, the average inter-bat distance in our highest-density simulations (0.27 m) is still smaller than those reported for Tadarida brasiliensis during dense emergences—further supporting the relevance of our model to such scenarios.
To support broader applicability, we also provide a supplementary graphical user interface (GUI) that allows users to modify key echolocation parameters and explore their impact on behavior—making the framework adaptable to additional species, including TB.
(4) Line 78: It is not clear how (or even if) the simulated bats estimate the direction of obstacles. The explanation given in lines 457-463 is quite confusing. What is the acoustic/neurological mechanism that enables this direction estimation? If there is some mechanism (such as binaural processing), how does this extrapolate to 3D?
This comment echoes a similar concern raised by a previous reviewer. As explained earlier, in the current simulation, the Direction of Arrival (DOA) was not modeled via an explicit binaural processing mechanism. The complete is detailed in to Reviewer #1, Line 457. This implementation is now clarified in the revised text, and a detailed description of the localization process is also provided in the Methods section (lines 583-592).
(5) The authors propose they are modeling the dynamic echolocation of bats in the simulation (line 79), but it appears (whether this is due to a lack of information in the manuscript or true lack in the simulation) that the authors only modeled a flight response. How did the authors account for bats dynamically changing their echolocation? This is unclear and from what I can tell may just mean that the bats can switch between foraging phase call types depending on the distance to a detected obstacle. Can the authors elaborate more on this?
The echolocation behavior of the bats—including dynamic call adjustments— was implemented in the simulation and is described in detail in the Methods section (lines 498-520 and Table 2). To avoid redundancy, the Results chapter originally referred to this section, but we have now added a brief explanation in the Results to clarify that the bats’ call parameters (IPI, duration, and frequency range) adapt based on the distance to detected objects, following empirically documented echolocation phases ("search," "approach," "buzz"). These dynamics are consistent with established bat behavior during navigation in cluttered environments such as caves.
(6) Figure 1 C3: "Detection threshold": what is this and how was it derived?
The caption also mentions yellow arrows, but they are absent from the figure. C4: Each threshold excursion is marked with an asterisk, but there are many more excursions than asterisks. Why are only some marked? Unclear.
C3: The detection threshold is determined dynamically. It is set to the greater of either 7 dB above the noise level (0 dB-SPL)(Kick, 1982; Saillant et al., 1993; Sanderson et al., 2003; Boonman et al., 2013) or the maximal received level minus 70 dB, effectively applying a dynamic range of 70 dB. This clarification has been added to the Methods section. The yellow arrow has been added.
C4: Thank you for this important observation. Only peaks marked with asterisks represent successful detections—those that were identified in both the interference-free and full detection conditions, as explained in the Methods. Other visible peaks result from masking signals or overlapping echoes from nearby reflectors, but they do not meet the detection criteria. To keep the figure caption concise, we have elaborated on this process more clearly in the revised Methods section. We added this information to the legend
(7) Figure 2: A line indicating RM, No Masking is absent
Thank you for pointing this out. The missing line for RM, No Masking has now been added in the revised version of Figure 2.
(8) Line 121: "reflected off conspecifics". Does this mean echoes due to conspecifics?
The phrase "reflected off conspecifics" refers to echoes originating from the bat’s own call and reflected off the bodies of nearby conspecifics. We have clarified the wording in the revised text to avoid confusion
(9) Line 125: Why are low-frequency channels stimulated by higher frequencies? This needs further clarification.
The cochlear filter bank in our model is implemented using gammatone filters, each modeled as an 8th-order Butterworth filter. Due to the non-ideal filter response and relatively broad bandwidths—especially in the lower-frequency channels—strong energy from the beginning of the downward FM chirp (at higher frequencies) can still produce residual activation in lower-frequency channels. While these stimulations are usually below the detection threshold, they may still be visible as early sub-threshold responses. Given the technical nature of this explanation (a property of the filter implementation) and it does not influence the detection outcomes, we have chosen not to elaborate on it in the figure caption or Methods.
(10) Lines 146-150: This is an interesting finding. Is there a theoretical justification for it?
This outcome arises directly from the simulation results. As noted in the Discussion (lines 359-365), although Pipistrellus kuhlii (PK) shows a modest advantage in jamming resistance due to its broader bandwidth, the redundancy in sensory information across calls—enabled by frequent echolocation—appears to compensate for these signal differences. As a result, the small variations in echo quality between species do not translate into significant differences in performance. We speculate that if the difference in jamming probability had been larger, performance disparities would likely have emerged.
(11) Line 151: The authors define a jammed echo as an echo entirely missed due to masking. Is this appropriate? Doesn't echo mis-assignment also constitute jamming?
We agree that echo mis-assignment can also degrade performance; however, in our model, we distinguish between two outcomes: (1) complete masking (echo not detected), and (2) detection with a localization error. As explained in the Methods (lines 500–507), we run the detection analysis twice—once with only desired echoes (“interference-free detection”) and once including masking signals (“full detection”). If a previously detected echo is no longer detected, it is classified as a jammed echo. If the echo is still detected but the delay shifts by more than 100 µs compared to the interference-free condition, it is also considered jammed. If the delay shift is smaller, it is treated as a detection with localization error rather than full jamming. We have clarified this distinction in the revised Methods section.
(12) Figure 2-E: Detection probability statistics are of limited usefulness without accompanying false alarm rate (FAR) statistics. Do the authors have FAR numbers?
We understand FAR to refer to instances where masking signals or other acoustic phenomena are mistakenly interpreted as real echoes from physical objects. As explained in the manuscript, we implemented two model versions: one without confusion, and one with full confusion.
Figure 2E reports detection performance under the non-confusion model, in which only echoes from actual physical reflectors are used, and no false detections occur—hence, the false alarm rate is effectively zero in this condition. In the full-confusion model, all detected echoes—including those originating from masking signals or conspecific calls—are treated as valid detections, which may include false alarms. However, we did not explicitly quantify the false alarm rate as a separate metric in this simulation.
We agree that tracking FAR could be informative and will consider incorporating it into future versions of the model.
(13) Line 161: RM bats suffered from a significantly higher probability of the "desired conspecific's echoes" being jammed. What does "desired conspecific's echoes" mean? This is unclear.
The term “desired conspecific's echoes” refers to echoes originating from the bat’s own call, reflected off nearby conspecifics, which are treated as relevant reflectors for collision avoidance. We have revised the wording in the text for clarity.
(14) Line 188: Why didn't the size of the integration window affect jamming probability? I couldn't find this explained in the discussion.
The jamming probability in our analysis is computed at the individual-echo level, prior to any temporal integration. Since the integration window is applied after the detection step, it does not influence whether a specific echo is masked (i.e., jammed) or not. Therefore, as expected, we did not observe a significant effect of integration window size on jamming probability.
(15) Line 217-218: Why do the authors think this would be?
Thank you for the thoughtful question. We agree that, in theory, increasing call intensity should raise the levels of both desired echoes and masking signals proportionally. However, in our model, the environmental noise floor and detection threshold remain constant, meaning that higher call intensities increase the signal-to-noise ratio (SNR) more effectively for weaker echoes, especially those at longer distances or with low reflectivity. This could lead to a higher likelihood of those echoes crossing the detection threshold, resulting in a small but measurable reduction in jamming probability.
Additionally, the non-linear behavior of the filter-bank receiver—including such as thresholding at multiple stages—can introduce asymmetries in how increased signal levels affect the detection of target versus masking signals.
That said, the effect size was small, and the improvement in jamming probability did not translate into any significant gain in behavioral performance (e.g., exit probability or collision rate), as shown in Figure 3C.
(16) Line 233: I'm not sure I understand how a slightly improved aggregation model that clustered detected reflectors over one-second periods is different. Doesn't this just lead to on average more calls integrated into memory?
While increasing the memory duration does lead to more detections being available, the enhanced aggregation model (we now refer to as multi-call clustering) differs fundamentally from the simpler one. As detailed in the Methods, it includes additional processing steps: clustering spatially close detections, removing outliers, and estimating wall directions based on the spatial structure of clustered echoes. In contrast, the simpler model treats each detection as an isolated point without estimating obstacle orientation. These additional steps allow for more robust environmental interpretation and significantly improve performance under high-confusion conditions. We have clarified it in revised text (lines 606-616) and added a Supplementary Figure 2B.
(17) Table 1: What about conspecific target strength?
We have now added the conspecific target strength as a tested parameter in Table 1, along with its tested range, default value, and measured effect sizes. A detailed sensitivity analysis is also presented in Supplementary Figure 4, demonstrating that variations in conspecific target strength had relatively minor effects on performance metrics.
(18) Figure 3-A: The x-axis is the number of calls in the integration window. But the leftmost sample on each curve is at 0 calls. Shouldn't this be 1?
“0 calls” refers to the case where only the most recent call is used for pathfinding—without integrating any information from prior calls. The x-axis reflects the number of previous calls stored in memory, so a value of 0 still includes the current call. We’ve clarified this terminology in the figure caption.
(19) Lines 282-283: This statement needs to be clarified that it is with the constraints of using a 2D simulation with at most 33 bats/m^2. It also should be clarified that it is assumed the bat can reliably distinguish between its own echoes and conspecific echoes, which is a very important caveat.
We have revised the text to clarify that the results are based on a 2D simulation with a maximum tested density of 33 bats/m². We also now explicitly state that the model assumes bats can distinguish between their own echoes and those generated by conspecifics—an assumption we recognize as a simplification. These clarifications help place the results within the scope and constraints of the simulation. Moreover, as described in the text (and noted in previous response): the average distance to the nearest bat in our simulation is 0.27m (with 100 bats), whereas reported distances in very dense colonies are 0.5m
(20) Line 294: What is this sentence referring to?
The sentence refers to the finding that, even under high bat densities, a substantial portion of the echoes—particularly those reflected from nearby obstacles (e.g., 1 m away)—were jammed due to masking. Nevertheless, the bats in the simulation were still able to navigate successfully using partial sensory input. We have clarified the sentence in the revised text to make this point more explicit, see line 333-336.
(21) Line 302: Was jamming less likely when IPI was higher or lower? I could not find this demonstrated anywhere in the manuscript.
We agree that the original text was not sufficiently clear on this point. While we did not explicitly test fixed IPI values as a parameter, the model does simulate the natural behavior of decreasing IPI as bats approach obstacles. This behavior is supported by empirical observations and is incorporated into the echolocation dynamics of the simulation. We have clarified this point in the revised text (see Lines 346-351) and explained that while lower IPI introduces more acoustic overlap, it also increases redundancy and improves detection through temporal integration.
(22) Lines 313-314: This is an interesting assumption, but it is not evident that is substantiated by the references.
The claim is based on well-established principles in signal processing and bioacoustics. Wideband signals—such as those emitted by PK bats— distribute their energy over a broader frequency range, which makes them inherently more resistant to narrowband interference and masking. This concept is commonly applied in both biological and artificial sonar systems and is supported by empirical studies in bats and theory in acoustic sensing.
For example, Beleyur & Goerlitz (2019) demonstrate that broader bandwidth calls improve detection in cluttered and jamming-prone environments. Similarly, Ulanovsky et al. (2004) and Schnitzler & Kalko (200) discuss how FM bats' wideband calls enhance temporal and spatial resolution, helping to reduce the impact of overlapping signals from conspecifics. These findings align with communication theory where spread-spectrum techniques improve robustness in noisy environments.
We agree with the reviewer that this is an important point and we have updated the manuscript to clarify this rationale and cite the relevant literature accordingly – lines 631-363,
(23) Lines 318-319: What is the justification for "probably"? Isn't this just a supposition?
We agree with the reviewer’s point and have rephrased the sentence
(24) Line 320: How does this 63% performance match the sentence in line 295?
The sentence in Line 295 refers to the overall ability of the bats to navigate successfully despite high jamming levels, highlighting the robustness of the strategy under challenging conditions. The figure in Line 320 (63%) quantifies this performance under the most extreme simulated scenario (100 bats / 3 m²), where both spatial and acoustic interferences are maximal. We have rephrased the text in the revised version (lines 324-327).
(25) Lines 341-345: It seems like this is more likely to be the main takeaway of the paper.
As noted in the Public Review above, there is substantial literature supporting the assumption that bats can recognize their own echoes and distinguish them from those of conspecifics (e.g., Schnitzler, Bioscience, 2001; Kazial et al., 2001, 2008; Burnett & Masters, 2002; Chiu et al., 2009; Yovel et al., 2009; Beetz & Hechavarría, 2022). Therefore, we consider our assumption of selfrecognition to be well-supported, at least under typical conditions. That said, we agree that the impact of echo confusion on performance is significant and highlights a critical challenge in dense environments.
To our knowledge, this is the first computational model to explicitly simulate both self-recognition and full echo confusion under high-density conditions. We believe that the combination of modeled constraints and the demonstrated robustness of simple sensorimotor strategies, even under worst-case assumptions, is what makes this contribution both novel and meaningful.
(26) Lines 349-350: What is the aggregation model? What is meant by "integration"?
We have revised the text to clarify that the “aggregation model” refers to a multi-call clustering process that includes clustering of detections, removal of outliers, and estimation of wall orientation, as described in detail in the revised Methods and Results sections.
(27) Line 354: Again, why isn't this the assumption we're working under?
As addressed in our response to Comment 25, our primary model assumes that bats can recognize their own echoes—an assumption supported by substantial empirical evidence. The alternative "full confusion" model was included to explore a worst-case scenario and highlight the behavioral consequences of failing to distinguish self from conspecific echoes. We assume that real bats may experience some degree of echo misidentification; however, our assumption of full confusion represents a worst-case scenario.
(28) Line 382: "Under the assumption that..." I agree that bats probably can, but if we assume they can differentiate them all, where's the jamming problem?
The assumption that bats can theoretically distinguish between different signal sources applies after successful detection. However, the jamming problem arises during the detection and localization stages, where acoustic interference can prevent echoes from crossing the detection threshold or distort their timing.
(29) Lines 386-387: The paper referenced focused on JAR in the context of foraging. What changes were made to the simulation to switch to obstacle avoidance?
While the simulation framework in Mazar & Yovel (2020) was developed to study jamming avoidance during foraging, the core components—such as the acoustic calculations, receiver model, and echolocation behavior—remain applicable. For the current study, we adapted the simulation extensively to address colony-exit behavior. These modifications include modeling cave walls as acoustic reflectors, implementing a pathfinding algorithm, integrating obstacle-avoidance maneuvers, and adapting the integration window and integration processes. These updates are detailed throughout the Methods section.
(30) Line 400-402: Something doesn't add up with the statement: each decision relies on an integration window that records estimated locations of detected reflectors from the last five echolocation calls, with the parameter being tested between 1 and 10 calls. Can the authors reword this to make it less confusing?
We have reworded the sentence to clarify that the default integration window includes five calls, while we systematically tested the effect of using 1 to 10 calls, see lines 486-487.
(31) Line 393: "30 deg/sec" why was this value chosen?
The turning rate of 30 deg/sec was manually selected to approximate the curvature of natural foraging flight paths observed in Rhinopoma microphyllum using on-board tags. Moreover, in Mazar & Yovel (2020), we showed that the flight dynamics of simulated bats in a closed room closely matched those of Pipistrellus kuhlii flying in a room of similar dimensions. However, in the current simulation, bats rarely follow a random-walk trajectory due to the structured environment and frequent obstacle detection. As a result, this parameter has no meaningful impact on the simulation outcomes.
(32) Line 412: "Harmony" --- do you mean harmonic? And what is the empirical evidence that RM bats use the 2nd harmonic compared to the 1st?
Perhaps showing a spectrogram of a real RM signal would be helpful.
The typo-error was corrected. For reference See (Goldshtein et al., 2025)
(33) Table 2: Something is incorrect with the table. The first row on the next page is the wrong species name. Also, where are the citations for these parameter values?
The table header has been corrected in the revised version. The parameter values for flight and echolocation behavior were derived from existing literature and empirical data: Pipistrellus kuhlii parameters were based on Kalko (1995), and Rhinopoma microphyllum parameters were extracted from our own recordings using on-board tags, as described in Goldstein et al. (2025). We have added the appropriate citations to Table 2.
(34) Line 442: How was the threshold level chosen?
The detection threshold in each level is set to the greater of either 7 dB above the noise level (0 dB-SPL) or the maximal received level minus 70 dB, effectively applying a dynamic range of 70 dB.
(35) Line 445: 100 micros: This is about 3cm. The resolution of PK is about 1cm. For RM it's about 10cm. So, this window is generous for PK, but too strict for RM.
To keep the model simple and avoid introducing species-specific detection thresholds, we selected a biologically plausible compromise that could reasonably apply to both species. This simplification ensures consistency across simulations while remaining within the known behavioral range.
(36) Line 448: What is the spectrum of the Gaussian noise, and did it change between PK and RM?
We used the same white Gaussian noise with a flat spectrum across the relevant frequency range (10–80 kHz) for both species. We have clarified this in the revised text in lines 570-572.
(37) Line 451: 4 milliseconds is 1.3m. Is this appropriate?
The 4 milliseconds window was selected based on established auditory masking thresholds described in Mazar & Yovel (2020), and supported by (Popper and Fay, 1995) ch. 2.4.5, ((Blauert, 1997), ch. 3.1 and (Mohl and Surlykke, 1989). These values provide conservative lower bounds on bats’ ability to cope with masking (Beleyur and Goerlitz, 2019). For simplicity, we used constant thresholds within each window, see lines 574-576.
(38) Line 452: Citation for the forward and backward masking durations?
See the to the previous comment.
(39) Lines 460-461: This is unclear. How does the bat get directional information? The authors claim to be able to measure direction-of-arrival for each detection, but it is not clear how this is done
As noted in our response to Reviewer 1 (Comment on Line 457), directional information is not computed via an explicit binaural model. Instead, we assume the bat estimates the direction of arrival with an angular error that depends on the SNR, based on established studies (e.g., Simmons et al., 1983; Popper & Fay, 1995). We have clarified this in the revised text in lines 583-592.
(40) Line 467: It seems like the authors are modeling pulse-echo ambiguity, at least in this one alternative model, which is good! However the alternative model doesn't get much attention in the paper. Is there a reason for this?
We would like to clarify that we did not model pulse-echo. In our confusion model, all echoes received within the IPI are attributed to the bat’s most recent call. This includes echoes that may in fact originate from conspecific calls, but the model does not assign self-echoes to earlier pulses or span multiple IPIs. Therefore, while the model captures echo confusion, it does not include true pulse-echo ambiguity. We have clarified this point in the revised text in lines 551-553.
(41) Line 41: "continuous" is more appropriate than "constant".
Thank you, we have rephrased the text accordingly.
(42) Line 69: "band width" should be one word.
Thank you, we have corrected it to “bandwidth”.
(43) Line 79: "bats" should be in the possessive.
Thank you, the text has been rephrased.
(44) Line 128: "convoluted" don't you mean "convolved"?
We have replaced “convoluted” with the correct term “convolved” in the revised text.
(45) Please check your references, as there are some incomplete citations and typos.
Thank you, we have reviewed and corrected all references for completeness and consistency.
References
Beetz, M.J. and Hechavarría, J.C. (2022) ‘Neural Processing of Naturalistic Echolocation Signals in Bats’, Frontiers in Neural Circuits, 16, p. 899370. Available at: https://doi.org/10.3389/FNCIR.2022.899370/BIBTEX.
Beleyur, T. and Goerlitz, H.R. (2019) ‘Modeling active sensing reveals echo detection even in large groups of bats’, Proceedings of the National Academy of Sciences of the United States of America, 116(52), pp. 26662–26668. Available at: https://doi.org/10.1073/pnas.1821722116.
Betke, M. et al. (2008) ‘Thermal Imaging Reveals Significantly Smaller Brazilian Free-Tailed Bat Colonies Than Previously Estimated’, Journal of Mammalogy, 89(1), pp. 18–24. Available at: https://doi.org/10.1644/07-MAMM-A-011.1.
Blauert, J. (1997) ‘Spatial Hearing: The Psychophysics of Human Sound Localization (rev. ed.)’.
Boerma, D.B. et al. (2019) ‘Wings as inertial appendages: How bats recover from aerial stumbles’, Journal of Experimental Biology, 222(20). Available at: https://doi.org/10.1242/JEB.204255/VIDEO-3.
Boonman, A. et al. (2013) ‘It’s not black or white-on the range of vision and echolocation in echolocating bats’, Frontiers in Physiology, 4 SEP(September), pp. 1–12. Available at: https://doi.org/10.3389/fphys.2013.00248.
Boonman, A.M., Parsons, S. and Jones, G. (2003) ‘The influence of flight speed on the ranging performance of bats using frequency modulated echolocation pulses’, The Journal of the Acoustical Society of America, 113(1), p. 617. Available at: https://doi.org/10.1121/1.1528175.
Burnett, S.C. and Masters, W.M. (2002) ‘Identifying Bats Using Computerized Analysis and Artificial Neural Networks’, North American Symposium on Bat Research, 9.
Chili, C., Xian, W. and Moss, C.F. (2009) ‘Adaptive echolocation behavior in bats for the analysis of auditory scenes’, Journal of Experimental Biology, 212(9), pp. 1392–1404. Available at: https://doi.org/10.1242/jeb.027045.
Fujioka, E. et al. (2021) ‘Three-Dimensional Trajectory Construction and Observation of Group Behavior of Wild Bats During Cave Emergence’, Journal of Robotics and Mechatronics, 33(3), pp. 556–563. Available at: https://doi.org/10.20965/jrm.2021.p0556.
Gillam, E.H. et al. (2010) ‘Echolocation behavior of Brazilian free-tailed bats during dense emergence flights’, Journal of Mammalogy, 91(4), pp. 967–975. Available at: https://doi.org/10.1644/09-MAMM-A-302.1.
Goldshtein, A. et al. (2025) ‘Onboard recordings reveal how bats maneuver under severe acoustic interference’, Proceedings of the National Academy of Sciences, 122(14), p. e2407810122. Available at: https://doi.org/10.1073/PNAS.2407810122.
Griffin, D.R., Webster, F.A. and Michael, C.R. (1958) ‘THE ECHOLOCATION OF FLYING INSECTS BY BATS ANIMAL BEHAVIOUR , Viii , 3-4’.
Hagino, T. et al. (2007) ‘Adaptive SONAR sounds by echolocating bats’, International Symposium on Underwater Technology, UT 2007 - International Workshop on Scientific Use of Submarine Cables and Related Technologies 2007, pp. 647–651. Available at: https://doi.org/10.1109/UT.2007.370829.
Hiryu, S. et al. (2008) ‘Adaptive echolocation sounds of insectivorous bats, Pipistrellus abramus, during foraging flights in the field’, The Journal of the Acoustical Society of America, 124(2), pp. EL51–EL56. Available at: https://doi.org/10.1121/1.2947629.
Jakobsen, L. et al. (2024) ‘Velocity as an overlooked driver in the echolocation behavior of aerial hawking vespertilionid bats’. Available at: https://doi.org/10.1016/j.cub.2024.12.042. Jakobsen, L., Brinkløv, S. and Surlykke, A. (2013) ‘Intensity and directionality of bat echolocation signals’, Frontiers in Physiology, 4 APR(April), pp. 1–9. Available at: https://doi.org/10.3389/fphys.2013.00089.
Jakobsen, L. and Surlykke, A. (2010) ‘Vespertilionid bats control the width of their biosonar sound beam dynamically during prey pursuit’, 107(31). Available at:
https://doi.org/10.1073/pnas.1006630107.
Kalko, E.K. V. (1995) ‘Insect pursuit, prey capture and echolocation in pipistrelle bats (Microchirptera)’, Animal Behaviour, 50(4), pp. 861–880.
Kazial, K.A., Burnett, S.C. and Masters, W.M. (2001) ‘ Individual and Group Variation in Echolocation Calls of Big Brown Bats, Eptesicus Fuscus (Chiroptera: Vespertilionidae) ’, Journal of Mammalogy, 82(2), pp. 339–351. Available at: https://doi.org/10.1644/15451542(2001)082<0339:iagvie>2.0.co;2.
Kazial, K.A., Kenny, T.L. and Burnett, S.C. (2008) ‘Little brown bats (Myotis lucifugus) recognize individual identity of conspecifics using sonar calls’, Ethology, 114(5), pp. 469– 478. Available at: https://doi.org/10.1111/j.1439-0310.2008.01483.x.
Kick, S.A. (1982) ‘Target-detection by the echolocating bat, Eptesicus fuscus’, Journal of Comparative Physiology □ A, 145(4), pp. 431–435. Available at: https://doi.org/10.1007/BF00612808/METRICS.
Kothari, N.B. et al. (2014) ‘Timing matters: Sonar call groups facilitate target localization in bats’, Frontiers in Physiology, 5 MAY. Available at: https://doi.org/10.3389/fphys.2014.00168.
Mohl, B. and Surlykke, A. (1989) ‘Detection of sonar signals in the presence of pulses of masking noise by the echolocating bat , Eptesicus fuscus’, pp. 119–124.
Moss, C.F. and Surlykke, A. (2010) ‘Probing the natural scene by echolocation in bats’, Frontiers in Behavioral Neuroscience. Available at: https://doi.org/10.3389/fnbeh.2010.00033.
Neretti, N. et al. (2003) ‘Time-frequency model for echo-delay resolution in wideband biosonar’, The Journal of the Acoustical Society of America, 113(4), pp. 2137–2145. Available at: https://doi.org/10.1121/1.1554693.
Popper, A.N. and Fay, R.R. (1995) Hearing by Bats. Springer-Verlag.
Roy, S. et al. (2019) ‘Extracting interactions between flying bat pairs using model-free methods’, Entropy, 21(1). Available at: https://doi.org/10.3390/e21010042.
Sabol, B.M. and Hudson, M.K. (1995) ‘Technique using thermal infrared-imaging for estimating populations of gray bats’, Journal of Mammalogy, 76(4). Available at: https://doi.org/10.2307/1382618.
Saillant, P.A. et al. (1993) ‘A computational model of echo processing and acoustic imaging in frequency- modulated echolocating bats: The spectrogram correlation and transformation receiver’, The Journal of the Acoustical Society of America, 94(5). Available at: https://doi.org/10.1121/1.407353.
Salles, A., Diebold, C.A. and Moss, C.F. (2020) ‘Echolocating bats accumulate information from acoustic snapshots to predict auditory object motion’, Proceedings of the National Academy of Sciences of the United States of America, 117(46), pp. 29229–29238. Available at: https://doi.org/10.1073/PNAS.2011719117/SUPPL_FILE/PNAS.2011719117.SAPP.PDF.
Sanderson, M.I. et al. (2003) ‘Evaluation of an auditory model for echo delay accuracy in wideband biosonar’, The Journal of the Acoustical Society of America, 114(3), pp. 1648– 1659. Available at: https://doi.org/10.1121/1.1598195.
Schnitzler, H., Bioscience, E.K.- and 2001, undefined (no date) ‘Echolocation by insecteating bats: we define four distinct functional groups of bats and find differences in signal structure that correlate with the typical echolocation ’, academic.oup.comHU Schnitzler, EKV KalkoBioscience, 2001•academic.oup.com [Preprint]. Available at: https://academic.oup.com/bioscience/article-abstract/51/7/557/268230 (Accessed: 17 March 2025).
Schnitzler, H.-U. et al. (1987) ‘The echolocation and hunting behavior of the bat,Pipistrellus kuhli’, Journal of Comparative Physiology A, 161(2), pp. 267–274. Available at: https://doi.org/10.1007/BF00615246.
Simmons, J.A. et al. (1983) ‘Acuity of horizontal angle discrimination by the echolocating bat , Eptesicus fuscus’. Simmons, J.A. and Kick, S.A. (1983) ‘Interception of Flying Insects by Bats’, Neuroethology and Behavioral Physiology, pp. 267–279. Available at: https://doi.org/10.1007/978-3-64269271-0_20.
Surlykke, A., Ghose, K. and Moss, C.F. (2009) ‘Acoustic scanning of natural scenes by echolocation in the big brown bat, Eptesicus fuscus’, Journal of Experimental Biology, 212(7), pp. 1011–1020. Available at: https://doi.org/10.1242/JEB.024620.
Theriault, D.H. et al. (no date) ‘Reconstruction and analysis of 3D trajectories of Brazilian free-tailed bats in flight’, cs-web.bu.edu [Preprint]. Available at: https://csweb.bu.edu/faculty/betke/papers/2010-027-3d-bat-trajectories.pdf (Accessed: 4 May 2023).
Ulanovsky, N. and Moss, C.F. (2008) ‘What the bat’s voice tells the bat’s brain’, Proceedings of the National Academy of Sciences of the United States of America, 105(25), pp. 8491– 8498. Available at: https://doi.org/10.1073/pnas.0703550105. Vanderelst, D. and Peremans, H. (2018) ‘Modeling bat prey capture in echolocating bats : The feasibility of reactive pursuit’, Journal of theoretical biology, 456, pp. 305–314.
Yovel, Y. et al. (2009) ‘The voice of bats: How greater mouse-eared bats recognize individuals based on their echolocation calls’, PLoS Computational Biology, 5(6). Available at: https://doi.org/10.1371/journal.pcbi.1000400.
Yovel, Y. and Ulanovsky, N. (2017) ‘Bat Navigation’, The Curated Reference Collection in Neuroscience and Biobehavioral Psychology, pp. 333–345. Available at: https://doi.org/10.1016/B978-0-12-809324-5.21031-6.