Author response:
The following is the authors’ response to the original reviews.
Public Reviews:
Reviewer #1 (Public review):
Summary:
Freas and Wystrach present a computational model of steering in insects. In this model, the central complex provides an error signal indicating the animal should turn left or right; this error signal biases the function of an oscillator composed of two mutually inhibiting self-exciting units. The output of these units generates a "steering signal" that is used both to set the direction and speed of the ant. Additionally, a separate module induces pauses, and an inverse relation between forward speed and turning speed is externally imposed. Statistics of the trajectories generated by the model are compared to the measured behaviors of ants.
Strengths:
While the model is very simple compared to state-of-the-art models, that simplicity makes it a potentially useful guide to researchers studying insect navigation. Some predictions that emerge from the model appear to be experimentally testable, although a more complete description of the model and its parameters, as well as an analysis of how this model's predictions differ from previous models' predictions, would be required to design these experiments.
Weaknesses:
I found it difficult to identify evidence in the paper supporting central elements of the abstract. Hopefully, these difficulties can be resolved with a clearer presentation and the addition of supporting detail, especially in the methods.
(1) The model is not clearly described
In the Materials and Methods, there is no description of the model, just "The computational model is presented in Figure 1." (This is probably a typo and may refer to Figure 2A-C), and a link to Matlab source code. It is inappropriate to ask readers or reviewers to examine source code in lieu of providing a method, but I attempted to do so anyway.
We have now added a full description of the model in the methods.
To my eye, the source code does not match the model presented in 2A-C. For instance, in 2C, "Steering signal" inhibits "Freeze", but I couldn't find this in the source. "Freeze" is shown to inhibit "steering signal," but as "steering signal" is a signed quantity, it's not clear what this means. Literally, since "ang_speed_raw = L-R," it would seem to indicate the "freeze" would bias towards right turns. In the code, "freeze" appears to be implemented through the boolean variable "speed_inhibition_time." The logic controlled by this variable doesn't appear to inhibit the "steering signal" but instead (depending on control parameters) either reduces the movement speed and amplifies the turning rate, or it turns the angular speed output into a temporal integral of the control signal.
We understand the confusion. Our neural implementation does not go downstream of the neural steering signal (Left and Right Descending neurons), and the way it is transformed into a movement (ang_speed_raw = L-R) is not modelled neurally (the formula is explicitly shown on the right hand side of Figure 2). Indeed, we did not attempt to put forward any assumption about neural implementation for our freezing signal (see our response to comment 2 below). To avoid confusion, we have now removed the reciprocal inhibition portion as it was previously drawn in Figure 2C, and replaced it by a non neural sign (a cross, indicating that the signal is blocked) acting between steering signal and movement.
There are a number of parameters in the source code that aren't described at all in the paper, including the internal oscillator parameters.
We now provide all the parameters in the methods, together with figures showing the dynamics of oscillations across parameter range, and a rationale for their choice (see Supplemental Figure 2).
Together, these limitations make it difficult to understand what is being simulated, what parts of the model are tied to biology, and where the model improves on or departs from previous work.
It is absolutely essential that authors fully describe the computational model, that they explain the meaning of all parameters of the model, and that they explain how the particular values of these parameters were chosen.
This is now done in the methods section under the “Model Overview” subsection.
(2) The biological inspiration is unclear
A central claim of the paper is that the model is "biologically grounded." But some elements, for instance, using a signed quantity to represent left-right steering drive, are not biologically possible; at best, these are shorthand for biologically possible implementations, e.g., opposing groups of left-right driving neurons.
The mechanism that produces fixations and saccades - the "freeze" module - is not tied to any particular anatomy of the insect brain. Initiation of a freeze occurs at a specific time coded into the model by the authors; it is not generated by an internal model signal. Release of a freeze is by drawing a random variable; there is no neural mechanism proposed to generate this signal.
We now clarified what is neural from is not from the introduction onwards, for instance:
“Because we did not want to form pre-assumptions for how such a ‘freeze signal’ could be implemented in the insect nervous system; in our model this was achieved using a simple external signal that halts forward motion at random intervals.”
In some versions of the model, instead of directly controlling the signal, during fixations, the angular drive signal is integrated into a variable "cumul_drive." No neural substrate is proposed for this integrator. In the code, if cumul_drive passes a threshold, the angular heading of the ant changes (saccades), but only if this threshold is passed before the Poisson process ends the fixation. No neural substrate is proposed for any of this logic.
This has now also be clarified in the introduction:
“During scanning, real ants display rotational saccades of variable duration and angular magnitude (Figure 1A–C). To replicate this, we introduced a threshold-based mechanism: after each fixation (i.e., zero angular and forward speed), the underlying angular steering signal accumulates until surpassing a threshold, triggering a saccade. The resulting angular magnitude of the saccade corresponds to the sum of the angular drive accumulated during the fixation. Here also we stuck to a non-neural, straight-forward algorithmic level, as we did not want to make assumptions about how such a cumulate-and-release mechanism could be neurally implemented in the insect brain (see discussion for potential implementations).”
The model steps forward in time by a fixed increment - the actual duration (in seconds) of this time step is not specified. From Figure 4F, G, it appears a simulation time step is meant to be about 10ms. This would imply an oscillator frequency of about 2 Hz (Fig 2B), that the heading oscillates at a similar frequency (2G), and that a forward crawling ant stops moving every 500 ms (2I). Are these plausible? Can they be compared to an experiment? Model parameters, including the ones that control the frequency of the oscillator, are non-dimensionalized. It is not possible to evaluate whether these parameters are biologically plausible or match experimental results.
We now added a figure showing the oscillatory dynamics of the oscillator across parameter ranges (supplemental figure 2). The step increment (i.e., and thus the sampling rate along an oscillatory cycle) necessarily varies according to the inhibition strength and self decay parameter chosen (e.g., small parameter values will lead to small step increment, and thus a high sampling rate along the oscillatory cycle). We chose oscillatory parameters to ensure that the sampling rate will be high enough to resolve multiple saccades within one oscillatory cycle and that sampling rate is small enough for computation time to remain practical.
Beyond these constraints, the oscillator parameters can be chosen arbitrarily, and a conversion of time step to actual time (ms) would be equally arbitrary and give the illusion that the model captures the data quantitatively. Because we did not model spiking neural dynamics (or brain region low field potential frequencies), we can not constrain our model through a temporal link between brain clock and behavioural speed. We thus prefer to stick to the true and non-dimensional label ‘time steps’ in our figures.
(3) Claims that behaviors emerge from the model may be overstated
The abstract claims that steering correction and fixations/saccades emerge naturally from the same model. But it appears to me that fixations/saccades are externally imposed by the specification of specific times for a "freeze." Faster angular rotation during saccades than during course correction is imposed and does not emerge naturally from neural simulations.
The abstract now clarifies that what emerges spontaneously is not scannings per se (indeed, the inhibition of movement is externally imposed) but their dynamics. Note that our model captures many aspects of scanning dynamics that are not trivial and which results from the dynamical interactions and contingencies between modules (figure 3 to 7), hence justifying the word ‘emerge’ insofar as these behavioural dynamics cannot be reduced to one module or parameter. Regarding the faster angular rotation during scanning, we agree that its cause is rather straightforward to understand: it results from the added bodily constraints of forward speed to rotational movements. Nonetheless it is not ‘imposed’ during saccades in the sense that 1.) it is biologically/physically evident rather than cherry picked and 2.) it is continuously present in our model, even during forward navigation. We believe the new version of the manuscript now conveys this message in a transparent manner.
(4) Citations to previous literature are difficult to follow, and modeling results are presented as though they are experimental data
I would ask the authors to be much clearer in their description and citation of previous work. It should be clear whether the cited work was experimental or computational. To the extent possible, the actual measurement should be described succinctly. Instead of grouping references together to support a sentence with multiple claims, references should be cited for each claim. Studies of computational models should not be presented as proving a biological result.
Indeed, This we now clearly separated citations referring to experimental evidence vs. modelling. See examples citations below
For example:
(a) Lines 141-146:
"Previous studies have established many key components of insect navigation, including .... the intrinsic oscillatory dynamics in the lateral accessory lobes (LALs) that support continuous zigzagging locomotion (Clément et al., 2023; Kanzaki, 2005; Namiki and Kanzaki, 2016;
Steinbeck et al., 2020)."
The first reference is to one author's previous modeling work - it hypothesizes that oscillations in the LAL support zigzagging but includes no data that would "establish" the fact. Kanzaki et al. 2005 describes numerical modeling and simulation with a physical robot. Namiki and Kanzaki, 2016 is a review article that links the LAL to zigzagging behavior. It describes the LAL as a winner-take-all bistable network but does not describe or hypothesize that the LAL has intrinsic oscillatory dynamics. Steinbeck et al. 2020 is a more comprehensive review; it reinforces that the LAL is a winner-take-all bistable network that drives left-right steering, including during zig-zagging behavior. But in my reading, I could not find a statement that the LAL has intrinsic oscillatory dynamics (the closest is Steinbeck et al. saying the activity pattern switches regularly, as does the behavior; this doesn't imply that the LAL is intrinsically oscillatory.)
It now reads:
“Previous studies have established many key components of insect navigation, notably, how goal headings are set in the central complex (CX) (Fisher, 2022; Green and Maimon, 2018). Modelling efforts have shown that the CX circuitry can naturally accommodate innate and learnt guidance such as path integration, learn vectors, visual route following or homing as observed in ants and bees. In parallel, oscillatory dynamics in the lateral accessory lobes (LALs) - produced by reciprocal inhibition across both hemispheres and conveyed by so-called descending flip-flopping neurons - were shown to drive the spontaneous zigzags displayed by moths upon losing their pheromone plume (Kanzaki and Mishima, 1996; Mishima and Kanzaki, 1998, 1999; Wada and Kanzaki, 2005; Kanzaki et al., 2005; Iwano et al., 2010). Here also, subsequent modelling efforts have shown how these circuits can equally support the continuous lateral oscillations displayed by a wide range of insect species, including ants.”
(b) Lines 701-703:
"In plume-tracking moths, CX output has been shown to modulate LAL flip-flop neurons driving zigzagging (Adden et al., 2022)."
This reads as though an experimental measurement was made, but in fact, this is modeling work.
Yes, this could be clearer, it now reads:
“In moths, descending neurons in the LALs exhibit characteristic 'flip-flop' activity patterns that correlate with zigzagging maneuvers (Olberg, 1983; Kanzaki and Ikeda, 1994). Computational models suggest that having these LAL neurons modulated by the CX output can explain aspects of the moths’ plume-tracking behaviour (Adden et al., 2022).”
(c) Lines 703-706:
"In ants, strong goal signals in the CX - whether elicited by the path integrator or visual familiarity (Wehner et al., 2016; Wystrach et al., 2020b, 2015) do not only sharpen directional accuracy but also increase oscillation frequency (Clément et al., 2023)."
Here again, modeling results are presented as though they were experimental data.
Here, we are referring to the experimental part of these works, although this comment demonstrates that our statement should be more clear in stating what are biological results. It now reads:
“In ants, behavioural studies show that strong directional drives elicited by the path integrator or visual familiarity do not only gain behavioural weights and sharpen directional accuracy (Wehner et al., 2016; Wystrach et al. 2015, Legge et al. 2014) but also increase the ants’ oscillation frequency (Clément et al., 2023). Assuming that path integrator and visual familiarity modulate goal signals in the CX, as modelled here and elsewhere (Wystrach et al., 2020b, Stone et al., 2017) and that the intrinsic oscillator is in the LAL (Clément et al., 2023, Steinbeck et al., 2020), it suggests that CX output modulates the intrinsic oscillatory activity of the LAL”
Reviewer #2 (Public review):
Summary:
The paper by Freas and Wystrach is an interesting computational study, exploring the detailed mechanisms of how simple neural circuits could explain complex behavioral patterns observed in navigating ants. The authors compare detailed, high-speed video recordings of Australian desert ants (Melophorus bagoti) with predictions made by their new computational model and find convincing similarities between the model and the behavioral data, at a level of detail not previously studied. Particularly interesting are emerging properties of the model, yielding behavioral motifs it was not designed to reproduce, but which occur in natural ant behavior.
Strengths:
A strength of the study is that the model is based on previous models, without making major novel explicit assumptions. It combines existing models of the insect central complex with a model of the lateral accessory lobe and adds a stochastic inhibition of forward velocity to the interaction of central complex and lateral accessory lobes. The central complex provides corrective steering signals when the goal direction and the current heading of an insect are not aligned, while the lateral accessory lobes provide an intrinsic oscillator underlying the behavioral oscillations shown by walking ants at all times. These background oscillations are modulated by the steering signals from the central complex. Depending on which phase of the intrinsic oscillations coincides with the corrective signals, and how fast the ant is moving forward during this time, a complex set of behaviors emerges. Most prominently, scanning behaviors, which are regularly carried out by the ants, are recapitulated in great detail by the model. Additionally, other behaviors, such as full loops, emerge naturally from the model. While computational models are not to be seen as definite evidence for any biological reality, they can provide strong support for particular neural implementations. The current study is an excellent example in that it provides evidence for a serial arrangement of central complex circuits upstream of the lateral accessory lobe circuits, modulated by speed-regulating input. While the latter is hypothetical, it yields a clear hypothesis that can be validated by connectomics studies and functional work in the future.
The study shows that even complex behavioral motifs do not require dedicated neural modules, but can rather emerge from the interplay of already known circuits - highlighting the efficiency of insect brains and possibly providing the path towards embodied hardware solutions of such circuits in autonomous agents.
Weaknesses:
There are several weaknesses in the paper as it is.
Firstly, the model is not described in the methods, but only found when following the link to the authors' GitHub repository. This is clearly not sufficient and prevents readers from evaluating the model's assumptions directly. Most importantly, how natural do the emerging properties indeed emerge from the model? What parameters need to be tuned to generate a match between data and model?
We have now added a full description of the model in the Methods section.
These include:
Mathematical equations for model components
Complete parameter table along with justifications
Description of what is fitted vs. what emerges
Key assumptions and limitations
Regarding the emergence of scanning properties: The model has two types of parameters:
Parameters tuned to match general navigation behavior (independent of scanning):
Motor gains (g_ang, g_fwd, k): adjusted to produce realistic continuous walking paths and species differences between desert ants and Myrmecia
CX gain (g_CX = 0.5): set to produce appropriate corrective steering strength during continuous navigation
Oscillator parameters (α, β, s): are taken from Clément et al. (2023)
Parameters tuned to match scanning behavior:
CPG angular threshold (θ_CPG = 2.0): adjusted to generate realistic saccade timing Scan termination probability (p_stop = 0.5/timestep): matched to the Poisson-like distribution of scan durations in M. bagoti
Properties that emerge without specific tuning:
Fixation-saccade alternation structure (emerges from angular drive accumulation mechanism)
Directional reversals (arise from oscillator dynamics competing with CX steering)
Corrective saccade amplitude increasing with angular deviation (Figure 3)
Rare full-loop scans (emerge from CX signal shifting oscillator phase)
The behavioral continuum from straight paths → oscillations → voltes → scans (Figure 8)
We have clarified this distinction in the Methods section and emphasized that our goal was qualitative demonstration of emergence rather than quantitative parameter optimization.
Second, it is often not entirely clear what is biological data and what is a computational model. This relates to figures, text, and references. As a reader, this makes it difficult to clearly judge what is new in the current paper, how it adds to previous models, and what the predictions and assumptions are for biology.
Indeed, we have now clarified the manuscript, clearly separating when we refer to behavioural data, neurobiological data and modelling. In the figures, each panel now clearly indicates if it is model data or biological data so that any reader can immediately tell the data type.
Third, while neural data from bees and flies are taken to motivate and design the computational model, the discussion and interpretation revolve almost exclusively around ants. For the most part, this is justified, as the behavioral data used to benchmark the model are taken from ants. Nevertheless, more broadly discussing the newly defined circuit in the context of flying insects would give a better idea of the broad relevance of the neural circuits predicted by the model.
To address this suggestion we have now added two paragraphs in the discussion called: “Scanning in flying hymenopterans”.
Also happy to add more to this section if requested.
Recommendations for the authors:
Reviewer #2 (Recommendations for the authors):
As mentioned in the public review, I suggest fixing the two concerns I have regarding methods and discussion.
(1) Include a full description of the model in the methods, so that the model remains reproducible even if the GitHub repo is deleted in the future.
True, the code’s internal explanations could indeed be removed from GitHub later. The model component overview are now included in text.
(2) Include the relevance of the model for flying insects in the discussion more prominently. This seems to be an implicit assumption in the model, as neural data from bees and, more prominently, from Drosophila are used to motivate the model to explain ant data.
Add an “Expression in flying hymenopterans” section at ~line 834.
Minor points:
(1) Line 207: I suggest adding the recent review by Collett, Graham, and Heinze (2025, Current Biology), as it proposes interactions between LAL and CX as well.
Added
(2) Figure 4: I'm interested in the conversion from steps in the model to real units (ms) in the ants. In Figures 4F and G, it seems that 5 model steps represent circa 100ms. Does this allow us to define the neuronal time constants of the model neurons? If so, are the resulting values biologically plausible? This seems important when describing real-world dynamics being created by a model circuit.
No the model is time agnostic.
(3) Figure 7: Font sizes of axis labels are much too small. Also applies to other figures. Please ensure that when printed, labels can be read.
Enlarged axis labels in all figures.
(4) Line 645: proprieties -> properties?
Fixed. Thanks!
(5) Figure 7: The figure heading states: "Slow forward speed (Myrmecia) example". This sounds as if real data from ants are shown here, while these are modeling data. It is clear after reading the text and caption in detail, but I was taken off course briefly here. Please make sure that there is no possibility of being misled here.
We have altered the subtitle to “Slow forward speed (Myrmecia Model) example”.
Additionally, we have added a Model tag under each of the model image labels so classification can be done at a glance.
(6) General discussion: What about search dynamics, i.e., increasing loops when not finding the nest entrance after homing? Are those emerging from this circuit as well? Or would that need to be a separate module? There have been discussions about search emerging from the PI circuit, but as far as I know, this is not settled, and it would be good to know if the current circuit adds something useful to this aspect.
Because we kept a fixed goal heading, our model does not bring insight about overall trajectories such as search pattern. We now mention in the discussion:
“In our simulations, the CX goal representation remained fixed in both direction and strength throughout each trial. This simplification allowed us to isolate and compare the effects of different CX strengths on scanning behaviour (Figure 6). However, goal headings in the CX are likely to be updated continuously, including during scans, by novel input from visual recognition in the MB (ref). This would in turn bias saccades direction and duration. Exploring such dynamics lies beyond the scope of the present study but would represent an interesting direction for future work. Notably, our proposed CX-LAL-Body relationship could be implemented downstream of an existing path integration or visual-based model (or both) to form predictions about the occurrence and dynamic of scans along the path, as well as their impact on the emerging trajectories.”
(7) Line 690: The modulation of PFL3 by PFL2 was presented as a hypothesis in Westeinde et al., consistent with the data, but as far as I know, this is not an established fact.
You are correct. We have now softened the text, which now reads: “In Drosophila, it has been proposed that PFL2 neurons, which respond maximally when the fly faces away from the goal, modulate steering gain by converging with PFL3 neurons (which drive left or right turns) onto downstream descending neurons (Westeinde et al., 2024).”
(8) Please ensure that Drosophila is consistently spelled with a capital D and in italics.
Fixed throughout the text.
(9) Line 702: Reference Adden et al 2022: This reference is a modeling paper; it sounds as if you are referring to an experimental moth paper, though. Rephrase to clarify.
You are correct, this could be unpacked much better regarding what is modelled and what has been experimentally shown. Changed to:
Descending neurons in the LALs exhibit characteristic 'flip-flop' activity patterns that correlate with the zigzagging maneuvers of plume-tracking moths (Olberg, 1983; Kanzaki and Ikeda, 1994). Recent computational models suggest that CX output directly modulates these LAL circuits to coordinate orientation (Adden et al., 2022).
(10) Line 761: I would assume that during scans, information is acquired that would decrease uncertainty and thus, as a result change the amplitude of the CX steering signal. Maybe I missed this, but is this closed-loop interaction integrated in the model?
In our simulation the CX goal representation remains stable in direction and strength throughout the trial. This enabled us to compare neatly the effect of different CX strengths on scanning. However, we fully agree with you that goal headings in the CX might well be continuously updated, both during scans and between scans! The goal heading novel strength or direction may thus bias the scan further left, right, in front or in the back, and also up or down regulate scan duration in both directions.
Modelling this would require adding a layer of complexity to determine how the goal heading is updated, which is beyond the scope of the current work, but would form a remarkable project for the future. We now mention this in a dedicated paragraph in the discussion section “Model limitations and future directions”
(11) Line 814: Please add 'fly' in front of larva. Other insect larvae have a fully developed CX.
Corrected. Added fly to this sentence
(12) Line 815: Maybe add the recent review, Heinze 2025.
Added this one (Heinze 2024) which seems to fit the best and the 2025 Curr Biol Review doesn't quite fit this line (cited elsewhere though):
Heinze, S. (2024). Variations on an ancient theme—the central complex across insects. Current Opinion in Behavioral Sciences, 57, 101390.
(13) Methods: Subheading formatting should start with capital letters.
Ah yes, the second level of subheadings got formatted weirdly. Fixed now.
