Shortcutting from self-motion signals: quantifying trajectories and active sensing in an open maze

Reviewer #1 (Public review):

Assessment:

This important work advances our understanding of navigation and path integration in mammals by using a clever behavioral paradigm. The paper provides compelling evidence that mice are able to create and use a cognitive map to find "short cuts" in an environment, using only the location of rewards relative to the point of entry to the environment and path integration, and need not rely on visual landmarks.

Summary:

The authors have designed a novel experimental apparatus called the 'Hidden Food Maze (HFM)' and a beautiful suite of behavioral experiments using this apparatus to investigate the interplay between allothetic and idiothetic cues in navigation. The results presented provide a clear demonstration of the central claim of the paper, namely that mice only need a fixed start location and path integration to develop a cognitive map. The experiments and analyses conducted to test the main claim of the paper -- that the animals have formed a cognitive map -- are conclusive. While I think the results are quite interesting and sound, one issue that needs to be addressed is the framing how landmarks are used (or not), as discussed below, although I believe this will be a straight forward issue for the authors to address.

Strengths:

The 90 degree rotationally symmetric design and use of 4 distal landmarks and 4 quadrants with their corresponding rotationally equivalent locations (REL) lends itself to teasing apart the influence of path integration and landmark-based navigation in a clever way. The authors use a really complete set of experiments and associated controls to show that mice can use a start location and path integration to develop a cognitive map and generate shortcut routes to new locations.

Weaknesses:

There were no major weaknesses identified that were not addressed during revisions.

Reviewer #3 (Public review):

Summary:

How is it that animals find learned food locations in their daily life? Do they use landmarks to home in on these learned locations or do they learn a path based on self-motion (turn left, take ten steps forward, turn right, etc.). This study carefully examines this question in a well designed behavioral apparatus. A key finding is that to support the observed behavior in the hidden food arena, mice appear to not use the distal cues that are present in the environment for performing this task. Removal of such cues did not change the learning rate, for example. In a clever analysis of whether the resulting cognitive map based on self-motion cues could allow a mouse to take a shortcut, it was found that indeed they are. The work nicely shows the evolution of the rodent's learning of the task, and the role of active sensing in the targeted reduction of uncertainty of food location proximal to its expected location.

Strengths:

A convincing demonstration that mice can synthesize a cognitive map for the finding of a static reward using body frame-based cues. Showing that uncertainty of final target location is resolved by an active sensing process of probing holes proximal to the expected location. Showing that changing the position of entry into the arena rotates the anticipated location of the reward in a manner consistent with failure to use distal cues.

Weaknesses:

The task is low stakes, and thus the failure to use distal cues at most costs the animal a delay in finding the food; this delay is likely unimportant to the animal, and the pre-training procedure is likely to make it clear to the animal's that distal cues are unreliable even if desirable to use. Thus, it is unclear whether this result would generalize to a situation where the animal may be under some time pressure, urgency due to food (or water) restriction, or due to predatory threat, or situations where distal cues are reliable. In such cases, the use of distal cues to make locating the reward robust to changing start locations may be more likely to be observed.

Author response:

The following is the authors’ response to the original reviews.

We would like to thank the reviewers and editors for their careful assessment and review of our article. The many detailed comments, questions and suggestions were very helpful in improving our analyses and presentation of data. In particular, our Discussion benefited enormously from the comments.

Below we respond in detail to every point raised.

We especially note that Reviewer #3’s small query on “trial where learning is defined to have occurred, we were not given the quantitative criterion operationalizing "learning" - please provide” led to deeper analyses and insights and a lengthy response.

This analysis prompted the addition of a sentence (red) to the Abstract.

“Animals navigate by learning the spatial layout of their environment. We investigated spatial learning of mice in an open maze where food was hidden in one of a hundred holes. Mice leaving from a stable entrance learned to efficiently navigate to the food without the need for landmarks. We developed a quantitative framework to reveal how the mice estimate the food location based on analyses of trajectories and active hole checks. After learning, the computed “target estimation vector” (TEV) closely approximated the mice’s route and its hole check distribution. The TEV required learning both the direction and distance of the start to food vector, and our data suggests that different learning dynamics underlie these estimates. We propose that the TEV can be precisely connected to the properties of hippocampal place cells. Finally, we provide the first demonstration that, after learning the location of two food sites, the mice took a shortcut between the sites, demonstrating that they had generated a cognitive map. ”

Note: we added, at the end of the manuscript, the legends for the Shortcut video (Video 1) and the main text figure legends; these are with a larger font and so easier to read.

Reviewer #1 (Public Review):

Assessment:

This important work advances our understanding of navigation and path integration in mammals by using a clever behavioral paradigm. The paper provides compelling evidence that mice are able to create and use a cognitive map to find "short cuts" in an environment, using only the location of rewards relative to the point of entry to the environment and path integration, and need not rely on visual landmarks.

Thank you.

Summary:

The authors have designed a novel experimental apparatus called the 'Hidden Food Maze (HFM)' and a beautiful suite of behavioral experiments using this apparatus to investigate the interplay between allothetic and idiothetic cues in navigation. The results presented provide a clear demonstration of the central claim of the paper, namely that mice only need a fixed start location and path integration to develop a cognitive map. The experiments and analyses conducted to test the main claim of the paper -- that the animals have formed a cognitive map -- are conclusive. While I think the results are quite interesting and sound, one issue that needs to be addressed is the framing of how landmarks are used (or not), as discussed below, although I believe this will be a straightforward issue for the authors to address.

We have now added detailed discussion on this important point. See below.

Strengths:

The 90-degree rotationally symmetric design and use of 4 distal landmarks and 4 quadrants with their corresponding rotationally equivalent locations (REL) lends itself to teasing apart the influence of path integration and landmark-based navigation in a clever way. The authors use a really complete set of experiments and associated controls to show that mice can use a start location and path integration to develop a cognitive map and generate shortcut routes to new locations.

Weaknesses:

I have two comments. The second comment is perhaps major and would require rephrasing multiple sentences/paragraphs throughout the paper.

(1) The data clearly indicate that in the hidden food maze (HFM) task mice did not use external visual "cue cards" to navigate, as this is clearly shown in the errors mice make when they start trials from a different start location when trained in the static entrance condition. The absence of visual landmark-guided behavior is indeed surprising, given the previous literature showing the use of distal landmarks to navigate and neural correlates of visual landmarks in hippocampal formation. While the authors briefly mention that the mice might not be using distal landmarks because of their pretraining procedure - I think it is worth highlighting this point (about the importance of landmark stability and citing relevant papers) and elaborating on it in greater detail. It is very likely that mice do not use the distal visual landmarks in this task because the pretraining of animals leads to them not identifying them as stable landmarks. For example, if they thought that each time they were introduced to the arena, it was "through the same door", then the landmarks would appear to be in arbitrary locations compared to the last time. In the same way, we as humans wouldn't use clouds or the location of people or other animate objects as trusted navigational beacons. In addition, the animals are introduced to the environment without any extra-maze landmarks that could help them resolve this ambiguity. Previous work (and what we see in our dome experiments) has shown that in environments with 'unreliable' landmarks, place cells are not controlled by landmarks - https://www.sciencedirect.com/science/article/pii/S0028390898000537, https://pubmed.ncbi.nlm.nih.gov/7891125/. This makes it likely that the absence of these distal visual landmarks when the animal first entered the maze ensured that the animal does not 'trust' these visual features as landmarks.

Thank you. We have added many references and discussion exactly on this point including both direct behavioral experiments as well as discussion on the effects of landmark (in)stability of place cell encoding of “place”. See Page 18 third paragraph.

“An alternate factor might be the lack of reliability of distal spatial cues in predicting the food location. The mice, during pretraining trials, learned to find multiple food locations without landmarks. In the random trials, the continuous change of relative landmark location may lead the mice to not identifying them as “stable landmarks”. This view is supported by behavioral experiments that showed the importance of landmark stability for spatial learning (32-34) and that place cells are not controlled by “unreliable landmarks” (35-38). Control experiments without landmarks (Fig. S6A,B) or in the dark (Fig. S6C-F) confirmed that the mice did not need landmarks for spatial learning of the food location.”

(2) I don't agree with the statement that 'Exogenous cues are not required for learning the food location'. There are many cues that the animal is likely using to help reduce errors in path integration. For example, the start location of the rat could act as a landmark/exogenous cue in the sense of partially correcting path integration errors. The maze has four identical entrances (90-degree rotationally symmetric). Despite this, it is entirely plausible that the animal can correct path integration errors by identifying the correct start entrance for a given trial, and indeed the distance/bearing to the others would also help triangulate one's location. Further, the overall arena geometry could help reduce PI error. For example, with a food source learned to be "near the middle" of the arena, the animal would surely not estimate the position to be near the far wall (and an interesting follow-on experiment would be to have two different-sized, but otherwise nearly identical arenas). As the rat travels away from the start location, small path integration errors are bound to accumulate, these errors could be at least partially corrected based on entrance and distal wall locations. If this process of periodically checking the location of the entrance to correct path integration errors is done every few seconds, path integration would be aided 'exogenously' to build a cognitive map. While the original claim of the paper still stands, i.e. mice can learn the location of a hidden food size when their starting point in the environment remains constant across trials. I would advise rewording portions of the paper, including the discussion throughout the paper that states claims such as "Exogenous cues are not required for learning the food location" to account for the possibility that the start and the overall arena geometry could be used as helpful exogenous cues to correct for path integration errors.

We agree with the referee that our claim was ill-phrased. Surely the behavior of the mouse must be constrained by the arena size to some extent. To minimize potential geometric cues from the arena, we carefully analyzed many preliminary experiments (each with a unique batch of 4 mice) having the target positioned at different locations. We added a paragraph to the section “Further controls” where we explain our choice for the target position. Page 12 last paragraph; Page 13 “Arena geometry” paragraph.

Also, following the suggestion from the reviewer, we probed whether the hole checks accumulated near the center of the arena for the random entrance mice, as a potential sign that some spatial learning is going on. In fact, neither the density of hole checks, nor the distance of the hole checks to the center of the arena change with learning: panel A below shows the probability density of finding a hole check at a given distance from the center of the arena; both trial 1 and trial 14 have very similar profiles. Panel B shows the density of hole checks near (<20cm) and far (>20cm) from the arena’s center.

Author response image 1.

It also doesn’t show any significant differences between trials 1 and 14.

So even though there’s some trend (in panel A, the peak goes from 60cm to a double peak, one at 30cm away from the center, and the other still at 60cm), the distance from the center is still way too large compared to the mouse’s body size and to the average inter-hole distance (<10cm). These panels are now in the Supplementary Figure S8B.

Finally, we enhanced the wording in our claim. We now have a new section entitled: “What cues are required for learning the food location?”. There, we systematically cover all possible cues and how they might be affected by their stability under the perturbation of maze floor rotation.

Reviewer #2 (Public Review):

Summary:

This manuscript reports interesting findings about the navigational behavior of mice. The authors have dissected this behavior in various components using a sophisticated behavioral maze and statistical analysis of the data.

Strengths:

The results are solid and they support the main conclusions, which will be of considerable value to many scientists.

Thank you.

Weaknesses:

Figure 1: In some trials the mice seem to be doing thigmotaxis, walking along the perimeter of the maze. This is perhaps due to the fear of the open arena. But, these paths along the perimeter would significantly influence all metrics of navigation, e.g. the distance or time to reward.

Perhaps analysis can be done that treats such behavior separately and the factors it out from the paths that are away from the perimeter.

In Page 4, we added a small section entitled: “Pretraining trials”. Our reference was suggested by Reviewer #3 (noted as “Golani” with first author “Fonio”). Our preliminary experiments used naïve mice and they typically took greater than 2 days before they ventured into the arena center and found the single filled hole. This added unacceptable delays and the Pretraining trials greatly diminished the extensive thigmotaxis (not quantified). The “near the walls” trajectories did continue in the first learning trial (Fig. 2A, 3A) but then diminished in subsequent trials. We found no evidence that thigmotaxis (trajectories adjacent to the wall) were a separate category of trajectory.

Figure 1c: the color axis seems unusual. Red colors indicate less frequently visited regions (less than 25%) and white corresponds to more frequently visited places (>25%)? Why use such a binary measure instead of a graded map as commonly done?

Thank you; you are completely correct. We have completely changed the color coding.

Some figures use linear scale and others use logarithmic scale. Is there a scientific justification? For example, average latency is on a log scale and average speed is on a linear scale, but both quantify the same behavior. The y-axis in panel 1-I is much wider than the data. Is there a reason for this? Or can the authors zoom into the y-axis so that the reader can discern any pattern?

We use logarithmic scale with the purpose of displaying variables that have a wide range of variation (mainly, distance, latency, and number of hole checks, since it linearly and positively correlates with both distance and latency – see new Fig. S4B,C). For example, Latency goes from hundreds of seconds (trial 1) to just a few seconds (trial 14). Similarly, the total distance goes from hundreds of centimeters (trial 1, sometimes more than 1000cm, see answer about the 10-fold variation of distance below) to just the start-target distance (which is ~100cm). These variables vary over a few orders of magnitude. We display speed in a linear axis because it does not increase for more than one order of magnitude.

Moreover, fitting the wide-ranged data (distance, latency, nchecks) yields smaller error in logscale [i.e., fitting log(y) vs. trial, instead of y vs. trial]. In these cases, the log-scale also helps visualizing how well the data was fitted by the curve. Thus, presenting wide-ranged data in linear scale could be misleading regarding goodness of fit.

We now zoomed into the Y axis scale in Panels I of Fig. 2 and Fig. 3. We kept it in log-scale, but linear Y scale produces Author response image 2 for Figs. 3I and 2I, respectively.

Author response image 2.

Thus, we believe that the loglog-scale in these panels won’t compromise the interpretation of the phenomenon. In fact, the loglog of the static case suggests that the probability of hole checking distance increases according to a power law as the mouse approaches the target (however, we did not check this thoroughly, so we did not include this point in the discussion). Power law behavior is observed in other animals (e.g, ants: DOI: 10.1371/journal.pone.0009621) and is sometimes associated with a stochastic process with memory.

1F shows no significant reduction in distance to reward. Does that mean there is no improvement with experience and all the improvement in the latency is due to increasing running speed with experience?

Correct and in the section “Random Entrance experiments” under “Results” (Page 5) we explicitly note this point.

“We hypothesize that the mice did not significantly reduce their distance travelled (Fig. 2A,B,F) because they had not learned the food location - the decrease in latency (Fig. 2D) was due to its increased running speed and familiarity with non-spatial task parameters.”

Figure 3: The distance traveled was reduced by nearly 10-fold and speed increased by by about 3fold. So, the time to reach the reward should decrease by only 3 fold (t=d/v) but that too reduced by 10fold. How does one reconcile the 3fold difference between the expected and observed values?

The traveled distance is obtained by linearly interpolating the sampled trajectory points. In other words, the software samples a discrete set of positions, for each recorded instant 𝑡. The total distance is

where is the Euclidean distance between two consecutively sampled points. However, the same result (within a fraction of cm error) can be obtained by integrating the sampled speed over time 𝑣! using the Simpson method

Since Latency varies by 10-fold, it is just expected that, given 𝑑 = 𝑣𝑡, the total distance will also vary by 10-fold (since 𝑣 is constant in each time interval Δ𝑡; replacing 𝑣! in the integral yields the discrete sum above).

The correctness of our kinetic measurements can be simply verified by multiplying the data from the Latency panel with the data from the Velocity panel. If this results in the Distance plot, then there is no discrepancy.

In Author response image 3, we show the actual measured distance, 𝑑total, for both conditions (random and static entrance), calculated with the discrete sum above (black filled circles).

Author response image 3.

We compare this with two quantities: (a) average speed multiplied by average latency (red squares); and (b) average of the product of speed by latency (blue inverted triangles). The averages are taken over mice. Notice that if the multiplication is taken before the average (as it should be done), then the product 〈𝑣𝑡〉45*( is indistinguishable from the total distance obtained by linear interpolation. Even taking the averages prior to the multiplication (which is physically incorrect, since speed and latency and properties of each individual mouse), yields almost exactly the same result (well within 1 standard deviation).

The only thing to keep in mind here is that the Distance panel in the paper presents the normalized distance according to the target distance to the starting point. This is necessary because in the random entrance experiments, each mouse can go to 1 of 4 possible targets (each of which has a different distance to the starting point).

Figure 4: The reader is confused about the use of a binary color scheme here for the checking behavior: gray for a large amount of checking, and pink for small. But, there is a large ellipse that is gray and there are smaller circles that are also gray, but these two gray areas mean very different things as far as the reader can tell. Is that so? Why not show the entire graded colormap of checking probability instead of such a seemingly arbitrary binary depiction?

Thank you. Our coloring scheme was indeed poorly thought out and we have changed it. Hopefully the reviewer now finds it easier to interpret. The frequency of hole checks is now encoded into only filled circles of varying sizes and shades of pink. Small empty circles represent the arena holes (empty because they have no food); The large transparent gray ellipse is the variance of the unrestricted spatial distribution of hole checks.

Figure 4C: What would explain the large amount of checking behavior at the perimeter? Does that occur predominantly during thigmotaxis?

Yes. As mentioned above, thigmotaxis still occurs in the first trial of training. The point to note is that the hole checking shown in Fig. 4C is over all the mice so that, per mice, it does not appear so overwhelming.

Was there a correlation between the amount of time spent by the animals in a part of the maze and the amount of reward checking? Previous studies have shown that the two behaviors are often positively correlated, e.g. reference 20 in the manuscript. How does this fit with the path integration hypothesis?

We thank the reviewer for pointing this out. Indeed, the time spent searching & the hole checking behavior are correlated. We added a new panel C to Fig. S4 showing a raw correlation plot between Latency and number of checks.

Also, in the last paragraph of the “Revealing the mouse estimate of target position from behavior” section under “Results”), we now added a sentence relating the findings in Fig. 4H and 4K (spatial distribution of hole checks, and density of checks near the target, respectively) to note that these findings are in agreement with Fig 3C (time spent searching in each quadrant).

“The mean position of hole checks near (20cm) the target is interpreted as the mouse estimated target (Fig. 4C,D,G,H; green + sign=mean position; green ellipses = covariance of spatial hole check distribution restricted to 20cm near the target). This finding together with the displacement and spatial hole check maps (Figs. 4F and 4H, respectively) corroborates the heatmap of time spent in the target quadrant (Fig. 3C), suggesting a positive correlation between hole checks and time searching (see also Fig. S4C).”

"Scratches and odor trails were eliminated by washing and rotating the maze floor between trials." Can one eliminate scratches by just washing the maze floor? Rotation of the maze floor between trials can make these cues unreliable or variable but will not eliminate them. Ditto for odor cues.

The upper arena floor is rotated between trials so that any scratches will not be stable cues. We clarified this in the Discussion about potential cues.

See “What cues are required for learning the food location?”

"Possible odor gradient cues were eliminated by experiments where such gradients were prevented with vacuum fans (Fig. S6E)" What tests were done to ensure that these were *eliminated* versus just diminished?

"Probe trials of fully trained mice resulted in trajectories and initial hole checking identical to that of regular trials thereby demonstrating that local odor cues are not essential for spatial learning." As far as the reader can tell, probe trials only eliminated the food odor cues but did not eliminate all other odors. If so, this conclusion can be modified accordingly.

We were most worried about odor cues guiding the mice and as now described at great length, we tried to mitigate this problem in many ways. As the reviewer notes, it is not possible to have absolute certainty that there are no odor cues remaining. The most difficult odor to eliminate was the potential odor gradient emanating from the mouse’s home cage. However, the 2 vacuum fans per cage were very powerful in first evacuating the cage air (150x in 5 minutes) and then drawing air from the arena, through the cage and out its top for the duration of each trial. We believe that we did at least vastly reduce any odor cues and perhaps completely eliminated them.

The interpretation of direction selectivity is a bit tricky. At different places in this manuscript, this is interpreted as a path integration signal that encodes goal location, including the Consync cells. However, studies show that (e.g. Acharya et al. 2016) direction selectivity in virtual reality is comparable to that during natural mazes, despite large differences in vestibular cues and spatial selectivity. How would one reconcile these observations with path integration interpretation?

Thank you. We had not been serious enough in considering the VR studies and their implications for optic flow as a cue for spatial learning. We now have a section (Optic flow cues) in the Discussion that acknowledges the potential role of such cues in spatial learning in our maze.

However, spatial learning in our maze can also occur in the dark. The next small section (Vestibular and proprioceptive cues) addresses this point. We cannot be certain about the precise cues used by the mouse to effectively learn to locate food in our maze, but it will take further behavioral and electrophysiological studies to go deeper into these questions.

An extended discussion is found in the sections entitled “What cues are required for learning the food location” and “A fixed start location and self-motion cues are required for spatial learning”. We may have missed some references or ideas regarding VR maze learning with optic flow signals – the Acharya et al reference was an excellent starting point, and we would be grateful for additional pointers that would improve our discussion of this point.

The manuscript would be improved if the speculations about place cells, grid cells, BTSP, etc. were pared down. I could easily imagine the outcome of these speculations to go the other way and some claims are not supported by data. "We note that the cited experiments were done with virtual movement constrained to 1D and in the presence of landmarks. It remains to be shown whether similar results are obtained in our unconstrained 2D maze and with only self-motion cues available." There are many studies that have measured the evolution of place cells in non- virtual mazes, look up papers from the 1990s. Reference 43 reports such results in a 2D virtual maze.

We understand the reviewer’s concerns with the length of the manuscript. However, both the first and third reviewer did find this extensive section useful. We did not add the many papers on the evolution of place fields in real world mazes simply to prevent even greater expansion of the discussion, but relied on the very thorough review of Knierim and Hamilton instead.

Reviewer #3 (Public Review):

Summary:

How is it that animals find learned food locations in their daily life? Do they use landmarks to home in on these learned locations or do they learn a path based on self-motion (turn left, take ten steps forward, turn right, etc.). This study carefully examines this question in a well-designed behavioral apparatus. A key finding is that to support the observed behavior in the hidden food arena, mice appear to not use the distal cues that are present in the environment for performing this task. Removal of such cues did not change the learning rate, for example. In a clever analysis of whether the resulting cognitive map based on self-motion cues could allow a mouse to take a shortcut, it was found that indeed they are. The work nicely shows the evolution of the rodent's learning of the task, and the role of active sensing in the targeted reduction of uncertainty of food location proximal to its expected location.

Strengths:

A convincing demonstration that mice can synthesize a cognitive map for the finding of a static reward using body frame-based cues. This shows that the uncertainty of the final target location is resolved by an active sensing process of probing holes proximal to the expected location. Showing that changing the position of entry into the arena rotates the anticipated location of the reward in a manner consistent with failure to use distal cues.

Thank you.

Weaknesses:

The task is low stakes, and thus the failure to use distal cues at most costs the animal a delay in finding the food; this delay is likely unimportant to the animal. Thus, it is unclear whether this result would generalize to a situation where the animal may be under some time pressure, urgency due to food (or water) restriction, or due to predatory threat. In such cases, the use of distal cues to make locating the reward robust to changing start locations may be more likely to be observed.

We have added “Combining trajectory direction and hole check locations yields a Target Estimation Vector” a section summarizing our main hypotheses and this section includes noting exactly this point + including the reference to the excellent MacIver paper on “robot aggression”.

The main point here follows the Knierim and Hamilton review and assumes that learning “heading direction” and “distance from start to food” require different cues and extraction mechanisms. “Here we follow a review by Knierim and Hamilton (12) suggesting independent mechanisms for extraction of target direction versus target distance information. Averaging across trajectories gave a mean displacement direction, an estimate of the average heading direction as the mouse ran from start to food. The heading direction must be continuously updated as the mice runs towards the food, given that the mean displacement direction remains straight despite the variation across individual trajectories. Heading direction might be extracted from optic flow and/or vestibular system and be encoded by head direction cells. However, the distance from home to food is not encoded by head direction signals.”

And

“We hypothesize that path integration over trajectories is used to estimate the distance from start to food. The stimuli used for integration might include proprioception or acceleration (vestibular) signals as neither depends on visual input. Our conclusion is in accord with a literature survey that concluded that the distance of a target from a start location was based on path integration and separate from the coding of target heading direction (12). Our “in the dark” experiments reveal the minimal stimuli required for spatial learning – an anchoring starting point and directional information based on vestibular and perhaps proprioceptive signals. This view is in accord with recent studies using VR (47, 48). Under more naturalistic conditions, animals have many additional cues available that can be used for flexible control of navigation under time or predation pressure (51).”.

Furthermore, we added panel G do Fig S4, where we show the evolution of the heading angle along the trajectory, plotted as a function of the trials. We see that the mouse only steer towards the target in the last segment of the trajectory, consistent with having the head direction being continuously updated along the path to the food.

Recommendations for the authors:

Reviewing Editor (Recommendations For The Authors):

All three reviewers agreed during the consultation that the context in which distal cues are described in the manuscript would benefit significantly from refinement. The distal cues may be made completely useless from an ethological perspective e.g. if they are seen as "moving" relative to the entrance point (i.e. if the animal were to think it were entering the same location), then the cues would appear as unstable in the random entrance. As such, they may be so unlike natural experiences as to be potentially confusing to the animal. Moreover, as reported in some of the reviews, the animals may be using the entrances and boundaries as cues to help refine path integration. The results are still very interesting, but more refinement in the text on the interpretation of cues would greatly improve the manuscript. Thus, we recommend that you revise your manuscript to address the reviews.

Thank you. We agree with this recommendation of the reviewers have greatly expanded our discussion on cue stability as already indicated above.

Should you choose to revise your manuscript, pleasse ensure the manuscript include full statistical reporting including exact p-values wherever possible alongside the summary statistics (test statistic and df) and 95% confidence intervals. These should be reported for all key questions and not only when the p-value is less than 0.05.

Done

Lastly, I want to personally apologize for the long delay in editing this manuscript. All three reviews were unfortunately quite delayed, including my own review. I want to thank you for submitting your work to eLife and hope that we can be more efficient in editing your work in the future.

It was a long review process, but we also appreciate that our article was dense and difficult to read. We tried to be comprehensive in our controls and analyses and we appreciate the considerable effort it must have taken to carefully review our paper.

Reviewer #3 (Recommendations For The Authors):

I quite enjoyed this paper and have some suggestions for further improvement.

First, while I appreciate that the format of the journal has Methods at the end, there are some key details that need to be moved forward in the study for proper appreciation of the results. These include:

(1) Location and size of distal cues.

Done

(2) Use of floor washing between mice.

Done

(3) Use of food across the subfloor to provide some masking of the location of the food reward.

Done

(4) A scale bar on one of the early figures showing the apparatus would be beneficial.

Done for Figure 1 where we also provide arena diameter and area.

(5) Motivational state of the mouse with respect to the food reward (in this case, not food restricted, correct?).

Done

Although we are told the trial where learning is defined to have occurred, we were not given the quantitative criterion operationalizing "learning" - please provide (unless I missed it!).

Thank you. This question turned out to be of importance and led to more detailed analyses and related Discussion. We therefore answer in depth.

We now realize that learning the distance to food versus learning the direction to food must be analyzed separately.

On Page 5 second paragraph we provide a definition of “learning distance to food”.

“Fitting the function dtotal = B*exp(-Trial/K) reveals the characteristic timescale of learning, K, in trial units (Fig. 2F). We obtained K= 26±24 giving a coefficient of variation (CV) of 0.92. The mean, K=26, is therefore very uncertain and far greater than the actual number of trials. Thus, we hypothesize that the mice did not significantly reduce their distance travelled (Fig. 2A,B,F) because they had not learned the food location – the decrease in latency (Fig. 2D) was due to its increased running speed and familiarity with non-spatial task parameters. ”

On Page 7 second paragraph the same analysis gives:

“Now the fitting of the function dtotal=B exp(-Trial/K) yielded K=5.6±0.5 with a CV = 0.08; the mean is therefore a reliable estimate of total distance travelled. We interpret this to indicate that it takes a minimum number of K= 6 trials for learning the distance to the target (see also Fig. S4D,E,F,G).

Learning is still not complete because it takes 14 trials before the trajectories become near optimal.”

Learning of distance to food is evident by Trial 6 but is not complete.

On Page 9 third paragraph we give a very precise answer to time taken to learn the direction from start to food. This was already very clear from Fig. 4I but we had missed the significance of this result.

“We compared the deviation between the TEV and the true target vector (that points from start directly to the food hole; Fig. 4I). While the random entrance mice had a persistent deviation between TEV and target of more than 70o, the static entrance mice were able to learn the direction of the target almost perfectly by trial 6 (TEV-target deviation in first trial mean±SD = 57.27o ± 41.61o; last trial mean±SD = 5.16o ± 0.20o; P=0.0166). A minimum of 6 trials is sufficient for learning both the direction and distance to food (Fig. 4I) (Fig. 3F) (see Discussion). The kinetics of learning direction to food are clearly different from learning distance to food since the direction to food remains stable after Trial 6 while the distance to food continues to approach the optimal value.”

Learning the direction from start to food is completely learned by Trial 6.

These analyses led to an addition to the Discussion on Page 20 (following the Heading).

“Here we follow a review by Knierim and Hamilton (12) that hypothesized independent mechanisms for extraction of target direction versus target distance information. Our data strongly supports their hypothesis. Target direction is nearly perfectly estimated at trial 6 (Fig. 4I and Results). The deviation of the TEV from the start to food vector is rapidly reduced to its minimal value (5.16o) and with minimal variability (SD=0.20o). Learning the distance from start to food is also evident at trial 6 but only reaches an asymptotic near optimal value at trial 14 (Fig. 3F). The learning dynamics are therefore very different for target direction versus target distance. As noted below, the food direction is likely estimated from the activity of head direction cells. The neural mechanisms by which distance from start to food is estimated are not known (but see (49)).”

We believe that this small addition summarizes the complicated answer to the reviewer’s question and is helpful in better connecting the Knierim and Hamilton paper to our data. However, if the reviewers and editors feel that we have gone too far or that this discussion is not clear, we can remove or alter the extra sentences as per any comments.

Reference #49 is to a review paper on spatial learning in weakly electric fish in the dark (https://doi.org/10.1016/j.conb.2021.07.002). The review summarizes data on a neural “time stamp” mechanism for estimating distance from start to food. In this review article, we explicitly hypothesized that rodents might utilize such a time stamp mechanism for finding food. We did not include this in the discussion because it was too distracting and would likely confuse readers but put in the reference in case some readers did want to access the “time stamp” hypothesis for spatial learning in the dark.

Second, the discussion was thoughtful and rich. I particularly enjoyed the segment describing the likely computations of the hippocampus. There are a few thoughts I have for the authors to think about that might be useful to potentially add to the discussion:

"The remaining one, mouse 34, went from B to the start location and then, to A."

This out-and-back pattern has been seen in the literature, such as multiple papers by Golani (here's one: https://www.pnas.org/doi/full/10.1073/pnas.0812513106). Would the authors speculate, given their suggested algorithm, what the significance of out and back may be? Is there something about the cell's encoding of direction and distance that requires a return to the start location, and would this be different if representation is based on self-motion versus based on distal cues in an allocentric representation?

We do discuss this for pretraining trials but have no idea what this mouse is doing in this case.

In a low-stakes task environment, for an animal that has a low acuity visual system, where the penalty for not using distal cues is at most some additional (likely enriching in itself to these mice who live a fairly unenriched life in small cages) search/learning/exploration time, perhaps it is not so surprising that body-frame cues are used. Considering the ethology of the animal, if it had multiple exits of an underground burrow, it might need to use distal cues to avoid confusion. The scenario you provide to the animal is essentially a deceptive one where it has no way of telling it is coming out to the arena from a different burrow hole, modulo some small landmarks on an otherwise uniform cylinder of space. This might be asking too much of an animal where the space it would enter normally would not be a uniform cylinder.

What happens with a higher-stakes case? This is clearly a different study, but you may find some recent work with a mobile predatory robot of interest (https://www.sciencedirect.com/science/article/pii/S2211124723016820). Visual cues are crucial in the avoidance of threats in this case. Re-routing, as shown by multiple videos of that study, is after a brief pause, and seemingly takes into account the likely future position of the threat.

Done. A fascinating paper that illustrates the unexpected “high level” behavior a rodent is capable of when placed in more naturalistic situations. I think our “two food location” experiments are along the same direction – unexpected rich behavior when the mouse are challenged.

Connected to the low-stakes vs high-stakes point, it might be nice for the paper to discuss situations in which cognitive-map-based spatial problem solutions make sense versus not.

Here is an example of such a discussion, around page 496:

https://www.dropbox.com/scl/fi/ayoo5w4jgnkblgfu7mpad/MacI09a_situated_cog.pdf?

rlkey=2qhh89ii7jbkavt6ivevarvdk&dl=0.

Right a very relevant discussion by MacIver. However, when I tried to write it in it took nearly half a page of dense writing to connect to the themes of our article. I figured that the already long discussion will try the patience of most readers and so decided to not include this extra discussion.

Minor points/ queries

Why the increase in sample density at about the 1/4 radius of arena distance? Static, trial 14, Figure 3I, shown also maybe Figure 4 H.

We were also puzzled when this occurred but have no explanation. And there are, in our figures, many other examples of the mice hole checking near their exit site. See next answer.

Why was the hole proximal to start so often probed in 7B?

We were also puzzled when this occurred but have no explanation.

Check Video 1 to exactly see this behavior. The mouse exits its home and immediately checks a nearby hole. It proceeds to Site B (empty) and then Site A (empty) with many hole checks along the way. After leaving Site A, the mouse proceeds to the wall located far from an entrance and does another hole check. The near the wall holes that are checked are in no way remarkable: a) they have never contained food; b) they are rotated between trials, and we wash the floor carefully, so they do not “smell” any particular hole; c) the food on the lower level floor is in no way “clumped” under that hole, etc.

We have discussed this phenomenon quite a lot and LM was able to come up with only one hypothesis for this behavior. In analogy to the electric fish work (responses of diencephalic neurons to “leaving or encountering a landmark”), the “near the entrance” hole check might be an active sensing probe to “time stamp” the exit from home while finding food would “time stamp” the end of a successful trajectory. Path integration between time stamps would then provide the estimate for time/distance from start to food – exactly our hypothesis for weakly electric fish spatial learning in the dark. This hypothesis is exceedingly speculative and so we do not want to include it.

Normally I would cite a line number. Since I do not see line numbers, I will leave it to you to do a search:

"A than the expected by chance" -> "than expected"

Done. I apologize for the lack of line numbers. I have, so far, been unable to get Word to confine line numbers to selected text and not run over onto the Figure Legends. I have put in page numbers and hope this helps.

RW, VR, MWM, etc - please expand the acronym on first use.

Done

It might be interesting to see differences in demand/reliance on active sensing in the individuals who learn the task less well than the animals who learn the task well. If the point is to expunge uncertainty, then does the need for such expunging increase with the poverty of internal representation resolution / fewer decimal places on the internal TEV calculation?

We do have variation in the mice learning time but the numbers are not sufficient for this interesting extension. This is just one of many follow up studies we hope to carry out.