An Experimental Study on the Formation of Spatial Cognitive Maps in Humans

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In my judgment, this study is solid. The conclusion that “cognitive maps can be holistic rather than item-dependent representations that emerge in a locally abrupt fashion” is intriguing and appears to be supported by the authors’ data.

The paper also has several strengths. It is concise and to the point, the visuals are clear and helpful, and the data is well-presented through graphs and charts.

That said, there are areas where the piece could be improved:

1. Engagement with classic literature: While the authors briefly reference Gestalt psychology, more sustained engagement could be valuable. There are also several relevant perspectives from what might be called philosophical psychology—for instance, the work of Merleau-Ponty (1945) or Gallagher (2007)—that resonate with the study’s findings. Admittedly, the literature in these areas is vast, often dense, and of variable quality, so it may be too much to ask the author to wade through it all. Still, a gesture toward these traditions may enrich (or may not?) the theoretical framing.

2. Depth of references: My background in wayfinding comes largely from classic environmental psychology, which the author does cite. However, while contemporary sources are also included, the reference list is somewhat limited. Expanding the bibliography—and especially exploring some more recent literature—could strengthen the paper’s grounding in the broader literature.  (To clarify, the author does discuss recent literature, so the suggestion here is merely to expand somewhat).

3. Clarity of expression: At times, I found the writing difficult to follow. This made it harder for me to offer a confident evaluation of some points. Efforts to sharpen and clarify the prose would go a long way.

4. Conceptual framing of cognition: One point I found somewhat peculiar was the claim that:

"Behavioral and neurophysiological research indicates that cognitive maps are no exact replicas of the real world: they can be distorted, biased by assumptions, fragmented, poor in detail, and sometimes even nonmetric."

The issue here is that this statement appears to assume a fairly traditional representational view of cognition—namely, that the mind’s function is to generate internal models that are accurate to the extent they match (or do not distort) the external world. This assumption, in my view, deserves scrutiny. A great deal of work—ranging from Dewey to  Merleau-Ponty to more recent 4E cognitive science—calls this framing into question.

Of course, it would be unreasonable to expect the author to go into this entire literature, more so since a lot of it is philosophical and difficult. But perhaps questions about conceptual framing and assumptions behind it could be highlighted a little? For example, one might follow a lead from a 2023 article, titled "Anticipating and Enacting Worlds: Moods, Illness, and Psychobehavioral Adaptation," which asserts:

"Cognition is a coping tool,” and “tools like shovels and even subway maps are for handling tasks, which typically does not entail exact modelling of the world.”

Such a shift would align well with the idea of cognitive maps as functional and emergent, rather than strictly representational.

Comments on the Quality of English Language

I always say the quality of English can be improved because nobody has total mastery. But as stated in my comments to the author, I sometimes found the writing difficult to follow. This made it harder for me to offer a confident evaluation of some points. Efforts to sharpen and clarify the prose would go a long way.

Author Response

1. Engagement with classic literature: While the authors briefly reference Gestalt psychology, more sustained engagement could be valuable. There are also several relevant perspectives from what might be called philosophical psychology—for instance, the work of Merleau-Ponty (1945) or Gallagher (2007)—that resonate with the study’s findings. Admittedly, the literature in these areas is vast, often dense, and of variable quality, so it may be too much to ask the author to wade through it all. Still, a gesture toward these traditions may enrich (or may not?) the theoretical framing.

Thank you for this thoughtful and suggestion. I fully agree that our findings on the formation of cognitive maps are related to broader philosophical discussions about the mind-body problem. However, I am an experimentalist and therefore cautious not to overstep into areas beyond my expertise, to avoid embarrassing misinterpretations of philosophical thought. In response to your comment, and as a gesture toward this interdisciplinary relevance, I have now added a reference to Köhler’s work on Gestalt psychology in statment “participants represented the object layout in a holistic fashion (Oliva & Torralba, 2001), not as a sum of elements but as an integrated spatial ‘Gestalt’ (Köhler, 1925).”

 

2. Depth of references: My background in wayfinding comes largely from classic environmental psychology, which the author does cite. However, while contemporary sources are also included, the reference list is somewhat limited. Expanding the bibliography—and especially exploring some more recent literature—could strengthen the paper’s grounding in the broader literature.  (To clarify, the author does discuss recent literature, so the suggestion here is merely to expand somewhat).

The revised manuscript includes three additional references from the present decade (Hegarty et al., 2022; Bays et al., 2024; Bao et al., 2025), increasing that number from 10 to 13.

 

3. Clarity of expression: At times, I found the writing difficult to follow. This made it harder for me to offer a confident evaluation of some points. Efforts to sharpen and clarify the prose would go a long way.

I have made a thorough effort to improve clarity throughout the manuscript. The main points of confusion likely arose in the Methods section, given the complexity of the experimental design and the need to control for multiple sources of bias. Accordingly, most changes (marked in red in the revised manuscript) have been made in that section.

 

4. Conceptual framing of cognition: One point I found somewhat peculiar was the claim that: "Behavioral and neurophysiological research indicates that cognitive maps are no exact replicas of the real world: they can be distorted, biased by assumptions, fragmented, poor in detail, and sometimes even nonmetric.".

 The issue here is that this statement appears to assume a fairly traditional representational view of cognition—namely, that the mind’s function is to generate internal models that are accurate to the extent they match (or do not distort) the external world. This assumption, in my view, deserves scrutiny. A great deal of work—ranging from Dewey to  Merleau-Ponty to more recent 4E cognitive science—calls this framing into question.

Of course, it would be unreasonable to expect the author to go into this entire literature, more so since a lot of it is philosophical and difficult. But perhaps questions about conceptual framing and assumptions behind it could be highlighted a little? For example, one might follow a lead from a 2023 article, titled "Anticipating and Enacting Worlds: Moods, Illness, and Psychobehavioral Adaptation," which asserts: "Cognition is a coping tool,” and “tools like shovels and even subway maps are for handling tasks, which typically does not entail exact modelling of the world.”

Such a shift would align well with the idea of cognitive maps as functional and emergent, rather than strictly representational.

Thank you for this helpful comment. I apologize for not being clear enough in the original text. What I meant to convey is that the expression “cognitive map” is used metaphorically rather than literally—much like “processing bottleneck” or “attentional window,” which do not imply physical bottlenecks or windows. Building on your suggestion, the revised text now states more clearly: “The term ‘cognitive map’ should not be interpreted literally, as an exact replica of the real world. Rather, like other cognitive phenomena, a cognitive map is a “coping tool … for handling tasks, which typically does not entail exact modeling of the world” (Crippen, 2023).”

Reviewer 2 Report

Comments and Suggestions for Authors

Thanks for the invitation to review this work. This study provides novel insights into the formation of cognitive maps, challenging the traditional view of gradual acquisition by proposing that spatial knowledge emerges abruptly at the individual level. By analyzing responses at granular participant-object levels, the authors argue that averaged gradual improvements in prior literature may mask abrupt, local transitions akin to "aha moments." The absence of a set-size effect suggests cognitive maps may rely on holistic, rather than item-dependent, representations, which could inform theories of spatial memory and navigation. These results have practical implications for designing navigation aids for populations with spatial orientation challenges, such as older adults or individuals with neurological impairments.

 

1. Repeated Figure 2 legends.
2. Tables 3, 4, and 5 (Page 10) are referenced in the text but lack explicit headers in the provided content.
3. The backward elimination process removed interactions like Test × Conditionwithout explicit justification, risking reader confusion. Were alternative models (e.g., forward selection, model averaging) considered to mitigate Type II errors? How do floor/ceiling effects in accuracy influence the interpretation of logistic regression results, particularly for abruptness claims?
4. Figure 2 notes "floor and ceiling effects" but does not quantify them (e.g., % of participants at 0% or 100% accuracy).
5. The lack of a boundary effect contrasts with prior work (e.g., Lee, 2017; Negen et al., 2020). The authors attribute this to the maze’s free-view design or insufficient object counts. Could the absence of physical barriers or perceptual boundaries in the virtual maze explain this? How might systematically manipulating boundary salience (e.g., walls vs. open edges) clarify this discrepancy?
6. The authors propose holistic processing to explain the absence of a set-size effect, likening cognitive maps to a camera sensor. What specific cognitive mechanisms (e.g., Gestalt principles, chunking) underpin this holistic integration? Are there behavioral or neuroimaging methods to directly test whether participants encode spatial layouts as unified "Gestalten" versus item-location pairs?
7. While the study finds no encoding-perspective differences, prior work (e.g., König et al., 2021) reports perspective-dependent performance. How do the task demands here (e.g., forced survey-perspective testing) differ from tasks requiring egocentric judgments? Could the lack of perspective effects reflect task-specific strategies rather than intrinsic map properties?
8. Consider including citations of Exploration, 2024, 4, 20230146

 

 

Author Response

1. Repeated Figure 2 legends.

I apologize for the typo, it now is corrected.

2. Tables 3, 4, and 5 (Page 10) are referenced in the text but lack explicit headers in the provided content.

My apologies for the omission, the headers are now explained as a note to Table 1.

3. The backward elimination process removed interactions like Test × Condition without explicit justification, risking reader confusion. Were alternative models (e.g., forward selection, model averaging) considered to mitigate Type II errors? How do floor/ceiling effects in accuracy influence the interpretation of logistic regression results, particularly for abruptness claims?

Thank you for raising these important points.

• Alternative models: I chose backward elimination because this study was largely explorative: there were no a priori assumptions regarding the significance of most terms in the full model. , Backward elimination is widely regarded as suitable in exploratory contexts (e.g., A. Field, Discovering Statistics, 2018). Given your comment, I checked that forward inclusion yields the same final models. Data Analysis section now adds: “Backward rather than forward elimination was used since this study is largely exploratory rather than confirmatory.”
• Explicit justification: the two criteria for removing a term - p-value and effect size - were justified in detail in the Data Analysis section.
• Floor and ceiling effects: The mean accuracy scores shown in Fig. 2 & 3 exhibit floor and ceiling effects, but these are not the data analyzed in the study. As the Data Analysis section explains, participants’ response were “… scored as 1 if correct on the first attempt, or 0 if incorrect or timed out upon first attempt. The resultant binary scores were analyzed using mixed-effects logistic regression.” Note that binary logistic regression estimates whether the odds (i.e., the ratio of correct to incorrect responses) differ across categories. For example, it estimates whether the ratio of correct to incorrect responses is higher in condition Control than in condition Maze. This statistical approach would only fail if all or nearly all responses in the to-be-compared categories were 1, or if all were 0; Fig. 2 & 3 show that this was not the case in the present data.

4. Figure 2 notes "floor and ceiling effects" but does not quantify them (e.g., % of participants at 0% or 100% accuracy).

As per the response to your comment 3, floor and ceiling effects of mean accuracy were not relevant for the statistical analysis which was based on binary scores. Fig. 2 & 3 were included only as a summarizing overview of the data structure.

5. The lack of a boundary effect contrasts with prior work (e.g., Lee, 2017; Negen et al., 2020). The authors attribute this to the maze’s free-view design or insufficient object counts. Could the absence of physical barriers or perceptual boundaries in the virtual maze explain this? How might systematically manipulating boundary salience (e.g., walls vs. open edges) clarify this discrepancy?

This is indeed an intriguing issue. More work is needed to determine precisely what creates or enhances the impression of a boundary in a virtual maze. For example, placing a threatening element (like fire) or an attention-capturing event (such as dancers) beyond the last accessible object may be more effective than merely extending the corridor or adding an external wall. Likewise, introducing explicit negative consequences for attempting to cross the boundary could reinforce its perceptual salience. Even simply mentioning in the instructions that danger or unpleasant outcomes await beyond that point may suffice to induce a strong boundary effect. Furthermore, the mazes in the present study were possibly just too small for splitting them into central and boundary regions.

6. The authors propose holistic processing to explain the absence of a set-size effect, likening cognitive maps to a camera sensor. What specific cognitive mechanisms (e.g., Gestalt principles, chunking) underpin this holistic integration? Are there behavioral or neuroimaging methods to directly test whether participants encode spatial layouts as unified "Gestalten" versus item-location pairs?

A range of experimental paradigms have been used to substantiate the existence of chunking and of holistic encoding in working memory. I am aware of no earlier behavioral or neuroimaging methods that would adapt these paradigms to the study of cognitive map formation. The present study seems to be the first one to adapt the set-size paradigm to cognitive mapping.

7. While the study finds no encoding-perspective differences, prior work (e.g., König et al., 2021) reports perspective-dependent performance. How do the task demands here (e.g., forced survey-perspective testing) differ from tasks requiring egocentric judgments? Could the lack of perspective effects reflect task-specific strategies rather than intrinsic map properties?

I apologize for the lack of clarity in the original manuscript. Since the main effect of Condition was reinstated in Table 1-5, the present data confirm the encoding-perspective differences reported earlier (König et al., 2021; Richardson et al., 1999; Thorndyke & Hayes‑Roth, 1982). However, since the hit:condition term was removed, the consequences of a preceding hit on response accuracy was independent of the encoding perspective. The revision spells this out in more clarity in the Results and Discussion sections:

• Results (text below Table 3): “According to Table 4 and 5, the main effect of Condition was reinstated for both experiments, which replicates the findings from Table 1 – 3. The main effect of Hit was reinstated as well: correctness following a hit (0.780 ±0.185) was higher than that following an incorrect response (0.542 ±0.244). All interactions of Hit were removed, indicating that the consequences of a preceding hit on response accuracy were comparable across tests and conditions.”
• Discussion (7^th paragraph): “With respect to the third purpose, the role of encoding perspective, the present data document that response accuracy depends on the encoding perspective since the main effects of Condition were reinstated in Table 1-5. This confirms earlier findings by others (König et al., 2021; Richardson et al., 1999; Thorndyke & Hayes‑Roth, 1982). However, the consequences of a preceding hit on response accuracy did not depend on the encoding perspective since the Condition:Hit and the Conditioin:Test:Hit terms were removed; this was the case both in Experiment 1 with 12 objects (Table 4) and in Experiment 2 with 16 objects (Table 5). It therefore appears that the emergence speed of cognitive maps and its sensitivity to set size do not depend on the encoding perspective, and therefore reflect intrinsic properties of cognitive maps rather than the properties of transformations between perspectives. In contrast, the accuracy of cognitive maps seems to depend on the encoding perspective and thus to reflect the costs associated with transformations between perspectives.”

8. Consider including citations of Exploration, 2024, 4, 20230146

Thank you for pointing out the work by Xu et al. (2024). While their discussion of brain–machine interfaces is indeed fascinating, and may have future applications for the enhancement of wayfinding skills e.g. in persons with beginning dementia, it falls well outside the scope of the current manuscript, which focuses exclusively on behavioral measures of cognitive‐map formation in healthy adults. So, while future work combining neural‐interface approaches with behavioral mapping could be a fruitful direction, I have opted not to cite it here.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Thanks for the invitation to review this work. This study presents valuable insights into cognitive map formation, addressing important questions about emergence patterns (abrupt vs. gradual), set-size effects, and encoding perspectives. While the authors have tried to solve the previous concerns, the manuscript contains several points of confusion, inconsistencies, and potential errors requiring careful proof-check before publication.

1. The justification for simulating lateral/backward movement without turns (Footnote 2, p.5) cites "(Bock, under review)." An unpublished/manuscript-under-review citation is generally unacceptable for justifying core methodology in a peer-reviewed journal. Replace with published evidence or robust justification within the manuscript.
2. Holistic vs. Perspective-Dependent Accuracy:The central conclusion states cognitive maps are "holistic" representations emerging abruptly regardless of encoding perspective (p. 12-13). However, the robust and significant finding of lower accuracy in the Maze (first-person) vs. Control (survey) condition (Tables 1-5, Figs 2-3) directly contradicts a pure holistic view. The "holistic" claim needs qualification.  Explicitly state this nuance in the abstract and discussion.
3. "First-person" vs. "Egocentric":The Abstract/Introduction use "first-person perspective" while the Introduction mentions "egocentric (body-centered)" frames. While related, these are not strictly synonymous. Egocentric typically implies a body-centered reference frame, while first-person perspective refers to the viewpoint during encoding.
4. "Survey Knowledge" vs. "Cognitive Map":The Introduction uses these terms closely but notes "cognitive map" isn't literal. The Abstract/Conclusions heavily favor "cognitive map." Ensure consistent usage and clarify the relationship between the terms as used in this study (is survey knowledge the tested expression of the cognitive map?).
5. "Abrupt" Definition:The analysis defines "abrupt" emergence at the object-participant level based on post-hit performance. While logical, explicitly state in the Methods/Results that this operationalizes "abrupt" as item-specific consolidation rather than a global "aha" moment for the entire map.
6. The 4x3 grid in Exp. 1 inherently lacks a single unambiguous "center" (asymmetric). How were "boundary" vs. "central" locations operationally defined? Specify the criteria (e.g., edge intersections vs. inner intersections) in the Methods. The null result (lack of boundary effect) might be influenced by this definition.
7. The predicted post-hit accuracy (Π_predicted) formula assumes chance performance (c) is independent across trials and solely based on the number of objects. However, learning occurs across trials. Justify why this simple chance model is appropriate despite potential non-independence and learning. Discuss limitations of this approach.
8. The power analysis (f=0.25, β=0.95) is mentioned but not justified. Why was a "large" effect size (f=0.25) assumed for the critical interactions (HitCondition, ExperimentCondition)? Given the small effect sizes found for main effects (e.g., f²=0.042 for Hit), was the study adequately powered to detect interactionsinvolving these factors, which likely have smaller effects? Discuss power limitations, especially for the non-significant interactions.
9. Tables 1 & 2 show the main effect of Boundaryhad significant p-values (p<0.001) but was removed due to small effect size (f²<0.02). This requires clearer explanation in the Results/Discussion. Emphasize that while statistically significant, the effect size was deemed negligible according to the pre-defined criteria, supporting the conclusion of no practically meaningful boundary effect in this paradigm. Avoid simply stating "no boundary effect" without this nuance.
10. The discussion compares cognitive maps to a digital camera sensor capturing objects with consistent resolution regardless of quantity (p.12). This analogy is problematic. Camera resolution isfinite; adding too many objects does eventually degrade detail per object (similar to working memory overload). The finding of no set-size effect up to 16 objects doesn't imply infinite Reframe the analogy (e.g., "like capturing a scene where adding distinct objects within the field of view doesn't inherently degrade the spatial relationships") or omit it.
11. Appleyard (1979):Cited in the Introduction (p.2) for "survey knowledge," but the References list only Appleyard (1970). Add the correct 1979 reference or verify the source.

Bays et al. (2024) Duplication: Listed twice in the References (p.14). Remove the duplicate entry.

Future Dates: Bao et al. (2025), Ou et al. (2025) are cited. Ensure these are not placeholder citations and that the cited works are indeed published/accepted in press. If not, update or remove.

DOI Formatting: Inconsistencies exist (e.g., doi.org/10.3758/BF03193146 vs. https://doi.org/10.1007/s00221-010-2168-8). Standardize all DOIs to the full https://doi.org/... format.

12. Other small issues or confusion: 

Abstract: "response accuracy increased gradually across test trials" – Emphasize this is the aggregate mean pattern, contrasting with the individual abrupt finding.

Methods (Practice Trials): Clarify if the "route shown in Fig. 1c" during the first Maze learning trial was the only route used in that first trial or just an example. The text implies it was the specific route used ("the route shown").

Methods (Power Analysis): "to enable full balancing" (p.7) – Briefly specify what was balanced (likely condition order and color-location sets).

Results (Fig 2 & 3): The figures are described but not included in the text. Ensure clear, well-labeled figures are present in the final submission.

Discussion (Boundary Effect): The alternative explanation (12/16 objects insufficient) is reasonable. Consider adding that the maze design (uniform corridors, grid layout) might also minimize boundary salience compared to more naturalistic or enclosed environments.

 

Author Response

Thank you for catching these points of concern. Here is my reply.

1. The justification for simulating lateral/backward movement without turns (Footnote 2, p.5) cites "(Bock, under review)." An unpublished/manuscript-under-review citation is generally unacceptable for justifying core methodology in a peer-reviewed journal. Replace with published evidence or robust justification within the manuscript.

The reference to our manuscript under review is now removed. Only the published paper by Richardson et al. (1999) remains, providing a robust justification.

 

2. Holistic vs. Perspective-Dependent Accuracy:The central conclusion states cognitive maps are "holistic" representations emerging abruptly regardless of encoding perspective (p. 12-13). However, the robust and significant finding of lower accuracy in the Maze (first-person) vs. Control (survey) condition (Tables 1-5, Figs 2-3) directly contradicts a pure holistic view. The "holistic" claim needs qualification.  Explicitly state this nuance in the abstract and discussion.

It is important to distinguish between two distinct findings discussed on page 12:

- “response accuracy depends on the encoding perspective since the main effects of Condition were reinstated in Table 1-5. This confirms earlier findings by others (König et al., 2021; Richardson et al., 1999; Thorndyke & Hayes‑Roth, 1982).”

- “the consequences of a preceding hit on response accuracy did not depend on the encoding perspective since the Condition:Hit and the Conditioin:Test:Hit terms were removed; this was the case both in Experiment 1 with 12 objects (Table 4) and in Experiment 2 with 16 objects (Table 5).”

The same paragraph therefore concludes:  “the emergence speed of cognitive maps and its sensitivity to set size do not depend on the encoding perspective … In contrast, the accuracy of cognitive maps seems to depend on the encoding perspective and thus to reflect the costs associated with transformations between perspectives”

(The bold highlights are not in the manuscript, they were added for your convenience.)

For more clarity, both conclusions rather than just one are now repeated in abstract and in the final Discussion paragraph:

• Abstract: “Unlike the speed, the accuracy was lower in the first-person compared to the survey encoding perspective. … In contrast to the emergence speed, map accuracy can be lower when the encoding perspective differs from the test perspective.”
• Discussion: “Unlike emergence speed, accuracy was found to be lower with the first-person perspective, probably reflecting the costs of transformation from the first-person to the survey perspective.”
•  

3. "First-person" vs. "Egocentric":The Abstract/Introduction use "first-person perspective" while the Introduction mentions "egocentric (body-centered)" frames. While related, these are not strictly synonymous. Egocentric typically implies a body-centered reference frame, while first-person perspective refers to the viewpoint during encoding.

For better clarity, the Introduction no longer mentions egocentric/allocentric frames but rather “multiple spatial reference frames”. A similar change is made in footnote 1.

4. "Survey Knowledge" vs. "Cognitive Map":The Introduction uses these terms closely but notes "cognitive map" isn't literal. The Abstract/Conclusions heavily favor "cognitive map." Ensure consistent usage and clarify the relationship between the terms as used in this study (is survey knowledge the tested expression of the cognitive map?).

Some authors use the term “survey knowledge” while others prefer “cognitive maps” though both appear to refer to the same underlying concept. The Introduction section refers to both terms to address readers from both backgrounds: “Successful wayfinding often relies on internal representations of space, called ‘cognitive maps’ (Tolman, 1948) or ‘survey knowledge’ (Appleyard, 1979).” To avoid confusion between the memory-related term “survey knowledge” and the perception-related term “survey perspective”, the revised manuscript now uses “survey knowledge” only in this initial mention.

 

5. "Abrupt" Definition:The analysis defines "abrupt" emergence at the object-participant level based on post-hit performance. While logical, explicitly state in the Methods/Results that this operationalizes "abrupt" as item-specific consolidation rather than a global "aha" moment for the entire map.

The Introduction section now explains and defines the term “locally abrupt”, and this term is  then used consistently throughout the text, e.g., in the last paragraph of the Discussion   section: “cognitive maps can be holistic constructs that emerge in a locally abrupt manner”

The Introduction section now also qualifies that “evidence for abrupt – albeit not locally abrupt – emergence is provided by the phenomenon of ‘reorientation’”, and the Discussion section accordingly states regarding reorientations and aha-effects: “Although these phenomena relate to global rather than local changes, they suggest that cognitive processes do not always unfold incrementally; rather, they can involve sudden cognitive reorganizations.”

 

6. The 4x3 grid in Exp. 1 inherently lacks a single unambiguous "center" (asymmetric). How were "boundary" vs. "central" locations operationally defined? Specify the criteria (e.g., edge intersections vs. inner intersections) in the Methods. The null result (lack of boundary effect) might be influenced by this definition.

The Data Analysis section now specifies in more clarity “Boundary (yes, no), to determine whether response correctness differed between shapes located at an edge of the virtual maze (= yes)and those located more centrally (= no)”

 

7. The predicted post-hit accuracy (Π_predicted) formula assumes chance performance (c) is independent across trials and solely based on the number of objects. However, learning occurs across trials. Justify why this simple chance model is appropriate despite potential non-independence and learning. Discuss limitations of this approach.

Thank you for raising this interesting point. It is indeed true that the overall proportion of correct responses due to chance alone is expected to decrease across repeated tests. However, Equation 2 does not model overall chance correctness across tests. Rather, it models correctness after a hit under the abrupt-emergence hypothesis. This hypothesis stipulates that a hit reflects either (a) a genuine, abruptly acquired representation after which all subsequent responses should be correct, or (b) a response correct by chance. In case (b), by definition, no genuine learning has yet occurred, and thus the probability of chance correctness remains constant  irrespective of the test on which the hit occurred. Therefore, under the assumptions of the abrupt-emergence hypothesis, the expected chance correctness for a hit is c across all tests.

 

8. The power analysis (f=0.25, β=0.95) is mentioned but not justified. Why was a "large" effect size (f=0.25) assumed for the critical interactions (HitCondition, ExperimentCondition)? Given the small effect sizes found for main effects (e.g., f²=0.042 for Hit), was the study adequately powered to detect interactions involving these factors, which likely have smaller effects? Discuss power limitations, especially for the non-significant interactions.

Thank you for this important comment. The study was a priori powered for f = 0.25, which is a medium-sized effect according to Cohen. Many authors assume medium-sized effects if they have no a priori knowledge about the actual effect size. The registered data revealed several effects smaller than this threshold, suggesting that the actual sample size provided sufficient power even for small effects. While it is true that interaction effects often have smaller effect sizes and thus are harder to detect, the fact that some small effects were statistically detectable indicates that the study was likely well-powered for detecting interactions of at least small-to-medium size. Nonetheless, we acknowledge that very subtle interactions might remain undetected with the current sample size.

 

9. Tables 1 & 2 show the main effect of Boundary had significant p-values (p<0.001) but was removed due to small effect size (f²<0.02). This requires clearer explanation in the Results/Discussion. Emphasize that while statistically significant, the effect size was deemed negligible according to the pre-defined criteria, supporting the conclusion of no practically meaningful boundary effect in this paradigm. Avoid simply stating "no boundary effect" without this nuance.

The criteria for removing effects were mentioned and justified in the Data Analysis section. They now are repeated in the Results section (Note to Table 1: “Effects were reinstated if p<0.05 and f² > 0.02, see Data Analysis section.”). Furthermore, statements like “no boundary effect” are now replaced In the Discussion section by statements like “Under the criteria for reinstation of effects described in the data Analysis section, the present data do not confirm better localization near physical or perceived boundaries of the explored space compared to more central regions.”

 

10. The discussion compares cognitive maps to a digital camera sensor capturing objects with consistent resolution regardless of quantity (p.12). This analogy is problematic. Camera resolution isfinite; adding too many objects does eventually degrade detail per object (similar to working memory overload). The finding of no set-size effect up to 16 objects doesn't imply infinite Reframe the analogy (e.g., "like capturing a scene where adding distinct objects within the field of view doesn't inherently degrade the spatial relationships") or omit it.

Please note that the camera metaphor mentioned “multiple”, not an infinite number of objects. Obviously, neither a camera sensor nor a cognitive map can capture an infinite number of objects. This is now clarified by the new  sentence “just as the sensor can typically capture 12 or 16 objects in its field of view with the same resolution, a cognitive map may be able to represent 12 or 16 objects with the same fidelity.”

 

11. Appleyard (1979):Cited in the Introduction (p.2) for "survey knowledge," but the References list only Appleyard (1970). Add the correct 1979 reference or verify the source.

The citation in the text is now changed to the correct Appleyard (1970).

 

12. Bays et al. (2024) Duplication: Listed twice in the References (p.14). Remove the duplicate entry.

Removed

 

13. Future Dates: Bao et al. (2025), Ou et al. (2025) are cited. Ensure these are not placeholder citations and that the cited works are indeed published/accepted in press. If not, update or remove.

Bao et al. (2025) is a published article accessible via the indicated doi. However, Ou et al. (2025) is a preprint and is therefore now removed.

 

14. DOI Formatting: Inconsistencies exist

Corrected

 

15. Other small issues or confusion: 

Abstract: "response accuracy increased gradually across test trials" – Emphasize this is the aggregate mean pattern, contrasting with the individual abrupt finding.

Changed to “Response accuracy, averaged across objects and participants …”

 

Methods (Practice Trials): Clarify if the "route shown in Fig. 1c" during the first Maze learning trial was the only route used in that first trial or just an example. The text implies it was the specific route used ("the route shown").

For more clarity, now changed to “specific route shown in Fig. 1c”

 

Methods (Power Analysis): "to enable full balancing" (p.7) – Briefly specify what was balanced (likely condition order and color-location sets).

This was already stated in the Procedures section: “.The assignment of color-location sets to conditions was balanced across participants, as was and the order in which the two conditions were administered.” It now is clarified by expanding the sentence you refer to: “… to enable full balancing of 2 color-location sets x 2 condition orders.”

 

Results (Fig 2 & 3): The figures are described but not included in the text. Ensure clear, well-labeled figures are present in the final submission.

This is strange, both figures are in my copy of the submitted manuscript. The spacing between figures and text is now increased to make the figures stand out more, and I will check their presence during submission.

 

Discussion (Boundary Effect): The alternative explanation (12/16 objects insufficient) is reasonable. Consider adding that the maze design (uniform corridors, grid layout) might also minimize boundary salience compared to more naturalistic or enclosed environments.

Thank you for this interesting suggestion. I have considered the possibility that the uniform, grid-shaped corridors might reduce boundary salience, but one might as well argue the opposite way:  in the absence of other prominent visual features, boundaries were the only available cues for spatial segmentation in the present virtual maze. Therefore, boundaries were possibly more rather than less salient than in more naturalistic settings. Future research should evaluate the relationship between environmental richness and boundary salience.