Group identification drives brain integration for collective performance

Reviewer #1 (Public review):

The article provides a timely and well-written examination of how group identification influences collective behaviors and performance using fNIRs and behavioral data.

Comments on revisions:

Most Reviewer concerns have been addressed in the revised manuscript, but some limitations persist with respect to core aspects of study design (e.g., long block durations and lack of counter-balancing) and analysis (i.e., the potential circularity of some analyses, the insufficiency of a mediation model to demonstrate causality, and a lack of clarity concerning the model us to map task activation).

Editor's note: Although the Reviewers found the reviews generally responsive, some fundamental concerns remain which will not be changed by further revision.

Author response:

The following is the authors’ response to the original reviews

Reviewer #1 (Public review):

Weaknesses (clarifications needed):

(1) Experimental Design:

The study does not mention whether the authors examined sex differences or any measures of attractiveness or hierarchy among participants (e.g., students vs. teachers). Including these variables could provide a more nuanced understanding of group dynamics.

We are grateful to the reviewer for pointing out this valuable question. We have clarified that future studies should include sex differences or any measures of attractiveness or hierarchy among participants (e.g., students vs. teachers) (p. 27).

“Finally, future research should investigate additional variables, including sex differences and measures of attractiveness or hierarchy among participants, such as students versus teachers.” p. 27

(2) fNIRS Data Acquisition:

The authors' approach to addressing individual differences in anatomy is lacking in detail. Understanding how they identified the optimal channels for synchrony between participants would be beneficial. Was this done by averaging to find the location with the highest coherence?

We apologize for missing some details here. We have included the following information in the fNIRS data acquisition and fNIRS data analyses to clarify the details (pp. 8 and 12).

We employed the one-sample t-test method to assess the GNS disparity between the baseline and task sessions, identifying particular channels of interest. This analysis did not ascertain the maximum coherence level, but rather pinpointed the channel exhibiting significant divergence between the two sessions, which we designated as pertinent to the group decision-making task. Furthermore, we selected the PFC and left TPJ as our reference brain regions, guided by existing literature.

“Two optode probe sets were used to cover each participant's prefrontal and left TPJ regions (Figure S1). The DLPFC plays a crucial role in group decision-making processes, with findings suggesting that individuals exhibiting reduced prefrontal activity were more prone to out-group exclusion and demonstrated stronger in-group preferences (Goupil et al., 2021; Jankovic, 2014; Yang et al., 2020). Similarly, the left TPJ has been previously reported to be associated with decision-making and information exchange (Freitas et al., 2019; Tindale et al., 2019).” p. 8

“Time-averaged GNS (also averaged across channels in each group) was compared between the baseline session (i.e., the resting phase) and the task session (from reading information to making decisions) using a series of one-sample t-tests. Here, p-values were thresholded by controlling for FDR (p < 0.05; Benjamini & Hochberg, 1995). When determining the frequency band of interest, the time-averaged GNS was also averaged across channels. After that, we analyzed the time-averaged GNS of each channel. Then, channels showing significant GNS were regarded as regions of interest and included in subsequent analyses.” p. 12

(3) Behavioral Analysis:

For group identification, the analysis currently uses a dichotomous approach. Introducing a regression model to capture the degree of identification could offer more granular insights into how varying levels of group identification affect collective behavior and performance.

Thank you for your suggestion. As suggested, we have conducted the regression model to examine how varying levels of group identification affect collective performance, with the score of group identification being the independent variable and collective performance as the dependent variable (pp.9 and 15).

“Moreover, we employed a regression model to examine how varying levels of group identification affect collective performance, using group identification scores as the independent variable and collective performance as the dependent variable.” p.9

“The results from the regression model highlighted a significant association between the degree of group identification and collective performance (β = 0.45, t = 4.56, p = 0.019).” p.15

(4) Single Brain Activation Analysis:

The application of the General Linear Model (GLM) is unclear, particularly given the long block durations and absence of multiple trials. Further explanation is needed on how the GLM was implemented under these conditions.

Thank you for your suggestion, we have added more details in this section (p.11).

“In the GLM model analysis, HbO was the dependent variable, and the regression amount was set for different task stages (a. Reading information, b. Sharing private information, c. Discussing information, d. Decision). After that, we convolved the regression factor with the Hemodynamic Response Function (HRF) and obtained the brain activation β value of each participant in each channel at different task stages through regression analysis.’ p.11

(5) Within-group neural Synchrony (GNS) Calculation:

The method for calculating GNS could be improved by using mutual information instead of pairwise summation, as suggested by Xie et al. (2020) in their study on fMRI triadic hyperscanning. Additionally, the explanation of GNS calculation is inconsistent. At one point, it is mentioned that GNS was averaged across time and channels, while elsewhere, it is stated that channels with the highest GNS were selected. Clarification on this point is essential.

We appreciate the reviewer for highlighting this inquiry. We utilized a conventional GNS calculation approach, as detailed in Line 296 of the manuscript, where the GNS was determined in pairs after the WTC computation, and then averaged. Further details regarding the second question have been provided in the article (p.12).

(6) Placement of fNIRS Probes:

The probes were only placed in the frontal regions, despite literature suggesting that the superior temporal sulcus (STS) and temporoparietal junction (TPJ) regions are crucial for triadic team performance. A justification for this choice or inclusion of these regions in future studies would be beneficial.

The original manuscript clearly stated the use of two optode probe sets to encompass the prefrontal and left TPJ regions of each participant (see Figure S1, p. 8).

(7) Interpretation of fNIRS Data:

Given that fNIRS signals are slow, similar to BOLD signals in fMRI, the interpretation of Figure 6 raises concerns. It suggests that it takes several minutes (on the order of 4-5 minutes) for people to collaborate, which seems implausible. More context or re-evaluation of this interpretation is needed.

The question you have pointed out is very pertinent, and we have added more explanation for this result (pp. 25-26).

As previous studies have shown, the BOLD signal collected by fNIRS is slowly increasing compared to neuronal activity, which means that it has hysteresis (Turner et al., 1998). In social interactions such as group decision-making, the time of neural synchronization is delayed because people need to spend time increasing the number of dialogues to improve collaboration efficiency and form the same preference (Zhang et al., 2019). For example, the study of group consensus found that participants would show significant neural alignment after completing a period of dialogue (Sievers et al., 2024). In the task of cooperation, with the improvement of tacit understanding between two participants, the higher degree of neural synchronization (Cui et al., 2012). Therefore, the generation of neural synchronization depends on the interaction over a period of time. Therefore, we believe that the 4-5 minutes of collaboration time shown in Figure 6 may be related to establishing consensus and the same preference of team members, which is reflected in the dynamic time change of neural synchronization.

Moreover, previous studies on neural synchronization during social interaction and group decision-making revealed that substantial neural synchronization occurred around 50-55 seconds into a teaching task involving prior knowledge (Liu et al., 2019) and persisted approximately 6 minutes into the discussion period (Xie et al., 2023). These results collectively validate the suitability of utilizing fNIRS signal response time in our study (pp. 25-26).

“Our study also has demonstrated significant increases in single-brain activation, DLPFC-OFC functional connectivity, and GNS at 7, 12, and 17 minutes, respectively, following task initiation. The significant increase in these neural activities together constructs the two-in-one neural model that explains how group identification influences the collective performance we proposed. As previous studies have shown, the BOLD signal collected by fNIRS is slowly increasing compared to neuronal activity, which means that it has hysteresis (Turner et al., 1998). In social interactions such as group decision-making, the time of neural synchronization is delayed because people need to spend time increasing the number of dialogues to improve collaboration efficiency and form the same preference (Zhang et al., 2019). For example, participants would exhibit significant neural alignment, but only after they had completed a period of dialogue (Sievers et al., 2024). In the task of cooperation, with the improvement of cooperation efficiency between two participants, the higher degree of neural synchronization (Cui et al., 2012). Therefore, the generation of neural synchronization depends on the interaction over a period of time, which can affect the estimation of collaboration time. Prior research has shown that when the teaching task with prior knowledge began 50-55 seconds, significant neural synchronization could be generated between teacher and students, which meant that students and teacher achieved the same goal of learning knowledge (Liu et al., 2019). Moreover, a noteworthy increase in GNS was observed approximately 6 minutes into the group discussion period for better discussing and solving the problem (Xie et al., 2023). These findings are similar to ours. Therefore, the time points we found could reflect the dynamic time change of the neural process of team collaboration.’ pp.25-26

Reviewer #2 (Public review):

Weaknesses:

The authors need to clearly articulate their hypothesis regarding why neural synchronization occurs during social interaction. For example, in line 284, it is stated that "It is plausible that neural synchronization is closely associated with group identification and collective performance...", but this is far from self-evident. Neural synchronization can occur even when people are merely watching a movie (Hasson et al., 2004), and movie-watchers are not engaged in collective behavior. There is no direct link between the IBS and collective behavior. The authors should explain why they believe inter-brain synchronization occurs in interactive settings and why they think it is related to collective behavior/performance.

Thank you for bringing these points to our attention, we have clarified the relationship between neural synchronization and collective behavior in the Introduction section. (p.4). Moreover, in order to investigate whether neural synchronization stems from a common task or environment, we pseudo-randomized all pairs of subjects and created a null distribution consisting of 1,000 pseudo-groups, as described in Lines 311-315. This approach enabled us to eliminate neural synchronization resulting from factors other than social interaction, allowing us to identify neural patterns associated with collective performance (p.12).

“Moreover, Ni et al. (2024) indicated that neural synchronization was linked to the strength of social-emotional communication and connections between individuals. An increase in neural synchronization has also been shown to predict the coordination and cooperation abilities of group members (Lu et al., 2023). Therefore, we hypothesize that neural synchronization may be related to group performance.” p.4

“After that, the nonparametric permutation test was conducted on the observed interaction effects on GNS of the real group against the 1,000 permutation samples. By pseudo-randomizing the data of all participants, a null distribution of 1000 pseudo-groups was generated (e.g., time series from member 1 in group 1 were grouped with member 2 in group 2 & member 3 in group 3). The GNS of 1,000 reshuffled pseudo-groups was computed, and the GNS of the real groups was assessed by comparing it with the values generated by 1000 reshuffled pseudo-groups.” p.12

The authors state that "GNS in the OFC was a reliable neuromarker, indicating the influence of group identification on collective performance," but this claim is too strong. Please refer to Figure 4B. Do the authors really believe that collective performance can be predicted given the correlation with the large variance shown? There is a significant discrepancy between observing a correlation between two variables and asserting that one variable is a predictive biomarker for the other.

Thank you for your suggestion, we have revised the relevant statement (p.18).

“Through correlation and regression model analysis, we found that in group decision-making, the increase in group identity would affect group performance by improving GNS in the OFC brain region.” p.18

Why are the individual answers being analyzed as collective performance (See, L-184)? Although these are performances that emerge after the group discussion, they seem to be individual performances rather than collective ones. Typically, wouldn't the result of a consensus be considered a collective performance? The authors should clarify why the individual's answer is being treated as the measure of collective performance.

We appreciate the insightful comment provided by the reviewer. The decision to utilize individual responses as a metric of overall performance is based on several key considerations. Previous studies on various hidden profile tasks have utilized averaged individual scores to represent collective performance (e.g., Stasser et al., 1995; Wittenbaum et al., 1996; Brockner et al., 2022). Secondly, while consensus outcomes are typically regarded as collective expressions, we argue that in the context of this study, individual responses are not independent entities but rather extensions of the group decision-making process. The collective deliberation process significantly influenced individual thinking and decision-making in this study. Through group discussions, members shared perspectives, adjusted their stances, and formulated their responses based on collective insights. The responses provided by participants in this study were molded by the dynamics of group conversations, serving as an indirect measure of group performance and potentially indicating the efficacy of collective deliberations.

Performing SPM-based mapping followed by conducting a t-test on the channels within statistically significant regions constitutes double dipping, which is not an acceptable method (Kriegeskorte et al., 2011). This issue is evident in, for example, Figures 3A and 4A.

Please refer to the following source: https://www.nature.com/articles/nn.2303

We have carefully reviewed the articles provided by the reviewer, and we acknowledge the concerns regarding selective analysis and double dipping in our statistical approach. To address this, we believe it is important to clarify this issue further in the Discussion section (pp.26-27).

Our study introduces a novel perspective while utilizing conventional fNIRS-based hyperscanning analyses (Liu et al., 2019; Pärnamets et al., 2020; Reinero et al., 2021; Számadó et al., 2021; Solansky, 2011), methods that are widely endorsed within the field. In our analysis, significant channels were first identified using a one-sample t-test, followed by additional analyses including ANOVA, independent samples t-tests, and other procedures. We would like to emphasize that the statistical assumptions underlying the one-sample t-test and paired-sample t-test in our study maintain a level of independence. Moreover, to further mitigate concerns about the potential for double dipping, we employed permutation testing to validate the robustness of our results and ensure that our findings are not influenced by biases inherent in the selection of significant regions.

We recognize the importance of rigorous statistical practices and are committed to upholding the highest standards of analysis. As such, we have revisited our methodology and included a more detailed explanation of the steps taken to avoid double dipping and ensure the integrity of our analyses in the revised manuscript.

“Although our study has found a new perspective, the analysis method still refers to and uses the traditional fNIR-based hyperscanning analyses (Liu et al., 2019; P¨arnamets et al., 2020; Reinero et al., 2021; Számadó et al., 2021; Solansky, 2011), which is generally accepted by the majority of fNIR-based hyperscanning researchers. For example, we would first identify significant channels through a one-sample t-test and then conduct further analyses, such as ANOVA or independent samples t-tests. Selective analysis is a powerful tool and is perfectly justified whenever the results are statistically independent of the selection criterion under the null hypothesis (Kriegeskorte et al., 2019). However, it may lead to double dipping and missing information. In this study, the absence of statistically significant TPJ activation in the analyzed data led to the TPJ being ignored. In the future, it should be made explicit in the analysis, and the reliability of the results should be ensured by appropriate statistical methods (e.g., cross-validation, independent data sets, or techniques to control for selective bias).” p.26-27

In several key analyses within this study (e.g., single-brain activation in the paragraph starting from L398, neural synchronization in the paragraph starting from L393), the TPJ is mentioned alongside the DLPFC. However, in subsequent detailed analyses, the TPJ is entirely ignored.

We thank the reviewer for your careful review and valuable comment. TPJ is referenced in certain analyses within this paper (as detailed in paragraphs L414 and L440); however, its role remains inadequately investigated and expounded upon in subsequent more intricate analyses. This is due to the absence of statistically significant TPJ activation in the analyzed data. As pointed out by the reviewer, limitations may exist in pursuing further analyses through ROIs, a point we also have addressed in the Discussion section (p.27).

The method for analyzing single-brain activation is unclear. Although it is mentioned that GLM (generalized linear model) was used, it is not specified what regressors were prepared, nor which regressor's β-values are reported as brain activity. Without this information, it is difficult to assess the validity of the reported results.

We have revised the relevant description to clarify the analyses of single-brain activation (p. 11)

While the model illustrated in Figure 7 seems to be interesting, for me, it seems not to be based on the results of this study. This is because the study did not investigate the causal relationships among the three metrics. I guess, Figure 5D might be intended to explain this, but the details of the analysis are not provided, making it unclear what is being presented.

We regret the confusion that has arisen. Firstly, as highlighted by the reviewer, the model depicted in Figure 7 is not directly derived from the causal analysis conducted in this study. Our investigation did not directly explore the causal relationships among the three indicators; instead, we constructed a model based on correlations and potential mechanisms. In the revised manuscript, we have explicitly stated that Figure 7 represents a descriptive model (p.22).

Regarding Figure 5D, the reviewer noted that while it may offer some explanatory value, it lacks the necessary analytical detail to elucidate the chart's significance clearly. We have clarified the details of the analysis in Figure 5 (pp.13-14). The model in Figure 5D suggested that the connection between the similarity in individual-collective performance and the correlation of brain activation, as well as whether the impact of each individual’s single-brain activation on the corresponding group’s GNS was regulated by their brain activation connectivity.

“Finally, we employed correlation and mediation analyses to assess if brain activation connectivity could explain the connection between individuals’ single-brain activation and the related group’s GNS. We examined the connection between the similarity in individual-collective performance and the correlation of brain activation, as well as whether the impact of each individual’s single-brain activation on the corresponding group’s GNS was regulated by their brain activation connectivity. We utilized the PROCESS tool in SPSS to investigate the proposed moderation effect. Specifically, we applied Model 1 with 5000 bootstrap resamples to examine the interaction between the independent variable (i.e., single-brain activation) and the moderator (i.e., brain activation connectivity) in predicting the dependent variable (i.e., GNS). It is noteworthy that prior to analysis, all variables in the moderation model were mean-centered to reduce multicollinearity and improve the interpretability of interaction terms.” p.13-14

“Building on the above results, we have developed a two-in-one neural model that explains how group identification influences collective performance. This descriptive model aims to illustrate the potential interrelationships among these indicators and establish a conceptual framework to inspire forthcoming research endeavors.” p.21

The details of the experiment are not described at all. While I can somewhat grasp what was done abstractly, the lack of specific information makes it impossible to replicate the study.

As suggested, we have clarified the details of the experiment in the manuscript.

(1) As stated in the public review, the details of the experiment are not described at all and while I can somewhat grasp what was done abstractly, the lack of specific information makes it impossible to replicate the study. In points a-e below, I list the aspects that I could not fully understand, but I am not asking for direct answers to these points. Instead, please provide a detailed description of the experiment so that it can be replicated.

Thank you for your suggestion; we have responded to each question sequentially and elaborated on the experiment specifics to ensure replicability.

(a) Please provide more detailed information about the Group Identification Task. How much did each participant speak (was there any asymmetry in the amount of speaking, and was there any possibility that the asymmetry influenced the identification rating)? Did the three participants interact in person, or online? Are they isolated from experimenters? How was the rating conducted, what I mean is that it's a PC-based rating?

We apologize for the lack of detail in our description of the procedures for the experiment.

For the first question, we draw upon previous studies concerning the manipulation of group identity while controlling the content of pre-task conversations. Specifically, the high-identity group engaged in self-introductions and identified similarities among the three members, whereas the low-identity group discussed topics related to the current semester's classes (Xie et al., 2023; Yang et al., 2020). Both discussions were conducted for the same duration of three minutes, ensuring that the number of exchanges between the two groups remained comparable. There was almost no asymmetry in the amount of speaking. We also conducted a manipulation check, which confirmed the effectiveness of our identity manipulation(pp.5-6).

Xie, E., Li, K., Gu, R., Zhang, D., & Li, X. (2023). Verbal information exchange enhances collective performance through increasing group identification. NeuroImage, 279, 120339.

Yang, J., Zhang, H., Ni, J., De Dreu, C. K., & Ma, Y. (2020). Within-group synchronization in the prefrontal cortex associates with intergroup conflict. Nature neuroscience, 23(6), 754-760.

“Both discussions were conducted for the same duration of three minutes, ensuring that the number of exchanges between the two groups remained comparable.” p.5-6

For the second question，the three participants interacted offline in a face-to-face setting, while the experimenter remained outside the laboratory (p.6).

“The three participants conducted face-to-face offline interaction throughout the manipulation process.” p.6

For the third question, at the beginning of the experimental task, participants were isolated from the experimenters (p.6).

“In addition to explaining the next phase of the task and controlling the timer, experimenters would be isolated from participants.” p.6

For the last question, the rating of group identification was conducted through a questionnaire presented on participants’ phones (p.6).

“The questionnaire was presented on participants’ phones.” p.6

(b) The procedures of the Main Task are also unclear. For the Reading Information (5 min): How was the information presented? PC-based or paper-based? How were the participants seated? Did they read it independently?

We apologize for the missing details. We have included the following information in the article.

For the first and last question, each participant would get a piece of paper, which presents the common information and private information. They read independently. (p.6)

“Each participant would get a piece of paper, which presented the information. Participants could read independently.” p.6

About how the participants sat, the three participants sat around a table without partitions between each other. Only in the discussion stage, they could communicate face-to-face (p.6).

“They sat around a table without partitions between each other.” p.6

“In this process of discussion, the participants were able to communicate face-to-face and verbally.” p.6

(c) For Sharing Private Information: The authors stated they share text messages using Tencent Meeting. If so, how and with what devices? How was the information displayed on the screen? Were the participants even in the same room?

Thank you for your reminder. We have added more details now (p.6). Firstly, the experimenter sent the Tencent Meeting link to the participants. After the participants entered the meeting through their mobile phones, they could text the information they wanted to share in the chat box of the meeting. They were in the same room, with Tencent Meeting recording shared information, the participants could view them at any time.

“During the group sharing, participants entered Tencent Meeting via their mobile phones and were able to text their private information in the chat box to their group members for 5 minutes.” p.6

(d) For Discussing Information: It's a verbal interaction. How did they interact with others? What is the distance between them? I found a very small picture in Figure 8, but that is all information about experiment settings, that is provided by the authors.

We are sorry about the missing details. As we have explained in the article it’s a verbal communication, so participants could talk face to face in one room. We have included the following information in the article (p.6).

“Participants were sitting and communicating around a table. The distance between adjacent participants was about 15 cm, and the distance between face-to-face participants was about 40 cm. In this process of discussion, the participants were able to communicate face-to-face and verbally.” p.6

(e) For the Decision Process (5 min): How did they answer (What I mean is verbally, writing, or computer-based input), and how did the experimenters record these answers?

The questions were presented on paper, so the participants could write down their answers and experimenters could count the answers on paper. We have included the following information in the article(p.7).

“After discussion, all triads were given 5 minutes to answer the following questions (i) the probability of three suspects, 0%-100% for each suspect; (ii) the motivation and tool of crime; and (iii) deduced the entire process of crime. The three questions were presented on paper, allowing participants to write their answers directly on the same sheet. Subsequently, three independent raters used these paper questionnaires to record and calculate the scores for each group.” p.7

(2) I find the model presented in Figure 7 to be intriguing. Understanding why inter-brain synchronization occurs and how it is supported by specific single-brain activations or intra-brain functional connectivity is indeed a critical area for researchers conducting hyperscanning studies to explore. However, the content depicted in this model is not based on the results of this study. This is because the study did not investigate the causal relationships among the three metrics. I guess, Figure 5D might be intended to explain this, but the details of the analysis are not provided, making it unclear what is being presented. Please include a detailed explanation.

The specific answers are available on page 5 of our response letter.

(3) The analysis of single-brain activation analysis (and probably other analyses) focuses on the period from reading to making decisions (L237). Why was this entire interval chosen for analysis? Reading does not involve social interaction. As mentioned in a previous comment, the details of the tasks are unclear, so it's difficult to understand what was actually done in the reading period. Anyway, why were these different phases combined as the focus of analysis? Please clarify the reasoning behind this choice.

Thank you for your feedback. The decision to analyze the entire interval, spanning from reading to decision-making, was primarily made to grasp the continuum of information processing comprehensively. While reading itself lacks social interaction, it serves as the foundation for subsequent decision-making, during which participants' cognitive states and affective responses gradually evolve. Therefore, examining these two phases collectively enables a more thorough investigation into how information influences decision-making. Furthermore, considering the task details remain ambiguous, we aim to uncover the underlying cognitive and affective mechanisms through a holistic analysis.

(4) The method for analyzing single-brain activation is unclear. Please provide a detailed description of the analysis methods.

Thank you for your suggestion, we have added more details in the Method section (p.11).

“In the GLM model analysis, HbO was the dependent variable, and the regression amount was set to different task stages (a. Reading information, b. Sharing private information, c. Discussion information, d. Decision). After that, we convolved the regression factor with the Hemodynamic Response Function (HRF), and obtained the brain activation β value of each participant in each channel at different task stages through regression analysis.” p.11

(5) In the periods of Reading Information and Sharing Private Information, there appears to be no social interaction between participants (Figure1D). However, Figure 6 shows an increase in brain activity correlation even during the first 10 minutes (it corresponds to the Reading and Sharing period). Why does inter-brain correlation (GNS, in this study) increase even though there is no interaction between participants? Please provide an explanation.

Sharing private information fosters interactive engagement, necessitating its exchange during Tencent Meetings to facilitate sharing. Previous research suggests that heightened correlations in brain activity can be attributed to (1) intrinsic cognitive processes, wherein participants display similar cognitive and emotional responses, fostering shared cognitive processing and brain activity synchronization despite limited external interaction; (2) emotional connections, as divulging private information elicits emotional responses that can be neurally correlated among individuals; and (3) environmental influences, where shared environments and contexts prompt neural interaction among participants even in the absence of direct social engagement. These factors collectively contribute to increased brain activity correlations without active interaction. Our primary focus, however, lies in the phase characterized by significant synchronized brain activity.

Minor Comments:

(6) Equation 1 Explanation: There is no explanation of Equation 1. It mentions Yi as the collective score, but what constitutes the collective score Yi is not defined in the manuscript. Additionally, while "i" is referred to as an item (in Line 196), the meaning of "item" is not clear. Therefore, the meaning of this equation is not understood.

We apologize for this confusion. We have added a description in the manuscript (p.9).

“In Eq.1, x is the individual score, y is the collective score (y is calculated from the three per capita scores), and i stands for the group number for the item. So, _x_i means the individual score of participants in the i group, and _y_i means the collective score of the i group. _d (x, y) r_epresents the distance from the individual to the collective score.” p.9

(7) Equation 2 Explanation: There is no explanation for Equation 2. Please provide descriptions for all variables such as S, t, and w.

We have clearly stated the meaning of s, t, and w in the first edition of the manuscript article (p.12).

As shown in L291-293: Here, t denotes the time, s denotes the wavelet scale, 〈⋅〉 represents a smoothing operation in time, and W is the continuous wavelet transform (Grinsted, Moore, & Jevrejeva, 2004).

(8) Acronyms: Please define all acronyms upon their first appearance (e.g., CFI, TLI, RMSEA in L380).

We apologize for these mistakes, and we have added full explanations for abbreviations upon their first use (p.16).

“The mediation model demonstrated a satisfactory fit (CFI = 0.93, TLI = 0.93, RMSEA = 0.04) (CFI-Comparative Fit Index; TLI-Tucker-Lewis index; RMSEA-Root-Mean-Square Error of Approximation), suggesting that the perceived group identification of each individual affected the alterations in single-brain activations in the DLPFC, consequently leading to variations in their performance (β_a = 0.16, t = 2.20, p = 0.030; β_b = 0.26, t = 3.56, p < 0.001; β_c = 0.18, t = 2.34, p = 0.020) (Figure 3C).” p.16

(9) Hyperscanning fMRI Studies: Since there are hyperscanning fMRI studies analyzing communication among three people (e.g., Xie et al., 2020, PNAS), it would be beneficial to cite this research. pnas.org/doi/pdf/10.1073/pnas.1917407117.

As suggested, we have cited this paper. (p.4)

(10) Line 272; Line 275: Should these references be to Benjamini & Hochberg (1995)?

As suggested, we have revised our citation.

(11) Research Objectives: The authors' aim seems to be understanding the relationship between Group Identification Level (High or Low), collective performance, and inter-brain synchronization (GNS). If so, shouldn't the results shown in Figure 6 illustrate how these differ between High and Low groups?

We are grateful to the reviewer for your insightful comment. This study aimed to investigate the impact of group identity levels on collective performance and interbrain synchronization. Our analysis primarily focused on inter-group disparities to elucidate the potential influence of varying levels of group identification on collective behavior and neural synchrony, as highlighted by the reviewer. It is important to note that the relationship between group identification levels and collective performance, as well as neural synchronization, may represent a continuous or correlational process, rather than a binary comparison between two distinct groups. Notably, we treated group identification as a continuous variable and, consequently, Figure 6 was designed to illustrate trends in the association between group identification levels and both collective performance and neural synchronization, without conducting significance tests between groups. We are confident that the depiction in Figure 6 effectively captures the evolving dynamics between group identification levels and both collective performance and neural synchronization.

(12) Figure 6 Star-Marker: What is the star marker shown in Figure 6? Please provide an explanation.

We apologize for this confusion. We have added this explanation to the article. (p.21)

“The red star sign indicates that at this time point, the neural signal began to increase significantly.” p.21

(13) Pearson's Correlation: Use "Pearson's correlation" instead of "Pearson correlation."

Thanks for your comments, we've changed Pearson correlation to Pearson's Correlation for a total of 10 places in the original text (pp. 9,11,13, 15,16, 19,23).

“Moreover, the Pearson’s correlation was used to examine the relationship between group identification_2 and collective performance.” p.9

“Subsequently, we used Pearson’s correlation analyses to investigate the relationship between single-brain activation and individual performance.” p.11

“Second, the Pearson’s correlation between GNS and collective performance was performed.” p.13

“Following that, we analyzed Pearson’s correlations between the original HbO data in the region related to individual and collective performance, denoted as brain activation connectivity (Lu et al., 2010).” p.13

“Subsequently, the Pearson’s correlation between the quality of information exchange and collective performance was assessed.” p.15

“Furthermore, the results of the Pearson’s correlation indicated that groups with higher group identification were more likely to exhibit better collective performance (r = 0.38, p = 0.003) (Figure 2B).” p.15

“The Pearson’s correlation and its associated analyses were based on the data from group identification_2. *p < 0.05.” p.16

“We first extracted the HbO brain activities related to individual performance (e.g., DLPFC, CH4) and collective performance (e.g., OFC, CH21) of each group member and conducted a Pearson’s correlation between the two.” p.19

“Subsequently, Pearson’s correlation was used to test whether individual differences in the similarity in individual-collective performance were reflected by DLPFC-OFC connectivity.” p.19

“Pearson’s correlation showed that the higher quality of information exchange, the better collective performance (r = 0.36, p = 0.007) (Figure 8C).” p.23

(14) MNI Coordinates: The MNI coordinates for each channel are listed in the supporting information. How were these coordinates measured? Were they consistent for all participants? Was MRI conducted for each participant to obtain these coordinates?

Thank you for your reminder, we have included the necessary instructions in the revised version. First, we need to clarify that we referred to previous literature to determine the placement of the optical probe plates. Following the completion of data collection, we utilized the Vpen positioning system to accurately locate the detection light poles, ultimately obtaining the MNI positioning coordinates. These coordinates were basically consistent for each participant. (p.8)

“For each participant, one 3 × 5 optode probe set (8 emitters and 7 detectors forming 22 measurement points with 3 cm optode separation, see Table S1 for detailed MNI coordinates) was placed over the prefrontal cortex (reference optode is placed at Fpz, following the international 10-20 system for positioning). The other 2 × 4 probe set (4 emitters and 4 detectors forming 10 measurement points with 3 cm optode separation, see Table S2 for detailed MNI coordinates) was placed over the left TPJ (reference optode is placed at T3, following the international 10-20 system for positioning). The probe sets were examined and adjusted to ensure consistency of the positions across the participants. After the completion of data collection, we utilized the Vpen positioning system to accurately locate the detection light poles, ultimately obtaining the MNI positioning coordinates.” p.8