In-group social bonding manipulation session.

Each three-person group was randomly assigned to the social bonding or no-bonding control session. The in-group bonding manipulation in the current study was adapted from several previously validated procedures [15,46–49]. Specifically, we merged 3 essential procedures used in previous studies to manipulate in-group bonding: shared preference [46], symbolic marker [47], and similarity among group members [48]. First, for each in-group bonding session, we invited 3 participants preferring the same color (black or white, as indicated in the preexperiment survey) and used this color preference to create group identities, with the individuals referring black over white being labeled as “Group Black” and those preferring white over lack being labeled as “Group White.” Second, each participant was then given either a black vest (for “Group Black”) or a white vest (for “Group White”) to wear during the entire experimental session. The same-colored uniforms serve as an arbitrary symbolic marker and have been proven as a strong approach to enhance group identification, group coordination, and in-group favoritism [49]. Third, each group participated in a 4-min online chat session to introduce themselves and identify common features among group members. Brief conversations have been recognized as an effective way to establish and maintain social bond [88] and to strengthen interconnections among group members, particularly when the topic involved similarities or interdependence among them [89]. In contrast, participants in the no-bonding control session did not share color preference nor wear group uniform [15] and talked about their main courses without being explicitly asked to find shared features during the online communications. No verbal communication was allowed in both bonding and control sessions.

Leader election and within-group interaction session.

Participants engaged in a 4-min within-group online chat session. Similar to previous studies [44,45], participants were asked to: (i) democratically elect a leader for their group; and (ii) discuss the strategies that their group would employ in potential intergroup contests. Participants had the autonomy to decide whether they preferred initiating discussions on strategies, electing a group leader first, or discussing both 2 topics in parallel. We made it clear to participants that leaders in the current experiment were elected rather than appointed and held symbolic roles without formal power or responsibility over other group members. During the online chatting, participants were labeled by different shapes and communicated via sending messages to remain anonymous (verbal communication was not allowed). For each three-person group, any group member could self-nominate or nominate their peers as the leader. Among all groups, 85% of groups (N = 149) nominated 1 candidate as the leader, who was then approved, while the remaining 15% of groups (N = 27) initially nominated multiple candidates but later identified one of them as the final leader later. Of all leaders, 37.5% (N = 66) self-nominated while 62.5% (N = 110) were nominated by their peers.

Leader election validation.

All 176 three-person groups elected their leaders within the 4-min session and successfully recognized group leader in the post-survey. We conducted conversation analysis and compared the total number and length of the utterance given by leader and followers. We found that the group leader was more talkative than followers during group communications (total number of utterances: t₁₇₅ = 5.418, p = 1.970 × 10⁻⁷, Cohen’s d = 0.408, 95% CI: 1.315, 2.822; total length of utterances: t₁₇₅ = 8.316, p = 2.468 × 10⁻¹⁴, Cohen’s d = 0.627, 95% CI: 26.932, 43.693). Moreover, the group leader was more likely to initiate group interaction (leader: 40.3% versus three-person-average: 33.3%, p = 0.039). In addition, we asked participants to report their willingness to be the group leader (0 = not willing at all, 10 = extremely willing). We found that, both in bonding and control conditions, the group leader showed higher willingness and motivation to be the group leader (main effect of leader: F_{1, 172} = 64.615, p = 1.40 × 10⁻¹³, η² = 0.273). Moreover, leaders who underwent social in-group bonding exhibited a higher level of willingness to be the group leader (leader × bonding interaction: F_{1, 172} = 0.067, p = 0.812, η² = 3.31 × 10⁻⁴). Finally, the chat transcriptions of all 176 groups were evaluated by independent raters, who were blind to experimental hypotheses and conditions, along domains of (i) identifying the group leader of each group (identification accuracy = 97.66%); and (ii) reporting perceived interaction quality and leadership. These results suggested that leaders were not randomly elected or coerced into their positions and validated our experimental setup for establishing the roles of the group leader and followers in three-person groups.

Economic games related to intergroup discrimination.

In the IDG, participants received an endowment of 100 monetary units (MUs) and decided how to split the 100 MUs between hypothetical in-group and out-group members. The different MUs to in-group and out-group members indicated the level of intergroup discrimination [15,58]. In the IPD-MDG, participants received an endowment of 100 MUs and decided how to split the 100 MUs among a self pool, a within-group pool, and a between-group pool [59,60]. Each MU to the self pool was kept as 1 MU to the participants themselves; each MU contributed to the within-group pool added 0.5 MU to each in-group member, including the contributor, and each MU contributed to the between-group pool added 0.5 MU to each in-group member and in addition, subtracted 0.5 MU from each out-group member. Contributions to the within-group pool reflects “ingroup love” without hurting out-group members. Contributions to the between-group pool, in contrast, reflects spiteful “out-group hate.”

Conversation analysis.

We analyzed the transcripts of turn-taking conversations for each three-person group. For the within-group communication of each group, we calculated: (i) the total number of utterances of group leader and followers, respectively; (ii) the number of turn-transition; and (iii) the turn response time (i.e., the time gap between turns) separately for inter-status and intra-status transitions. The inter-status turn-transition was defined as a discrete pair of a leader utterance followed by a follower utterance, or vice versa, whereas the intra-status turn-transition was defined as a follower utterance followed by another follower. The turn response time was then log transformed to avoiding skewness. To control for the total length of utterances of all 3 group members, we include the total word number as covariate in the further analysis. These conversation-related indices were submitted to two-way mixed-model ANCOVAs with a within-subjects factor hierarchy (inter-status versus intra-status or leader versus follower), a between-subjects factor bonding (bonding versus control), and total word number as covariate. It should be noted that, the mean turn response time in the current study deviated largely away from the verbal conversation turn response time of about 200 ms, possibly due to that group members communicated via online messaging rather than verbal communication. In addition, to mitigate the potential impact of displaying “typing” in the group chat window on response latency measurement, we have opted not to show status information (i.e., whether someone is typing or not) in the chat window. Only after participants completed and submitted their messages into the group chat window, other members were then able to read others’ messages.

Participants’ subjective ratings.

Participant’s self-report of inter-status cohesion (i.e., cohesion between leader and follower) and intra-status cohesion (i.e., cohesion between followers) were submitted to a two-way mixed-model ANOVA with a within-subjects factor hierarchy (inter-status versus intra-status) and a between-subjects factor bonding (bonding versus control). Follower’s ratings of perceived social influence and attraction of the group leader was compared between bonding and control conditions with two-tailed independent-sample t tests. Moreover, we performed partial correlation analyses to test the relationship between the perceived social influence (attraction) and the turn transition (response time) separately for inter- and intra-status, controlling the utterance length of leaders and followers, respectively.

We next conducted mediation analysis to examine whether the effect of social bonding (the independent variable, X) on the leader’s social influence or attraction (the dependent variable, Y) was mediated by social cohesion (the mediator, M). The mediation analyses were performed using PROCESS (model 4) in SPSS. For each mediation analysis, we computed both the indirect effect (c) and direct effect (c’), where c measures the extent to which X influences Y through M, while c’ represents the effect of X on Y that cannot be explained by c. If c is nonzero and c’ is zero, it indicates full mediation; otherwise, it suggests partial mediation. The significance of mediation was assessed using both Sobel test and Preacher–Hayes bootstrapping. The Sobel test was employed to determine if introducing M significantly reduced the relationship between X and Y. A two-tailed z-test was used to establish statistical significance level. On the other hand, bootstrapping method involved a nonparametric examination of whether zero fell within the bootstrapped 95% confidence intervals (5,000 times). If zero did not fall within the confidence intervals, we could conclude that there existed a significant indirect effect. It showed be noted that causal direction in the mediation analysis was not directly examined. Further research employing experimental and longitudinal approaches is warranted to validate our current findings from the mediation analysis.

Intergroup discrimination.

Participants completed the IDG and IPD-MD before the experiment (as baseline) and at the end of the experiment. We were interested in the intergroup discrimination, i.e., differences in monetary allocation to in-group members and out-group members. Moreover, in IPD-MD, we were also interested in the amount of MU allocated to the within-group pool (i.e., “ingroup love”) and the between-group pool (i.e., “outgroup hate”), respectively. We first compared the baseline intergroup discrimination measured before the experiment between bonding and control sessions and between leaders and followers. We found comparable baseline intergroup discrimination (main effect of bonding: F_{1, 174} = 0.541, p = 0.463, η² = 0.003; main effect of hierarchy: F_{1, 174} = 0.017, p = 0.897, η² = 9.712 × 10⁻⁵; bonding × hierarchy interaction: F_{1, 174} = 0.007, p = 0.935, η² = 3.855 × 10⁻⁵), ingroup love (main effect of bonding: F_{1, 174} = 0.149, p = 0.700, η² = 0.001; main effect of hierarchy: F_{1, 174} = 0.257, p = 0.613, η² = 0.001; bonding × hierarchy interaction: F_{1, 174} = 1.484, p = 0.225, η² = 0.008), and outgroup hate (main effect of bonding: F_{1, 174} = 1.140, p = 0.287, η² = 0.007; main effect of hierarchy: F_{1, 174} = 0.447, p = 0.505, η² = 0.003; bonding × hierarchy interaction: F_{1, 174} = 0.320, p = 0.572, η² = 0.002) among the 4 conditions. The intergroup discrimination in the IDG, the ingroup love and outgroup hate in the IPD-MDG, measured at the end of the experiment, were submitted to bonding × hierarchy (leader versus follower) ANOVAs to examine bonding effects on intergroup discrimination in leader and followers.

Independent ratings on within-group interaction.

To objectively quantify the within-group interactions perceived by third-party observers, independent raters were asked to identify the leader of each group and leader emergence time and to evaluate the chatting messages of all the 176 groups along the following dimensions on a 9-point Likert scale: (i) interaction frequency (1 = least frequent, 9 = most frequent); (ii) interaction intensity (1 = least intense, 9 = most intense); (iii) group cohesion (1 = least cohesive, 9 = most cohesive); and (iv) prominence of the group leader (1 = least prominent leader, 9 = most prominent leader). The independent raters correctly identified the group leader (accuracy: 97.66%). The ratings were reliable among the 14 raters (interaction frequency: ICC consistency: 0.940, agreement: 0.885; interaction intensity: ICC consistency: 0.814, agreement: 0.710; group cohesion: ICC consistency: 0.855, agreement: 0.757; leader prominence: ICC consistency: 0.813, agreement: 0.746). For each rating dimension, rating scores were first z-score transformed for each rater. The normalized ratings were then averaged across raters and compared between bonding and control conditions using two-tailed independent-sample t tests. The rating data of one group was missing. We showed that social bonding indeed facilitated the outsider-perceived group interaction frequency (t₁₇₃ = 4.426, p = 1.696 × 10⁻⁵, Cohen’s d = 0.669, 95% CI: 0.264, 0.688, S3A Fig) and intensity (t₁₇₃ = 3.943, p = 1.166 × 10⁻⁴, Cohen’s d = 0.596, 95% CI: 0.157, 0.472, S3B Fig). Moreover, independent raters identified the leader of groups under bonding (versus control) condition faster (t₁₇₃ = −2.547, p = 0.012, Cohen’s d = −0.385, 95% CI: −40.522, −5.140, S3C Fig) and also recognized the prominence of group leader in the bonding condition to a greater degree than that in the control condition (t₁₇₃ = 2.001, p = 0.047, Cohen’s d = 0.303, 95% CI: 0.002, 0.339, S3D Fig).

Data quality check.

The following steps were performed to check and ensure the data quality of fNIRS signals. First, prior to data recording, the resistance for each optode probe was monitored and adjusted to meet the minimum criteria defined in the LABNIRS recording software, aiming to achieve a good signal-to-noise ratio [94]. Second, during data recording, the raw optical density signal in each channel was transformed into concentration changes in HbO and HbR in real time, which were visually inspected to assess signal quality [95]. Third, during preprocessing of the fNIRS signals, we applied an automatic sliding-window detection to further evaluate data quality. Specifically, for each HbO and HbR time series, extreme values exceeding mean ± 3 standard deviations (SD) within a 10-s time-window were identified as outliers [96]. Channels with severe motion artifacts or containing more than 5% extreme values were labeled as bad. In order to maintain the same number of channels across all groups, any group with one or more bad channels was excluded from further analyses. Based on these criteria, a total of 8 groups were excluded from the final dataset due to poor data quality.

Inter-brain neural synchronization (INS).

We performed INS analysis on the neural data collected during the resting-state session (4 min, served as a baseline) and within-group interaction session (4 min). Similar to previous studies [15,34–37,44,45], we employed the WTC analysis to assess the cross-correlations between 2 oxy-Hb time series of dyads of participants as a function of frequency and time [97]. Specifically, within each three-person group, the 3 same-length oxy-Hb time series for each channel (i.e., oxy-Hb_leader, oxy-Hb_follower1, and oxy-Hb_follower2) were simultaneously acquired by the same fNIRS system. We applied WTC analysis to each pair of 3 oxy-Hb time series and generated 3 time-frequency matrices of the coherence values for each group (i.e., Coherence_{leader-follower1}, Coherence_{leader-follower2}, and Coherence_{follower1-follower2}). The coherence values from the leader-follower dyads (averaged value of Coherence_{leader-follower1} and Coherence_{leader-follower2}) indicated the inter-status INS, and the coherence value from the follower–follower dyads (i.e., Coherence_{follower1-follower2}) indicated the intra-status INS. In each time-frequency matrix (Fig 3A), each row corresponded to a specific frequency point, each column corresponded to a specific time point and the color bar corresponded to the coherence value. To ensure consistent data size for inter- and intra-status INS, we conducted a set of control analyses by calculating coherence values between the group leader and a randomly selected follower to index inter-status INS. With this approach, the data size and calculation of inter- and intra-status INS were matched. The results obtained from these control analyses replicated our main findings (S10 Fig).

fNIRS signals not only reflected task-evoked brain activity but also systemic physiological interference arising from cardiac pulsation (approximately 1 Hz), breathing rate (approximately 0.3 Hz), and other homeostatic processes [95]. Similar to previous studies [4,98], we employed the baseline subtraction approach to mitigate the impact of physiological noise. Specifically, we recorded a resting state session with an identical duration as the task session. As the resting-state predominantly reflects spontaneous hemodynamic oscillations [98], it served as the baseline for comparison. We performed WTC analysis on the neural data collected during both the resting-state session (4 min, serving as a baseline) and within-group interaction session (4 min). To reveal the effects of bonding and hierarchy on INS specific to group interaction, we focused on the increased INS during group interaction relative to the baseline (i.e., the resting-state). First, we compared coherence values (averaged across all channels and for each channel) between the within-group interaction session and resting-state session by performing paired-sample t tests for each frequency (frequency range 0.01 to 1 Hz) [99] to identify the FOI (Fig 3A). This analysis identified increased coherence values in 2 frequency bands: between 0.136 Hz and 0.192 Hz (corresponding to the period between 5.20 and 7.35 s) and between 0.407 and 0.432 Hz (corresponding to the period between 2.31 and 2.46 s). These 2 frequency bands were chosen as the frequency of interest for the subsequent analyses (FOI, Bonferroni family-wise error (FWE) corrected for multiple comparisons). It is worth noting that no significant results were found in the frequency band of 0.407 to 0.432 Hz (full statistics were reported in S9 Table); therefore, only results based on 0.136 to 0.192 Hz were reported in the main text. This chosen period also effectively captures the temporal structure of the within-group interaction task since one-round within-group messaging typically took an average time of 5 to 7 s. In addition, this frequency band also excluded high- and low-frequency physiological noises, such as those related to respiration (about 0.2 to 0.3 Hz), cardiac pulsation (0.7 to 4 Hz), and high-frequency head movements (>1 Hz) [98].

We then calculated the session- and FOI-averaged coherence values and converted into Fisher z-scores. The increased INS (coherence differences between within-group interaction and resting-state) was submitted to bonding × hierarchy (inter-status versus intra-status) ANOVAs. Note that, the WTC algorithm normalized the amplitude of the signal within each time-window defined by the wavelet to make the data less vulnerable to transient spikes or motor artifacts [34–36]. Moreover, we conducted 2 sets of complementary analyses to further control the potential impact of physiological noises. First, we applied a wavelet-based denoising method to identify global physiological components per channel and extracted them out of the hemodynamic signals [15,61]. After the denoising process, the same WTC calculation and statistical analyses were applied, and the observed results were reserved (main effect of hierarchy at channel 3, F_{1, 174} = 6.296, p = 0.013, η² = 0.035, hierarchy × bonding interaction effect at channel 9, F_{1, 174} = 5.311, p = 0.022, η² = 0.030, S3A Table). Second, we controlled the globally co-varying signal using ANCOVA analyses [62], with the global mean INS (averaged coherence values across all channels) as the covariate. Significant results were fully replicated (main effect of hierarchy at channel 3, F_{1, 174} = 9.220, p = 0.003, η² = 0.051, hierarchy × bonding interaction effect at channel 9, F_{1, 174} = 8.373, p = 0.004, η² = 0.046, S3B Table).

Time-lagged analysis.

To investigate the directionality of the inter- and intra-status INS, we conducted time-lag analysis [63–65] for the channels that showed increased INS during the within-group interaction stage, i.e., channel 3 in the rTPJ and channel 9 in the rDLPFC. For each leader–follower (or follower–follower) dyad, the time courses of neural activity of the leader (1 follower) were shifted relative to that of the follower (the other follower) from −10 to 10 s (in 1-s increment). We then recalculated the inter- and intra- status INS on each time lag for both resting-state and within-group interaction. The time-lagged inter- and intra-status neural alignment increases (i.e., lagged INS during within-group interaction minus that during resting) on each time lag were compared with 0 using one-sample t tests and compared between bonding and control conditions using two-tailed independent-sample t tests. Significant effects were thresholded at p < 0.05, FDR corrected for multiple comparisons of the 21 time lags. Next, we performed correlation analysis between the neural alignment on each time lag and intergroup discrimination, for inter-status and intra-status dyads, respectively, the correlation coefficients were FDR corrected for multiple comparisons of the 21 time lags. We also performed Pearson’s correlation coefficient analysis separately for bonding and control conditions.

Permutation test.

First, we aimed to validate the INS increases (i.e., group interaction versus resting-state) in real groups. To this end, we examined which conditions showed increased INS (i.e., significant INS increases during group interaction compared to resting-state). Specifically, we compared INS differences (group interaction minus resting-state) against zero for the channels that exhibited significant effects of interest (i.e., channel 3 in the rTPJ and channel 9 in the rDLPFC). We found increased INS for the inter-status dyads at channel 3 in the rTPJ under control condition (t_1,86 = 3.943, p = 1.64 × 10⁻⁴) and bonding condition (t_1,88 = 3.394, p = 0.001; survived multiple correction) and at channel 9 in the rDLPFC (bonding: t_1,88 = 3.378, p = 0.001; survived multiple correction). We then performed permutation test to examine whether these conditions showed increased INS in real group than pseudo groups. Specifically, within each condition, we generated three-person pseudo-groups by randomly grouping 3 participants from different original real groups. For each pseudo-group, the INS of each dyad was recalculated. This procedure was repeated for 1,000 times to generate a pseudo-group INS distribution. The increased INS in the aforementioned conditions of real groups were compared with each condition-specific permutation distributions. The significance level, p-value was indicated as: p = j/1,000, where j is the number of samples out of the 1,000 permutation samples, of which the examined value was larger than the observed value of real groups. The results indicated that the increases in inter-status INS in the rTPJ (control: p = 0.022; bonding: p = 0.047) and rDLPFC (bonding: p = 0.032) of real groups all exceeded the upper 95% CI of the permutation distribution. These findings further confirmed an increased INS in these specific conditions within real (rather than random) groups.

Next, to validate the observed bonding and/or hierarchy effects on INS, we performed another 2 sets of permutation tests: (i) the within-condition permutation test; and (ii) cross-condition permutation test. First, within the bonding and control conditions, leader and followers of the real groups were randomly reassigned into new groups to form three-person pseudo groups. We then recalculated the inter- and intra-status INS for the 176 pseudo groups. This shuffling and recalculation procedures were repeated 1,000 times to generate permutation distributions for the observed hierarchy effect in rTPJ and bonding × hierarchy interaction effect in the rDLPFC. We then compared the observed effects of real interacting groups against 1,000 permutation samples and examined whether real effect exceeded the upper limits 95% or 99% CI of the permutation distribution. Second, similar procedures and statistical analyses were conducted for the cross-condition permutation test except that we generated cross-condition, three-person pseudo groups by randomly grouping 1 leader and 2 followers across bonding and control conditions as a pseudo-group.

rDLPFC-rTPJ functional connectivity.

We applied cross-correlation analysis using the Functional Connectivity Toolbox [100] implemented in MATLAB to assess the functional connectivity of each rDLPFC-rTPJ channel pair (49 channel pairs, 7 channels in TPJ, and 7 channels in DLPFC) for each participant, which was then Fisher z transformed [101]. We also averaged the 49 channel pairs to index the grand mean of functional connectivity. The channel-pairwise connectivity and grand mean connectivity were separately submitted to bonding × hierarchy (leader versus follower) ANOVAs (FDR correction for multiple comparisons of 49 channel pairs was applied to channel-pairwise analysis). Next, the channel showing significant bonding effect on leader-to-follower neural alignment (i.e., CH9 in the rDLPFC) was used as the seed channel and the averaged functional connectivity across the 7 CH9-rTPJ channel pairs was used to index the channel-based functional connectivity. We then conducted correlation analysis between the channel-based functional connectivity and the leader-to-follower neural alignment in rDLPFC.

Additional analyses and results.

To test whether the effects of social in-group bonding on hierarchical interaction were modulated by different interaction stages, we conducted additional analyses. First, we identified the specific time point at which the group leader explicitly emerged in each group. This analysis revealed that the establishment of a group leader occurred approximately halfway through the within-group interaction (with a mean value of 145.60 s, SE = 5.76). Second, based on this identified time point for leader emergence, we divided the within-group interaction session into 2 stages: pre- and post-leader emergence stages. Third, we conducted 3-way ANOVAs to examine whether these interaction stages influenced our main findings regarding hierarchy and/or bonding effects on both behavioral and neural indices. The results showed no significant impact of the interaction-stage on our main findings (S10A Table). Furthermore, despite observing an average occurrence of leader emergence around the middle of the within-group interaction period, we further balanced the duration between pre- and post-leader emergence stages by dividing it equally into 2 parts for subsequent analyses. This mid-split approach replicated our observation of no significant impact of different interaction stages (S10B Table). These results suggested that the effects of social bonding on hierarchical interaction remained consistent across different stages of within-group interaction. Alternatively, it is possible that in the current experimental setting, the group leader implicitly emerged prior to the explicit emergence time point (e.g., during the bonding section). Supporting this possibility, we observed that the group leader was more likely to initiate group interaction at the beginning of within-group interaction and was already more talkative in the pre-emergence stage (total number of utterances: t₁₇₅ = 4.877, p = 2.404 × 10⁻⁶; total length of utterances: t₁₇₅ = 7.451, p = 4.076 × 10⁻¹²). Furthermore, a majority of groups (85%, N = 149) early on nominated the individual who later emerged as their leader. We encourage future studies to directly investigate these possibilities. In addition, it is important to note that this examination of time effect was merely an initial exploration conducted at a coarse time scale. Thus, the neural dynamics at second or millisecond resolution needs to be directly and systematically examined in future studies.

To present the measured brain activity from different perspectives, we repeated our analysis on the deoxygenated hemoglobin signals (HbR). Specifically, we calculated the INS and intra-brain rDLPFC-rTPJ functional connectivity on HbR signals. We then performed the bonding × hierarchy ANOVAs on HbR-INS and HbR-FC to examine whether the main findings obtained with HbO signals would be similarly observed with HbR signals. Similar to the pattern of the HbO signals, we observed a significant, although weaker (did not survive multiple corrections), hierarchy effect in rTPJ (channel 3, F_{1, 174} = 4.736, uncorrected p = 0.031, η² = 0.026, S11 Table and S11A Fig), with stronger inter-status INS than intra-status dyads. However, no bonding × hierarchy interaction effect was observed on HbR signals (channel 9, F_{1, 174} = 0.420, p = 0.518, η² = 0.002). The difference observed on INS based on HbO and HbR signals may be caused by different sensitivities of these 2 types of signals in reflecting task-induced changes in neural signals. Regarding the intra-brain FC index, the leader effect on the rDLPFC-rTPJ functional connectivity (stronger in leader than followers) based on HbO signals was similarly observed in the HbR-FC analysis (48 rDLPFC-rTPJ channel pairs survived FDR correction for 49 channel pairs, S12 Table; S11B Fig for the grand mean rDLPFC-rTPJ connectivity, F_{1, 174} = 27.345, p = 4.842 × 10⁻⁷, η² = 0.136).