Solitary movement style predicts collective foraging while whom to follow emerges only in company

Hiroshi Higashi

physics.soc-phOct 27, 2026

Solitary movement style predicts collective foraging while whom to follow emerges only in company

Authors: Hiroshi Higashi

Organizations: Faculty of Engineering Science, Kansai University, Suita, Osaka, Japan.

Abstract

How far can behaviour inside a group, and the group's performance, be predicted from members measured while alone? We tested this on three public datasets of human collective foraging (621, 128 and 1,133 participants). A low-dimensional individual representation estimated from private-phase movement was mapped onto behaviour inside the group through a mapping learned on other participants. Private information processing was stable between the two halves of a session (split-half reliability, the correlation between the halves, 0.60--0.83) and predicted behaviour inside the group with correlations of 0.30--0.66. Selective social learning, following those who have succeeded or stopped, showed stable individual differences inside the group (reliability 0.45--0.59) yet was not predicted at all from the same person's private behaviour. Group performance was predicted with a correlation of 0.55 in all three datasets by simulations never fitted to group outcomes or by the mean of individually measured performance, a prediction carried by mobility and individual performance rather than by social weights. We found no credible evidence for an effect of how members were combined (equivalence bound 0.06). Whom to follow thus emerges only in company, which delimits what solitary measurements can predict and compose.

Figures & tables

Figure 1: Individual style measured in private and the four directions in which its transfer was tested. A low-dimensional individual representation

z

is estimated from behaviour recorded while a participant is alone (Wu et al.) or away from the resource (Chirkov et al., Hawkins et al.) and used to predict (1) private information processing inside the group, (2) social attraction, (3) selective (payoff- or state-dependent) social learning, and (4) roles in the attention network and group performance (group performance is predicted from individually fitted policies in Chirkov et al. and from the mean of individually measured performance in Wu et al. and Hawkins et al.). Arrow colour summarises the result across the three datasets. Green: transfers (private processing up to the split-half ceiling; roles follow an additive own-plus-others structure; group performance is predicted by the members’ mean). Orange: partial transfer. Red dashed: no transfer although the trait is reliable inside the group.

Dataset	Task	Size	Private phase / social phase
Chirkov et al. 2026 [ 24 ]	Track a moving resource for 15 min in an immersive 3-D environment. Alone (A) or in groups of five (no payoff information NP / voluntary sharing VP / full payoff information FP) $\times$ resource speed (slow / fast). 10-Hz recording; the attention network (who sees whom) reconstructed each second from a 90 ∘ field of view	621 participants (144 alone, 477 in groups); 103 groups (65 of five, 38 of four)	Search phase (more than 40 m from the resource) / tracking phase (on the resource)
Wu et al. 2025 [ 37 ]	16 rounds of 120 s searching for reward blocks in Minecraft (8 solo, 8 in groups of four; random / smooth reward environments). 20-Hz recording; field of view reconstructed in Unity	128 participants; 32 sessions (groups of four)	Solo rounds / group rounds
Hawkins et al. 2023 [ 38 ]	1–6 players search a 2-D screen for an invisible circular scoring region that moves, in games of 5–6 min. Experiment 1: binary payoff display; Experiment 3: graded payoff field and waiting-room recording. 8-Hz recording	Experiment 1: 682 participants, 294 games; Experiment 3: 451 participants, 223 games; group level 281 games (169)	Search state (outside the region) and waiting room / scoring state (inside the region)

Table 1: The three public datasets analysed. Group counts are the groups used in the analyses (Chirkov: groups with four or five analysed members; Hawkins: games with at least two players, in parentheses at least three).

Figure 2: Split-half reliability of individual parameters by trait class. Split-half reliability of each individual parameter (Pearson

r

between the first and second half of the session; Wu: rounds 1–2 vs 3–4 of each block), grouped by trait class. Colour = dataset (legend below). The figure shows representative parameters of each class; RewardPrediction in Wu (0.43) and Experiment 3 of Hawkins are not shown (all parameters in Supplementary Table 2).

Figure 3: Transfer from the private phase to behaviour inside the group. Out-of-fold Pearson

r

between the target measured in the social phase and its prediction from the private-phase

z

(ridge regression; folds of whole groups, sessions or games). Black ticks: split-half reliability of the target (ceiling). Bar colour: trait class of the target (legend bottom right). (A) Chirkov et al.: tracking-phase random effects predicted from the search-phase

z

(PLS, 4 dimensions;

n=568

), and later roles in the attention network predicted from the first-3-min movement

z

(PCA, 4 dimensions;

n=477

; no ceiling computed for roles). (B) Wu et al.: group-round targets predicted from the solo-round

z

(PCA of 21 movement and foraging statistics, 4 dimensions; 8 folds of 4 sessions;

n=128

). (C) Hawkins et al., Experiment 1: second-half targets predicted from the first-half search-state

z

(PCA, 4 dimensions; 10 folds of games;

n=682

; residualised within experiment

\times

group size

\times

field).

Figure 4: Variance decomposition of roles in the attention network (being attended to and attending to others). Increment in marginal

R^{2}

of being attended to (in-degree) and attending to others (out-degree) when adding, in order, the participant’s own

z

(blue), the mean

z

of the other members (orange) and the within-group SD of

z

(red) to a mixed model with a group random intercept and a performance control, for the three datasets. Likelihood-ratio

p

values of the SD term are given in the text and in Table 2 .

Figure 5: Prediction of group performance from the members’ individually measured traits. Observed group performance against its prediction (both standardised within cell). (A) Chirkov et al.: score of each group simulated with the members’ individually fitted ABM policies (leave-one-group-out; mean of 100 seeds; 103 groups; blue slow, orange fast).

r=0.55

[0.42, 0.67]. (B) Wu et al.: group reward (mean of the four group rounds per session

\times

environment, 64 cells) against the mean of the members’ solo-round reward in the same environment.

r=0.55

. (C) Hawkins et al.: second-half group score against the mean of the members’ first-half individual scores (281 games with at least two players; Experiment 1 blue, Experiment 3 orange).

r=0.55

[0.44, 0.64]. Nothing was fitted to group performance.

Figure 6: Change in out-of-sample prediction when within-group heterogeneity is added (composition effect). Change in out-of-sample

r

(

\Delta r

, 95 % cluster-bootstrap confidence interval) when within-group heterogeneity is added to a model that already carries the members’ mean traits. Chirkov: individually fitted agents

-

group-mean agents (ABM policy; neural policy; 103 groups). Wu: the same contrast in the original grid ABM without the mobility term (64 session

\times

environment cells), and member means + SDs

-

means in a leave-one-session-out ridge (256 group rounds). Hawkins: means + SDs

-

means (169 games with at least three players). Black diamonds: pooled estimates from a stratified cluster bootstrap over all units. One contrast per dataset (Chirkov ABM policy, Wu statistical, Hawkins statistical;

\Delta r=-0.04

[-0.07, -0.01]) and all five contrasts (

+0.01

[-0.03, +0.05]); one-sided 95 % upper bounds

-0.01

and

+0.04

	Chirkov et al.	Wu et al.	Hawkins et al.
Reliability, private processing	0.76 / 0.60	0.83 / 0.76	0.69 / 0.64
Reliability, selective social learning	0.09–0.12	0.45 / 0.27	0.55 / 0.25
Transfer, private processing ( $r$ / ceiling)	0.50 / 0.76	0.64 / 0.83	0.37 / 0.69
Transfer, selective social learning	not evaluable (ceiling $\leq 0.12$ )	$\approx 0$ (negative)	0.06
Roles: contribution of within-group SD ( $p$ )	0.22–0.95	0.26–0.76	0.048–0.53
Group performance, prediction $r$	0.55 (103 groups)	0.55 (64 cells)	0.55 (281 games)

Table 2: Summary of the main results in the three datasets. Reliability is split-half reliability (two representative parameters). Transfer is the out-of-fold

r

from the private-phase

z

and its ceiling. Roles, SD: range of likelihood-ratio

p

for adding the within-group SD in the variance decomposition. Group performance: the

r

of Fig 5 .

\Delta r

: the primary contrast of Fig 6 (95 % confidence interval).

Supplementary Fig. 1: Chirkov et al.: leave-one-group-out prediction of all collective metrics by the individually fitted ABM policies and comparison with the controls. (A–H) Observed (vertical) against predicted (horizontal; mean of 100 seeds with the members’ individual policies) score, tracking time, tracking efficiency (points per second of tracking), median distance from the resource centre, in-degree, out-degree, between-member in–out correlation and discoverer attention gain. All standardised within condition

\times

speed. Blue slow, orange fast. Each panel shows

r

with its 95 % group-bootstrap confidence interval;

n=103

groups (discoverer attention gain: 77 groups with discovery events). (I) Within-cell

r

of each simulation variant: members’ own policies; group-mean agents (all members replaced by the group’s mean parameters); each member alone; mean-preserving re-composition; random re-composition within the same cell; the original study’s default parameters; the within-cell mean parameters of the training fold. The out-degree

r\approx 0.48

shared by all variants reflects the number of analysed members (groups of four vs five) and carries no policy information.

Supplementary Fig. 2: Chirkov et al.: the same panels for the neural policy conditioned on the participant embedding

\bm{e}

(vectorised environment). (A–H) Predictions of the neural policy in the same layout as Supplementary Fig. 1. (I) Within-cell

r

of each variant: members’ own

\bm{e}

; group-mean

\bm{e}

; each member alone; the population policy (

\bm{e}=0

); the within-cell mean

\bm{e}

of the training fold. Score

r=0.43

[0.24, 0.59], tracking time 0.38, efficiency 0.52; difference from the group-mean-agent control for score

\Delta r=+0.02

[-0.07, +0.12].

Supplementary Fig. 3: Agreement between the vectorised environment and the original mesa ABM. Homogeneous agents with the original study’s default parameters were run on the grid of Fig 5B of Chirkov et al. (social-information sensitivity

k\in\{0.1,1,10\}

, resource speed 0.2–1.0; solitary agents as triangles, groups of five as circles; colour = resource speed). (A) Tracking time and (B) tracking efficiency (points per tracking step), mesa ABM (horizontal; 100 runs per cell) against the numpy re-implementation used for the neural policy and the search over social rules (vertical; 200 runs per cell). Dashed: identity.

r=0.997

and 0.996.

Supplementary Fig. 4: Wu et al.: the original grid ABM without and with a per-agent mobility term. (A) Observed group reward (mean of the four group rounds per session

\times

environment, 64 cells, standardised within environment) against the zero-shot simulation with the members’ fitted choice weights and the original one-cell-per-step movement (

r=0.20

). (B) The same with each agent moving on a step with probability

p_{i}=

(mean solo-round path length) / (maximum over participants), calibrated from the solo rounds only (

r=0.44

). Blue random, orange smooth environment. (C) Within-environment

r

(session-cluster bootstrap 95 % confidence interval) of the four variants (members’ own weights, group-mean agents, population weights, each member alone). Open: without the mobility term; filled: with it. (D) Absolute level of group reward per environment: without mobility, with mobility, group-mean agents (with mobility), observed.

Supplementary Fig. 5: Chirkov et al.: search over social rules in the vectorised environment. The 103 analysed groups were each simulated 50 times with their members’ fitted ABM parameters under the baseline rule (R0) and seven rules that change a single element of the social part of the decision rule: R1 turn towards the nearest visible other instead of the mean bearing of visible others; R2 judge the quality of social information from the best-informed visible other; R3 wide scanning turns ( $p=0.2$ ) while searching; R4 align with the others’ mean heading instead of turning towards them; R5 use only others on the resource as a source of social information; R6 scale rotation while tracking by 0.8; R7 = R5 + R3. (A) Within-cell $r$ between the seed-mean simulation and the observed group metrics (colour and number; colour bar at right). (B) Levels (mean over groups) of discoverer attention gain, in–out correlation, in-degree and tracking time for R0–R7 (points) and observed (dashed). Rules that direct attention to others on the resource (R2, R5, R7) reproduce the level of attention to discoverers (0.31–0.41 vs 0.33 observed), but no rule reproduces the between-group variation of the network metrics.

Dataset	Parameter	Meaning	Trait class
Chirkov (RE)	Intercept	Baseline amount of rotation while tracking (motor activity)	Private processing
	Detector	Sensitivity to the resource detector (change in distance to the resource); strength of heading correction when about to lose the resource	Private processing
	SocPosInFOV	Weight on turning towards the mean position of others in view	Social attraction
	SocMovDir	Weight on aligning with the others’ mean movement direction	Social attraction
	SocPos $\times$ SocQual, SocMov $\times$ SocQual	Increment of the above weights when visible others are closer to the resource than oneself (payoff selectivity)	Selective social learning
Chirkov (ABM policy)	$I$ , $S$	Baseline rotation while tracking and sensitivity to the detector	Private processing

Supplementary Table 1: Meaning of the individual parameters and their trait classes. RE = participant-level random effect of the original study’s computational model (teacher model). Behavioural measures are summary statistics. Trait classes correspond to the colours of Figs 2–3.

Dataset	Parameter	$r$	Dataset	Parameter	$r$
Chirkov (RE)	Intercept	0.76	Wu (choice weights)	Locality	0.83
	Detector	0.60		BlockVisibility	0.76
	SocPosInFOV	0.30		RewardPrediction	0.43
	SocMovDir	0.17		SuccessfulProximity	0.45
	SocPosInFOV:SocQual	0.12		UnsuccessfulProximity	0.27
	SocMovDir:SocQual	0.09		AdaptLocality	0.39

Supplementary Table 2: Split-half reliability of the individual parameters (all parameters). Chirkov: random effects of the tracking model (first vs second half, empirical-Bayes teacher,

n=611

) and ABM policy parameters (

n=621

). Wu: rounds 1–2 vs 3–4 of each block (

n=128

). Hawkins: first vs second half, within experiment

\times

group size

\times

field (Experiment 1

n=557

–682, Experiment 3

n=338

–450).

Variant	$r$	95 % CI	$r$ (random)	$r$ (smooth)
Own	0.20	$[-0.03,0.42]$	0.16	0.24
Group mean	0.04	$[-0.21,0.29]$	$-0.03$	0.11
Population	0.05	$[-0.23,0.33]$	0.06	0.04
Alone	0.10	$[-0.14,0.36]$	0.13	0.08
Own + mobility	0.44	$[0.24,0.64]$	0.67	0.22
Group mean + mobility	0.47	$[0.23,0.67]$	0.64	0.29

Supplementary Table 3: Wu et al.: prediction of group reward by the grid ABM without and with the mobility term. Top: within-environment

r

of each variant (64 session

\times

environment cells; session-bootstrap 95 % confidence interval) and

r

by environment. Middle:

\Delta r

between variants. Bottom: absolute level of group reward per environment (simulation vs observed). Own = the participants’ own choice weights, group mean = group-mean choice weights and mobility, population = population choice weights, alone = each member simulated alone; “+ mobility” = with the own (group-mean) mobility term.

Dataset	SD added	$\Delta r$	95 % CI	$p$	$\Delta R^{2}$ ( $p$ )
Wu	SuccessfulProximity	$+0.007$	$[-0.065,+0.047]$	0.41	0.029 (0.041)
Wu	Both social weights	$-0.006$	$[-0.079,+0.072]$	0.55	0.034 (0.10)
Wu	All 5 weights	$-0.051$	$[-0.116,+0.026]$	0.89	0.053 (0.18)
Hawkins	Facing stopped others	$-0.004$	$[-0.023,+0.014]$	0.63	0.004 (0.34)
Hawkins	Selectivity index	$-0.005$	$[-0.020,+0.011]$	0.72	0.008 (0.17)
Hawkins	Teacher $b_{\mathrm{stop}}$	$-0.006$	$[-0.019,+0.007]$	0.81	0.000 (0.81)

Supplementary Table 4: Composition test with selectivity measured inside the group. Out-of-sample

\Delta r

(cluster-bootstrap 95 % confidence interval and

p

) and in-sample

\Delta R^{2}

(permutation

p

of the SD block) when the within-group SD of selectivity measured inside the group is added to the model of member means (baseline). Wu: SD of the weights fitted on the first two rounds of each block → group reward of the last two rounds (128 group rounds); baseline

r=0.14

[-0.09, 0.36]. Hawkins: SD of the first-half measures → second-half group score (169 games with at least three players); baseline

r=0.45

[0.33, 0.57].

Hypothesis	Decision rule (pre-specified)	Result
(i) Search → tracking	The $z$ of a sequence encoder of the search phase predicts the tracking-phase random effects with $\Delta r\geq 0.10$ , $p<0.01$ against the condition $\times$ speed mean, and outperforms a linear ridge	Failed . Mean $r=0.09$ for the CNN vs 0.17 for ridge. The condition-mean baseline gives $r\approx 0$ by the definition of random effects and is uninformative ( $\Delta r=0.47$ is trivial). Unchanged with a GRU, $M=2,8$ , six learning rates $\times$ 500/10k/50k epochs
(ii) Cross-individual transfer	Distance between individuals in $z$ space explains transfer error (slope $p<0.001$ ) and outperforms the summary-statistic distance	Held (linear $z$ : slope 0.124 for the $z$ distance vs 0.087 for the summary-statistic distance; log-likelihood $-23{,}883$ vs $-24{,}505$ )
(iii) Early movement → roles	The first-3-min $z$ predicts later roles with $\Delta r\geq 0.05$ , $p<0.01$ against the initial-score baseline	In-degree held ( $\Delta r=0.114$ , group-cluster bootstrap $p=0.007$ ); out-degree failed (0.079, $p=0.14$ ). The reading (testing $\Delta r$ directly by cluster bootstrap) was decided on 2026-10-20
(iv) Payoff information and roles	Prediction is best in the FP condition	Not supported (in-degree $r$ : NP 0.18 / VP 0.27 / FP 0.18)
Payoff sharing	Exploratory (no verdict)	The fraction shared is exhausted by tracking time (Supplementary Note 1)
(v) Individual → group performance	Agents with individual parameters predict score and efficiency with $\Delta r\geq 0.10$ , $p<0.01$ against the default-parameter and mean-parameter controls	Held (score $\Delta r=0.65$ and 0.93). Both controls, however, are constant within cell ( $r\approx 0$ ) and trivial

Supplementary Table 5: Pre-specified hypotheses, decision rules and verdicts, and deviations from the specification. Transcribed from the analysis specification fixed before the analysis and from the dated decision log kept during the analysis.

Target	Score only	Tracking time only	Search-phase $z$	First-3-min $z$	Tracking RE
Fraction shared (overall; $n=165$ )	0.23 $[0.08,0.37]$	0.29 $[0.14,0.42]$	0.23 $[0.08,0.38]$	0.16 $[-0.00,0.31]$	0.32 $[0.18,0.46]$
Fraction shared (while tracking)	$-0.34$ $[-0.47,-0.20]$	$-0.30$ $[-0.44,-0.16]$	$-0.11$ $[-0.26,0.05]$	$-0.10$ $[-0.25,0.06]$	0.10 $[-0.05,0.24]$
Fraction shared (while searching; $n=162$ )	$-0.01$ $[-0.15,0.15]$	$-0.14$ $[-0.30,0.02]$	0.09 $[-0.08,0.24]$	$-0.17$ $[-0.32,-0.00]$	0.02 $[-0.12,0.17]$
Sharing after entering the resource ( $n=163$ )	0.03 $[-0.12,0.19]$	0.07 $[-0.09,0.22]$	0.21 $[0.06,0.37]$	0.14 $[-0.02,0.29]$	0.16 $[0.01,0.29]$
Sharing after one’s own discovery ( $n=88$ )	$-0.13$ $[-0.34,0.10]$	0.04 $[-0.16,0.25]$	0.10 $[-0.12,0.31]$	0.21 $[0.00,0.42]$	$-0.18$ $[-0.37,0.04]$

Supplementary Table 6: Out-of-fold prediction of voluntary payoff sharing (Spearman

\rho

, participant-bootstrap 95 % confidence interval).

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