SUPPLEMENTAL MATERIAL

Appendix A

Table reporting characteristics of each horse (breed, age, hierarchical rank, boldness scores).
Individual / Breed / Age (yr) / Hierarchical rank / Boldness scores
Alo / NF / 2 / 8 / 0.57
Ang / NF / 1 / 28 / -0.4
Cara / NF / 2 / 18 / 0.7
Carr / NF / 1 / 29 / -0.3
Cer / FB / 4 / 16 / 1.35
Chan / HT / 3 / 14 / 0.71
Chat / NF / 2 / 13 / -0.3
Chau / FB / 2 / 21 / -0.29
Chi / NF / 6 / 1 / 0.61
Cho / NF / 1 / 26 / 0.74
Cig / NF / 1 / 30 / -0.21
Cre / W / 2 / 2 / 1.93
Cro / NF / 1 / 25 / 0.67
Enc / AB / 1 / 33 / -2.04
Epi / NF / 2 / 6 / -0.34
Fin / FB / 1 / 34 / -2.12
Fjo / F / 1 / 23 / 0.84
Glu / FB / 2 / 11 / 1.46
Mel / FB / 1 / 36 / -2.12
Mou / FB / 2 / 10 / 0.64
Nua / NF / 2 / 27 / 0.07
NzR / NF / 2 / 5 / -0.57
Pip / NF / 2 / 7 / 0.85
Pom / PT / 3 / 4 / 0.73
Pri / FB / 2 / 15 / 0.56
Ras / NF / 2 / 12 / 0.61
Rei / FB / 3 / 19 / -0.44
Ros / AB / 2 / 32 / -1.79
Sab / W / 2 / 3 / 0.16
Ser / FB / 1 / 35 / -1.82
Sou / HT / 1 / 9 / -0.65
Swa / HT / 1 / 17 / 0.23
Tac / NF / 1 / 24 / 0.46
Tra / AB / 1 / 31 / -0.3
Val / FB / 2 / 22 / -0.15
Ven / FB / 2 / 20 / -0.06
Breeds: NF=New Forest; WP=Welsh Pony; FB=French Breed; PT=Pony Type; HT=Horse Type; AB=Arabian Breed; F=Fjord
Foals are not included

Appendix B

Summary of principal components analysis results for the personality questionnaire and gregariousness index.
Question 3 was removed for being not significantly repeatable. Question 7 corresponds to the gregariousness index split into 5 categories to mimic the 5-point-scale. For each question the scale goes from 1 (very rarely) to 5 (repeatedly).
Questions / Factor loadings (questions only) / Factors loadings
(questions + gregariousness)
1. How frequently does the individual shy, is startled, or take fright? / 0.93 / 0.92
2. Does the individual become alarmed when distant from others and does it quickly seek to join them? / 0.92 / 0.93
3. How often the individual redirects certain behaviours towards its conspecifics after an agonistic interaction or when at a high level of activity/nervosity?
4. Is the individual agitated within the group? / 0.64 / 0.66
5. When faced with an unknown object, does the individual approach it? / -0.86 / -0.84
6. When faced with an unknown object, does the individual interact with it (sniffing, grabbing or biting)? / -0.82 / -0.78
7. Gregariousness index / 0.78
Eigenvalue / 4.06
% of variance / 68

Appendix C

Results of the MCMC model for the relationship between affinities (SRIG) and differences in age, hierarchical rank and boldness scores.
Differences in age (diffage), hierarchical rank (diffrank) and boldness scores (diffbold) were used as fixed effects, and individual identities nested in dyad as random factors. Posterior means and their lower (L − 95% CI) and upper (U − 95% CI) credibility intervals are provided. Significant P values (pMCMC) are shown in bold print.
Variables / Posterior mean / L - 95% CI / U – 95% CI / pMCMC
Intercept / 1.97 / 1.71 / 2.27 / < 0.001
diffage / -0.05 / -0.18 / 0.09 / 0.452
diffrank / -0.02 / -0.03 / -0.0002 / 0.036
diffbold / -0.56 / -0.73 / -0.40 / 0.001

Appendix D

Results of the MCMC models for the relationship between joining associations and affinities, differences in age, hierarchical rank and boldness scores.
Affinities (SRIG), differences of age (diffage), hierarchical rank (diffrank) and boldness scores (diffbold) were used as fixed effects and individual identities nested in dyad as random factors. Posterior means and their lower (L − 95% CI) and upper (U − 95% CI) credibility intervals are provided. Significant P values (pMCMC) are presented in bold print.
Direct / Pathway
Variables / Posterior mean / L –
95% CI / U – 95% CI / pMCMC / Posterior mean / L –
95% CI / U – 95% CI / pMCMC
Intercept / 2.65 / 2.24 / 3.10 / < 0.001 / 1.82 / 1.33 / 2.33 / <0.001
SRIG / 0.82 / 0.71 / 0.92 / < 0.001 / 1.06 / 0.93 / 1.19 / <0.001
diffage / 0.05 / -0.13 / 0.23 / 0.632 / 0.09 / -0.10 / 0.29 / 0.388
diffrank / -0.03 / -0.06 / -0.008 / 0.008 / -0.06 / -0.08 / -0.03 / 0.001
diffbold / -0.13 / -0.37 / 0.11 / 0.284 / -0.06 / -0.33 / 0.22 / 0.690