Transitivity and structural balance in marmot social networks

Abstract

Social relationships are composed of both positive (affiliative) and negative (agonistic) interactions, representing opposing effects. Social network theory predicts that positive relationships should be transitive; thus, the friend of a friend is more likely to be a friend. Further, when considering both positive and negative relationships jointly, structural balance theory predicts that certain configurations of positive and negative relationships in a triad are inherently less stable (unbalanced) and should tend to be eliminated. However, structural balance has been rarely examined in nonhuman social systems. We tested for transitivity and structural balance in social networks of socially flexible yellow-bellied marmots (Marmota flaviventer) and asked if group size, network density, or group composition affected the degree of structural balance. We found a consistent pattern of significant transitivity in positive interactions, some transitivity in negative interactions, and some evidence of structural balance. In particular, a “weak” definition of structural balance is probably more common than “strong” structural balance, which used a stricter definition of balance. Network size limited the ability to detect these social processes, and smaller networks were less likely to show significant transitivity or structural balance. The proportion of adult females in a group affected the level of transitivity but did not affect the degree of structural balance. Our study suggests that there are intriguing similarities in social processes across diverse animal societies and that studying triads and network motifs may help identify basic social mechanisms linking local to global structure. SIGNIFICANCE STATEMENT: Social network theory predicts that basic social mechanisms should lead to similar structural properties across different societies. For example, positive relationships should be transitive (a friend of a friend is a friend), and certain combinations of positive and negative relationships represent conflict and should be unstable over time (e.g., a friend of a friend being an enemy is an unstable state). This latter theory, called structural balance, has rarely been examined in nonhuman societies; hence, we tested for transitivity and structural balance in groups of free-living yellow-bellied marmots. Positive interactions were generally transitive, but evidence for structural balance was inconsistent. Furthermore, group composition could affect network transitivity, and small network size (associated with few interactions) limits ability to detect significant patterns. Our results suggest that transitivity is fundamental in structuring positive relationships, while some forms of structural balance are present but not widespread.