Usually when we think about social relationships, we think about dyads. We think about the attributes of a relationship between one individual and the other. There could be many ways to describe a social relationship, including its strength, symmetry, predictability, etc. A detailed review of these properties can be found in this interesting paper by Joan Silk et al. However, sometimes social decisions may not be dependent only on the properties of the two individuals involved in a dyad, but rather on constraints imposed by the social structure. Here comes to effect the relationships they have with other individuals. One such constraint is described by the theory of structural balance, formalizing the saying "the friend of my friend is my friend". The idea is that a dyad may be influenced by a 3rd party. If I am a friend of John, and he is a friend of Alex, their friendship affects my decision about becoming a friend of Alex. If I don't like Alex, that will create a tension between me and my friend John. For example, if John is having a party, I would not like him to invite Alex. This situation is called an unbalanced triad. In contrast, if both John and me do not favor Alex, there is no social tension in the triad, since John and I have the same opinions. There is no incentive for any of us to make a change.
The theory of structural balance was developed by Austrian psychologist Heider back in 1946. It was later formally applied to social networks by Cartwright & Harary. It was found to be relevant for human societies, and also for international relationships. One study suggested that the lack of balance was the trigger behind World War I.
I tested if structural balance may also be relevant for animal societies. I thought that similar social tensions as in humans may affect animals. In a recent paper, we found that rock hyraxes do seem to care about it. We used data from our long-term study, and compared the social network to random networks retaining some properties of the observed ones. We found that balanced triads were more common than expected by chance, while unbalanced triads were less common than expected. Interestingly, we found what is called "weak" structural balance. That means that triads in which all three individuals were not in positive relationship were more common than expected. In contrast, strong structural balance predicts that such triads should be unbalanced, and two individuals are expected to form an alliance against the other. I think that our finding is more relevant to animal societies, in which there are usually more than two groups in a population. Thus a balanced animal network is usually composed of groups, in which in general individuals favor each other, but are not associated with individuals from other groups.
To test if structural balance is not merely a consequence of another process, we followed each triad across years. First, we found a marginally significant effect of triad type on survival. Hyraxes in unbalanced triads had a lower chance of surviving to the following year. Then we found that balanced triads usually stayed in the same configuration, while unbalanced triads mostly changed to balanced ones. That suggests that hyraxes "care" about the triads, and actively change the unbalanced ones.
The implication of a balanced network is the clustering of individuals into groups of cooperators. Thus, structural balance could be a mechanism involved in the widely observed phenomena of living in groups.
