Structural balance in the social networks of a wild mammal Amiyaal Ilany a, b, * , Adi Barocas a, c , Lee Koren d , Michael Kam e , Eli Geffen a a Department of Zoology, Tel Aviv University, Israel b National Institute for Mathematical and Biological Synthesis, Knoxville, TN, U.S.A. c Department of Zoology and Physiology and Program in Ecology, University of Wyoming, Laramie, WY, U.S.A. d The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, Israel e Desert Animal Adaptations and Husbandry, Wyler Department of Dryland Agriculture, The Jacob Blaustein Institutes for Desert Research, Ben Gurion University of the Negev, Beer Sheva, Israel article info Article history: Received 6 December 2012 Initial acceptance 2 January 2013 Final acceptance 6 March 2013 Available online 21 April 2013 MS. number: A12-00922R2 Keywords: network motif Procavia capensis rock hyrax social network social structure structural balance theory The social structure of a population is based on individual social associations, which can be described using network patterns (motifs). Our understanding of the forces stabilizing specific social structures in animals is limited. Structural balance theory was proposed for exploring social alliances and suggested that some network motifs are more stable than others in a society. The theory models the presence of specific triads in the network and their effect on the global population structure, based on the differential stability of specific triad configurations. While structural balance was shown in human social networks, the theory has never been tested in animal societies. Here we use empirical data from an animal social network to determine whether or not structural balance is present in a population of wild rock hyraxes, Procavia capensis. We confirm its presence and show the ability of structural balance to predict social changes resulting from local instability. We present evidence that new individuals entering the popu- lation introduce social instability, which counters the tendency of social relationships to seek balanced structures. Our findings imply that structural balance has a role in the evolution of animal social structure. Ó 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved. Long-term social alliances have been studied extensively in various taxa, although the focus has been mainly on primates and cetaceans (e.g. Silk 2007; Randi c et al. 2012). It has been argued that cognition is important in the maintenance of long-term relation- ships (Emery et al. 2007; Holekamp et al. 2007). Social integration has been shown to affect reproductive success (e.g. Silk 2007; Cameron et al. 2009) and longevity (Barocas et al. 2011). Never- theless, our knowledge about the structure and function of social bonds in many species is lacking (Silk 2007). We have limited un- derstanding of the reasons why certain animals aggregate in groups of various sizes, and of various internal social structures and levels of stability. These structures are the result of behavioural choices of individuals that construct them, and therefore individual prefer- ences are expected to affect changes in social networks through time. To understand these mechanisms, there is a need to examine how local social structures emerge and change, and how individual actions contribute to local and global changes in the social network. The recent application of network theory to animal sociality has refuelled an interest in animal social structure (McDonald 2007; Croft et al. 2008; Wey et al. 2008; Krause et al. 2009). Analyses of social networks have produced remarkable insights, such as iden- tifying key individuals in a social structure (Lusseau & Newman 2004), describing the cohesion of social groups (Lusseau 2003) and deciphering the interaction between sociality and disease transmission (Hamede et al. 2009). However, little is known about how social preferences at the individual level affect the global social landscape and its temporal dynamics (Lusseau et al. 2006). The analysis of small network motifs as building blocks of complex networks has recently gained recognition (Milo et al. 2002; Mangan & Alon 2003). An early use of network motifs can be found in the theory of structural balance, one of the most influential theories describing social structure in humans (Heider 1946; Cartwright & Harary 1956). This theory describes the re- lationships between individuals in terms of triads, with each triad containing three individuals and three signed ties (ties having positive or negative values) between them (Fig. 1). Triads are considered balanced if all three nodes are ‘friends’ of each other (þþþ), or if two of them are ‘friends’ while both are ‘enemies’ of the third node (þ). The other two options (þþ,) are considered unbalanced, since the inherent tension in these triads may drive them into more balanced configurations. In a þþ triad, the theory predicts a shift towards þþþ or þ, which are considered balanced. For a  triad, the theory posits that * Correspondence: A. Ilany,1122 Volunteer Blvd, Room 106, NIMBioS/University of Tennessee, Knoxville, TN 37996, U.S.A. E-mail address: amiyaal@gmail.com (A. Ilany). Contents lists available at SciVerse ScienceDirect Animal Behaviour journal homepage: www.elsevier.com/locate/anbehav 0003-3472/$38.00 Ó 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anbehav.2013.03.032 Animal Behaviour 85 (2013) 1397e1405