Comparative transitive and temporal orderliness in dominance networks

Dominance is a social relation between a subordinate animal and the dominant to which it submits. Animal groups seem regularly to form dominance hierarchies in which dominance relations are transitive and stable, but comparative studies are rare. Dominance hierarchies can be formalized as social networks, with arrows (directed edges) pointing from dominant animals (nodes) to subordinates. Using this network perspective, we explored the orderliness of 40 published datasets for taxa from ants to elephants. To quantify orderliness, we used the triad census, a technique from sociology, that enumerates the proportion of orderly (transitive) triads (e.g., A dominates B and C, B dominates C, yielding clear top, middle, and bottom rankings) versus disorderly (cyclic) triads (e.g., A dominates B, B dominates C, but C in turn dominates A). All 40 datasets showed a significant excess of orderly (transitive) triads and a deficit of disorderly (cyclic) triads compared with the null model of random networks. Most datasets showed relatively high rank stability (mean stability index of 0.81 on a scale from 0 to 1). Steep hierarchies arise when the scores used to rank contestants differ sharply, further promoting stability. All 40 dominance hierarchies were steeper than expected from randomized sequences of contests. The overwhelming conclusion was that animal groups are orderly, as assessed by a high proportion of transitive relations, a paucity of disorderly cycles, and high temporal stability in rankings. Thus, a certain degree of self-organization may characterize even agonistic interactions across many different kinds of animal societies.