Linear hierarchies, the classical pecking-order structures, are formed readily in both nature and the laboratory in a great range of species including humans. However, the probability of getting linear structures by chance alone is quite low. In this paper we investigate the two hypotheses that are proposed most often to explain linear hierarchies: they are predetermined by differences in the attributes of animals, or they are produced by the dynamics of social interaction, i.e., they are self-organizing. We evaluate these hypotheses using cichlid fish as model animals, and although differences in attributes play a significant part, we find that social interaction is necessary for high proportions of groups with linear hierarchies. Our results suggest that dominance hierarchy formation is a much richer and more complex phenomenon than previously thought, and we explore the implications of these results for evolutionary biology, the social sciences, and the use of animal models in understanding human social organization.L inear hierarchies, classic pecking-order structures, are formed readily in nature and the laboratory by many species: some insects and crustaceans and various fish, birds, and mammals including human children and adolescents (1-10). However, the probability of generating linear hierarchies by chance alone is low. We do not know how these social structures develop their linear form, and even the types of mechanisms that might produce linearity are controversial. In this paper we evaluate hypotheses concerning the two most commonly proposed factors for explaining the formation of linear hierarchies through a series of experimental studies using cichlid fish.Two individuals have a dominance relationship if one chases, threatens, or bites, but receives little or no aggression, from the other. Dominance hierarchies, known in the mathematical literature as tournaments, are social structures consisting of dominance relationships between all pairs of individuals in a group. In a linear hierarchy one individual dominates all the other individuals in a group, a second dominates all but the first, and so on down to the last individual who is dominated by all the others. Dominance relationships in a linear hierarchy are always transitive. For any three individuals (triad) in the group, if A dominates B and B dominates C, then A also dominates C. If a hierarchy is not linear, it contains at least one intransitive triad (A dominates B, B dominates C, but C dominates A), and the more intransitive triads there are, the further the hierarchy is from linearity (by many measures of linearity). Perfectly linear hierarchies are most common in groups under 10 members, and as groups grow larger, irregularities may appear (11). Rank in hierarchies influences such important things as behavior, physiology, health, and ability to produce offspring (12-16).The first and most often suggested hypothesis concerning the mechanisms accounting for linearity is that individuals' positions in hierarchies are predetermined by diffe...