Abstract: 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.