Abstract: The `jigsaw puzzle' approach is a general method for investigating how interactions among individuals cumulate to form the overall patterns of dominance behaviour in groups. Here, the model is used to discover how aggressive interactions between pairs of individuals modify subsequent interactions with bystanders or third parties. The model indicates that four sequences of successive, aggressive acts are possible in component triads of larger groups: two ensure transitive attack relationships and two can lead to either transitive or intransitive relationships. An application of the model to 14 groups of four hens demonstrates that the two sequences guaranteeing transitivity make up 77% of all sequences. More specifically, hens attacking one group member usually go on to attack a second member, and hens receiving one attack frequently receive a second attack from a bystander. In contrast, an attacked hen rarely `redirects' an attack to a bystander, and a bystander rarely attacks a group member who has just attacked another individual. The application of the jigsaw puzzle approach to aggressive sequences in other species is discussed. Data available for several primate species corroborate the findings in hens and provide support for the method as a general tool for investigating the proximate mechanisms of hierarchy formation.