The standard approach in accounting for hierarchical differentiation in biology and the social sciences considers a hierarchy as a static distribution of individuals possessing differing amounts of some valued commodity, assumes that the hierarchy is generated by micro-level processes involving individuals, and attempts to reverse engineer the processes that produced the hierarchy. However, sufficient experimental and analytical results are available to evaluate this standard approach in the case of animal dominance hierarchies (pecking orders). Our evaluation using evidence from hierarchy formation in small groups of both hens and cichlid fish reveals significant deficiencies in the three tenets of the standard approach in accounting for the organization of dominance hierarchies. In consequence, we suggest that a new approach is needed to explain the organization of pecking orders and, very possibly, by implication, for other kinds of social hierarchies. We develop an example of such an approach that considers dominance hierarchies to be dynamic networks, uses dynamic sequences of interaction (dynamic network motifs) to explain the organization of dominance hierarchies, and derives these dynamic sequences directly from observation of hierarchy formation. We test this dynamical explanation using computer simulation and find a good fit with actual dynamics of hierarchy formation in small groups of hens. We hypothesize that the same dynamic sequences are used in small groups of many other animal species forming pecking orders, and we discuss the data required to evaluate our hypothesis. Finally, we briefly consider how our dynamic approach may be generalized to other kinds of social hierarchies using the example of the distribution of empty gastropod (snail) shells occupied in populations of hermit crabs.