Inferring longitudinal hierarchies: Framework and methods for studying the dynamics of dominance.

Social inequality is a consistent feature of animal societies, often manifesting as dominance hierarchies, in which each individual is characterized by a dominance rank denoting its place in the network of competitive relationships among group members. Most studies treat dominance hierarchies as static entities despite their true longitudinal, and sometimes highly dynamic, nature. To guide study of the dynamics of dominance, we propose the concept of a longitudinal hierarchy: the characterization of a single, latent hierarchy and its dynamics over time. Longitudinal hierarchies describe the hierarchy position (r) and dynamics (∆) associated with each individual as a property of its interaction data, the periods into which these data are divided based on a period delineation rule (p) and the method chosen to infer the hierarchy. Hierarchy dynamics result from both active (∆a) and passive (∆p) processes. Methods that infer longitudinal hierarchies should optimize accuracy of rank dynamics as well as of the rank orders themselves, but no studies have yet evaluated the accuracy with which different methods infer hierarchy dynamics. We modify three popular ranking approaches to make them better suited for inferring longitudinal hierarchies. Our three "informed" methods assign ranks that are informed by data from the prior period rather than calculating ranks de novo in each observation period and use prior knowledge of dominance correlates to inform placement of new individuals in the hierarchy. These methods are provided in an R package. Using both a simulated dataset and a long-term empirical dataset from a species with two distinct sex-based dominance structures, we compare the performance of these methods and their unmodified counterparts. We show that choice of method has dramatic impacts on inference of hierarchy dynamics via differences in estimates of ∆a. Methods that calculate ranks de novo in each period overestimate hierarchy dynamics, but incorporation of prior information leads to more accurately inferred ∆a. Of the modified methods, Informed MatReorder infers the most conservative estimates of hierarchy dynamics and Informed Elo infers the most dynamic hierarchies. This work provides crucially needed conceptual framing and methodological validation for studying social dominance and its dynamics.