The construction of dominance order: comparing performance of five methods using an individual-based model

In studies of animal behaviour investigators correlate dominance with all kinds of behavioural variables, such as reproductive success and foraging success. Many methods are used to produce a dominance hierarchy from a matrix reflecting the frequency of winning dominance interactions. These different methods produce different hierarchies. However, it is difficult to decide which ranking method is best. In this paper, we offer a new procedure for this decision: we use an individual-based model, called DomWorld, as a test-environment. We choose this model, because it provides access to both the internal dominance values of artificial agents (which reflects their fighting power) and the matrix of winning and losing among them and, in addition, because its behavioural rules are biologically inspired and its group-level patterns resemble those of real primates. We compare statistically the dominance hierarchy based on the internal dominance values of the artificial agents with the dominance hierarchy produced by ranking individuals by (a) their total frequency of winning, (b) their average dominance index, (c) a refined dominance index, the David's score, (d) the number of subordinates each individual has and (e) a ranking method based on maximizing the linear order of the hierarchy. Because dominance hierarchies may differ depending on group size, type of society, and the interval of study, we compare these ranking methods for these conditions. We study complete samples as well as samples randomly chosen to resemble the limitations of observing real animals. It appears that two methods of medium complexity (the average dominance index and David's score) lead to hierarchical orders that come closest to the hierarchy based on internal dominance values of the agents. We advocate usage of the average dominance index, because of its computational simplicity.