A practical guide for inferring reliable dominance hierarchies and estimating their uncertainty

Many animal social structures are organized hierarchically, with some individuals monopolizing resources. Dominance hierarchies have received great attention from behavioural and evolutionary ecologists. There are many methods for inferring hierarchies from social interactions. Yet, there are no clear guidelines about how many observed dominance interactions (i.e. sampling effort) are necessary for inferring reliable dominance hierarchies, nor are there any established tools for quantifying their uncertainty. We simulate interactions (winners and losers) in scenarios of varying steepness (the probability that a dominant defeats a subordinate based on their difference in rank). Using these data, we (1) quantify how the number of interactions recorded and the steepness of the hierarchy affect the performance of five methods for inferring hierarchies, (2) propose an amendment that improves the performance of a popular method, and (3) suggest two easy procedures to measure uncertainty and steepness in the inferred hierarchy. We find that the ratio of interactions to individuals required to infer reliable hierarchies is surprisingly low, but depends on the steepness of the hierarchy and the method used. We show that David's score and our novel randomized Elo-rating are the best methods when hierarchies are not extremely steep, where the original Elo-rating, the I&SI and the recently described ADAGIO perform less well. In addition, we show that two simple methods can be used to estimate uncertainty at the individual and group level, and that the randomized Elo-rating repeatability provides researchers with a standardized measure valid for comparing the steepness of different hierarchies. We provide several worked examples to guide researchers interested in studying dominance hierarchies. Methods for inferring dominance hierarchies are relatively robust. We recommend that a ratio of observed interactions to individuals of at least 10 (for steep hierarchies), and ideally 20 serves as a good benchmark. Our simple procedures for estimating uncertainty in the observed data will facilitate evaluating whether sufficient data have been collected, while plotting the shape of the hierarchy will provide new insights into the social structure of the study organism.