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

Abstract

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.

Effects of supplementary feeding on interspecific dominance hierarchies in garden birds

“…A total of 816 interspecific interactions were recorded at supplementary feeders, far exceeding the recommended sampling effort required to reliably estimate the dominance hierarchy between the ten species of interest [34]. House sparrow was estimated to be the most dominant species, while coal tit was the least dominant, with 95% confidence intervals indicating a high level of certainty in the species rank assignments, particularly amongst the lowest ranking species (Table 1).…”

“…[34] to infer the dominance hierarchy and estimate associated uncertainty in species’ rankings, implemented using the “aniDom” R package [35]. The original Elo-rating method considers interactions sequentially and updates subjects’ ratings after each dominance interaction in which they participate, based on the difference in the actual outcome from the probablity of the higher-rated subject (e.g.…”

“…Therefore it does not require a complete interaction matrix, where all subjects are observed competing with every other subject, and ratings can subsequently be used to infer dominance rank. The randomised Elo-rating procedure [34] is advantagous for the current study as we are interested in between-species interactions, rather than those occuring between individuals, and therefore the specific sequence of events in not important. Further, the randomisation (n = 1000) improves the estimation of species ranks and can also be used to generate associated 95% confidence intervals, which convey the level of uncertainty in the ranking of each species.…”

“…Further, the randomisation (n = 1000) improves the estimation of species ranks and can also be used to generate associated 95% confidence intervals, which convey the level of uncertainty in the ranking of each species. In order to assess the robustness of the between-species dominance hierarchy estimation, (1) we calculated the repeatability score for species ranks based on the randomised Elo-ratings and (2) we estimated the degree of linearity, or ‘orderliness’, within the hierarchy using triangle transitivity (T tri ) [34]. …”

Meta-analysis challenges a textbook example of status signalling: evidence for publication bias

“…Mean sampling effort was 36 interactions/individual (SD = 24), which highlights that, overall, dominance hierarchies were inferred reliably across groups (Sánchez-Tójar, Schroeder, & Farine, 2018). The mean Elo-rating repeatability was 0.92 (SD = 0.07) and the mean triangle transitivity was 0.63 (SD = 0.28).…”