Extending Bayesian Elo-rating to quantify the steepness of dominance hierarchies

The steepness of dominance hierarchies provides information about the degree of competition within animal social groups and is thus an important concept in socioecology. The currently most widely-used metrics to quantify steepness are based on David’s scores (DS) derived from dominance interaction networks. One serious drawback of these DS-based metrics is that they are biased, i.e., network density systematically decreases steepness values. Here, we provide a novel approach to estimate steepness based on Elo-ratings, implemented in a Bayesian framework (STEER: Steepness estimation with Elo-rating). Our new metric has two key advantages. First, STEER is unbiased, precise and more robust to data density than DS-based steepness. Second, it provides explicit probability distributions of the estimated steepness coefficient, which allows uncertainty assessment. In addition, it relies on the same underlying concept and is on the same scale as the original measure, and thus allows comparison to existing published results. We evaluate and validate performance of STEER by means of experimentation on empirical and artificial data sets and compare its performance to that of several other steepness estimators. Our results suggest that STEER provides a considerable improvement over existing methods to estimate dominance hierarchy steepness. We provide an R package EloSteepness to calculate the new steepness measure, and also show an example of using steepness in a comparative analysis. ### Competing Interest Statement The authors have declared no competing interest.