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

Abstract

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, that is, network density systematically decreases steepness values. We provide a novel approach to estimate steepness based on Elo-ratings, implemented in a Bayesian framework (STEER: Steepness estimation with Elo-rating). We evaluate and validate its performance by means of experimentation on empirical and artificial datasets and compare its performance to that of several other steepness estimators. STEER has two key advantages. First, it 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. STEER provides a considerable improvement over existing methods to estimate dominance hierarchy steepness. We demonstrate its application with an example comparing within- and between species variation in steepness in a comparative analysis and present guidelines on how to use it. The R package EloSteepness allows convenient numeric and graphical assessment of the new steepness measure.