Reducing the bias due to unknown relationships in measuring the steepness of a dominance hierarchy

Measuring the steepness of a dominance hierarchy is important for classifying a social system in a continuum between egalitarian and despotic. For this, often the steepness-slope from de Vries et al. (Animal Behaviour, 2006, 71, 585–592) is often used. It compares the cardinal and ordinal dominance rank of each individual using the slope of the linear regression. The disadvantage of this measure is that the slope becomes lower the higher the proportion of unknown relationships (dyads without interactions). In the present paper, we investigate what causes this bias, and propose a solution. (1) We show that the bias is due to the treatment of unknown relationships by the dominance index currently used in this methodology, the David's score (namely by assuming, among other things, an equal number of wins and losses for both members of the pair). (2) Instead, using the Average Dominance Index (the average proportion of wins by each individual from all its opponents) reduces the bias due to unknown relationships, because it excludes these relationships, and (3) the standard error of the steepness-slope based on the Average Dominance Index is smaller. (4) The two indices (David's score and Average Dominance Index) result in similar steepness-slopes when all relationships are known. To compare the two indices we use empirical data (from four group-years of wild vervet monkeys, Chlorocebus pygerythrus) and data from a computational model on dominance interactions in a group (DomWorld). We conclude that the Average Dominance Index (compared to the David's score) is preferable for measuring the steepness-slope.