Effect of unknown relationships on linearity, steepness and rank ordering of dominance hierarchies: simulation studies based on data from wild monkeys.

The presence of unknown dyadic relationships is a common problem in constructing dominance hierarchies for groups of social animals. Although previously acknowledged, the influence of unknown relationships on hierarchy measures like linearity and steepness has not been studied in detail. Using real data-sets from four groups of wild monkeys, we illustrate how unknown relationships affect linearity and steepness of hierarchies and the consistency of rank ordering based on de Vries' I&SI method. Monte Carlo simulations revealed significant negative linear relationships between the proportion of unknown relationships and both linearity and steepness. These simulations over-estimated steepness and linearity indices relative to additional real-data input matrices. Rank orders became inconsistent at 26-38% unknown relationships, depending on the group. Group size and the specific input matrix substantially affected how much unknown relationships influenced steepness and linearity, the values of these indices and the point at which rank order became inconsistent. We recommend caution in characterizing the dominance structure of a group with many unknown relationships, and in drawing conclusions about hierarchy linearity and steepness based on few input matrices, especially if they contain many unknown relationships. Quantitative characterizations of hierarchies are perhaps best viewed as a somewhat fluid range rather than fixed values.