title: Finding an appropriate order for a hierarchy based on probabilistic dominance.
abstract: Methods of ranking individuals in a dominance hierarchy that use transitivity of relationships may obscure irregularities. Furthermore, these methods use only a small proportion of the information available from dominance encounters. This paper presents an intuitively appealing and easily implemented alternative to existing methods for ordering dominance data, developed from the work of Batchelder et al. (1992 Journal of Mathematical Psychology36, 185-212). The procedure presented here is based on a mathematical model of paired comparisons and it involves only simple estimation procedures. We illustrate its use with data on dominance among red deer Cervus elaphus, stags. The results indicate that dominance relationships are well characterized by the scale values that the model provides, and, because the method provides predictions for all pairings of animals, dominance predictions also exist for pairs of animals that have yet to be observed. Moreover, the dominance outcomes predicted by the model using the order scale are highly correlated with actual dominance observations at all levels. Overall, the procedure described provides a solution to the problem of identifying an appropriate order for a near-linear dominance hierarchy. Copyright 1999 The Association for the Study of Animal Behaviour.