Abstract: Dominance hierarchies are widely described in nature. Commonly, an individual's ordinal rank is used as a measure of its position in the hierarchy, and, therefore its priority of access to resources. This use of ordinal ranks has several related drawbacks: (1) it is difficult to assess the magnitude or the significance of the difference in degree of dominance between two individuals; (2) it is difficult to evaluate the significance of differences between dominance matrices based on different behaviours or on the same behaviour at different times, and (3) it is difficult to use parametric statistical techniques to relate dominance rank to other quantities of interest. In this paper we describe a method for assigning cardinal dominance indices that does not suffer from these drawbacks. This technique is based on the Bradley-Terry model from the method of paired comparisons. We show how this model can be reinterpreted in terms of dominance interactions. and we describe a simple iterative technique for computing cardinal ranks. We then describe how to evaluate (1) whether the rank differences between individuals are significant, and (2) whether differences in the cardinal hierarchies based on different behaviours or the same behaviour at different times are significant. We then show how to generalize the method to deal with behaviours that sometimes have ambiguous outcomes, or behaviours for which the rank difference between a pair of individuals affects the rate of interaction between them.

Abstract: Sixteen horses, divided into 2 groups of 8, were used to study observational learning in horses. One group served as controls while the other group served as the treated group (observers). Observers were allowed to watch a correctly performed discrimination task for 5 days prior to testing their learning response using the same task. Discrimination testing was conducted on all horses daily for 14 days, with criterion set at 7 out of 8 responses correct with the last 5 consecutively correct. The maximum number of trials performed without reaching criterion was limited to 20 per day. Mean trials to criteria (MT) by group were: control, 11.25; observer, 10.70. Mean error (ME) scores were: control, 2.37; observer, 2.02. Average initial discrimination error scores were 11.13 for control and 10.38 for observers (P < 0.10). Asymptote was reached by Day 8 for both control and observer groups. Analysis of variance with repeated measures showed an extreme-day effect indicative of learning (P < 0.01), with non-significant differences in learning rate between experimental groups. Whether the initial ability of the horses to perform a discrimination learning task was enhanced by observation of other horses' performance of that task was not obvious from these data.