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: Pigeons were trained on a matching-to-sample task in which sample hue and required sample-specific observing behavior provided redundant, relevant cues for correct choices. On trials that involved red and yellow hues as comparison stimuli, a fixed-ratio 16 schedule (FR 16) was required to illuminate the comparisons when the sample was red, and a differential-reinforcement-of-low-rates 3-sec schedule (DRL 3-sec) was required when the sample was yellow. On trials involving blue and green hues as comparison stimuli, an FR 16 schedule was required when the sample was blue and a DRL 3-sec schedule was required when the sample was green. For some pigeons, a 0-sec delay intervened between sample offset and comparison onset, whereas other pigeons experienced a random mixture of 0-sec and 2-sec delay trials. Test trial performance at 0-sec delay indicated that sample-specific behavior controlled choice performance considerably more than sample hue did. Test performance was independent of whether original training involved all 0-sec delay trials or a mixture of 0-sec and 2-sec delays. Sample-specific observing response requirements appear to facilitate pigeons' matching-to-sample performance by strengthening associations between the observing response and correct choice.