A three-component model of relational responding in the transposition paradigm.

We present a new model of transposition behavior that involves 3 predictors: (a) the disparity in generalized associative strength from the previously reinforced and nonreinforced stimuli (g) to the stimuli in the testing pair; (b) relational disparity (r), the difference in the logarithmically scaled sensory values of the testing stimuli; and (c) familiarity (f), the inverse of the Euclidean distance from the testing pair to the nearest training pair in 2-dimensional stimulus space. We evaluated the model with pigeons as subjects and with circle diameter (Experiment 1) and speed of motion (Experiment 2) as sensory dimensions. In each experiment, we presented 1, 2, or 3 training pairs as well as a wide range of testing pairs, including those comprising nonadjacent training stimuli. The control that was exerted by g did not depend on the number of training pairs and predicted behavior better than r and f after 1-pair training. In contrast, the influence of r increased dramatically with an increase in the number of training pairs. The contribution of f depended on the stimulus domain: When circle area was used (Experiment 1), the influence of f was similar to r; however, when speed of motion was used (Experiment 2), f had no discernible effect on pigeons' behavior. In sum, our results suggest that pigeons' transposition behavior is affected by both reinforcement history (g) and the relation between the experimental stimuli (r and f); our model provides a principled means for assessing the relative contribution of each predictor to choice behavior.