A two-stage model for concurrent sequences

Schneider and Davison [Schneider, S.M., Davison, M., 2005. Demarcated response sequences and the generalised matching law. Behav. Proc. 70, 51-61] showed that the generalised matching law applied to concurrent free-operant two-response sequences. When sufficient temporal spacing is required between the responses, however, neither the response-level nor the sequence-level forms of the generalised matching law provide good fits. An alternative “two-stage sensitivity” model with fewer free parameters features two types of sensitivity to the reinforcement contingencies on sequences. When temporal spacing between the responses is long, the “response distribution sensitivity” parameter describes sensitivity only of the individual responses to the sequence-level contingencies. At a threshold level, this sensitivity reaches a maximum. When spacing is shorter than threshold, the “response order sensitivity” parameter reflects a new sensitivity to the order of the responses within sequences. As this sensitivity approaches its maximum, sequence matching is achieved. For both stages, a changeover parameter describes bias against sequences that require changeovers between the two responses. The model fit data ranging from near-response matching with long minimum inter-response times (IRTs) to sequence matching with no minimum IRTs, using two species and a variety of sequence reinforcer distributions. Rats differed from pigeons in achieving sequence matching only at a nonzero minimum IRT. In a comparison based on pigeon data with no minimum IRT, the two-stage sensitivity model was more efficient than the generalised matching law according to the Akaike criterion. The logic of the model suggests a new way of understanding the mechanisms underlying behavioural units.