Rationale: Mathematical principles of reinforcement (MPR) provide the theoretical basis for a family of models of schedule-controlled behaviour. A model of fixed-ratio schedule performance that was applied to behaviour on progressive ratio (PR) schedules showed systematic departures from the data.
Objective: This study aims to derive a new model from MPR that will account for overall and running response rates in the component ratios of PR schedules, and their decline toward 0, the breakpoint.
Method: The role of pausing is represented in a real-time model containing four parameters: T (0) and k are the intercept and slope of the linear relation between post-reinforcement pause duration and the prior inter-reinforcer interval; a (specific activation) measures the incentive value of the reinforcer; δ (response time) sets biomechanical limits on response rate. Running rate is predicted to decrease with negative acceleration as ratio size increments, overall rate to increase and then decrease. Differences due to type of progression are explained as hysteresis in the control by reinforcement rates. Re-analysis of extant data focuses on the effects of acute treatment with antipsychotic drugs, lesions of the nucleus accumbens core, and destruction of orexinergic neurones of the lateral hypothalamus.
Results: The new model resolves some anomalies evident in earlier analyses, and provides new insights to the results of these interventions.
Conclusions: Because they can render biologically relevant parameters, mathematical models can provide greater power in interpreting the effects of interventions on the processes underlying schedule-controlled behaviour than is possible for first-order data such as the breakpoint.