Frequency versus magnitude of reinforcement: New data with a different procedure

Two pigeons, with previous exposure to concurrent schedules, were submitted to 29 sessions of 8 hours each with concurrent variable-interval variable-interval schedules in which reinforcement parameters changed from session to session. In the first nine sessions reinforcement durations were equal in both schedules while reinforcement frequencies varied; in Sessions 10 through 18, both frequency and duration of reinforcement were varied; in Sessions 19 through 29, only reinforcement duration was varied. Results with this different procedure confirm previous findings that behavior is more sensitive to changes in reinforcement frequency than to reinforcement magnitude.     

Choice between fixed-interval schedules: Graded versus step-like choice functions

Pigeons chose between two fixed-interval schedules of food reinforcement. A single peck on one of two lighted keys started the fixed-interval schedule correlated with that key. The schedule had to be completed before the next choice opportunity. The durations of the fixed intervals were varied over conditions from 15 s to 40 s. To maximize the rate of reinforcement, the pigeons had to choose exclusively the shorter of the two schedules. Nevertheless, choice was not all-or-none. Instead, relative choice, and the rates of producing the fixed intervals, varied in a graded fashion with the disparity between the two schedules. Choice ratios under this procedure (single response to choose) were highly sensitive to the ratios of the fixed-interval schedules.     

An integrative model for the study of behavioral momentum.

Behavioral momentum is the product of response rate and resistance to change. The data on relative resistance to change are summarized for pigeons responding on single-key two-component multiple schedules, in the initial links of two-key multiple chained schedules, and in equivalent components of two-key serial schedules. For single-key procedures, the ratio of resistance to change in two schedule components is shown to depend on the ratio of reinforcer rates obtained in the presence of the component stimuli. For two-key procedures, the ratio of resistance to change in equivalent components is shown to depend on the ratio of reinforcer rates correlated with key locations. A model based on stimulus-reinforcer contingencies that combines the reinforcer rates in schedule components summed over key locations and reinforcer rates correlated with key locations summed over components, each expressed relative to the session average reinforcer rate, gives a good account of the data. An extension of the relative law of effect for multiple schedules fails to provide a complete account of resistance to change, but both approaches are needed for a comprehensive understanding of behavioral momentum.     

Independence of response force and reinforcement rate on concurrent variable-interval schedule performance

Five pigeons were trained over 43 experimental conditions on a variety of concurrent variable-interval schedules on which the forces required on the response keys were varied. The results were well described by the generalized matching law with log reinforcement ratios and log force ratios exerting independent (noninteractive) effects on preference. A further analysis using the Akaike criterion, an information-theoretic measure of the efficiency of a model, showed that overall reinforcement rate and overall force requirement did not affect preference. Unlike reinforcement rate changes, force requirement increases did not change the response rate on the alternate key, and an extension of Herrnstein's absolute response rate function for force variation on a single variable-interval schedule is suggested.     

Human fixed-interval performance with concurrently programmed schedules: A parametric analysis

Young adults pressed a lever for points, exchangeable for money, programmed on concurrent schedules in which one component was a fixed-interval and the other component either a fixed-ratio (Experiment 1) or a differential-reinforcement-of-low-rate (Experiment 2). Two general patterns of fixed-interval responding, postreinforcement pause or constant rate, occurred in both experiments as a function of the parameter values of each component. Also patterns of interaction between the component schedules developed, in which responding or point delivery on one component appeared to be discriminative for responding on the other component. Once a pattern of responding was established, it tended to persist when the parameter values of the schedule were changed. On many schedules, subjects with an experimental history responded differently than did naive subjects, although certain schedule values were resistant to the history effects. The role of verbal strategies in mediating history effects was discussed.     

Temporal constraint on choice: Sensitivity and bias in multiple schedules

In multiple schedules of reinforcement, ratios of responses in successive components are relatively insensitive to ratios of obtained reinforcers. An analysis is proposed that attributes changes in absolute response rates to concurrent interactions between programmed reinforcement and extraneous reinforcement in other components. The analysis predicts that ratios of responses in successive components vary with reinforcer ratios, qualified by a term describing the reinforcement context, that is, programmed and extraneous reinforcers. Two main predictions from the analysis were confirmed in an experiment in which pigeons' responses were reinforced in the components of a multiple schedule and analog extraneous reinforcement was scheduled for an alternative response in each component. Sensitivity of response and time ratios to reinforcer ratios in the multiple schedules varied as a function of the rate of extraneous reinforcers. Bias towards responding in one component of the multiple schedule varied as an inverse function of the ratios of extraneous reinforcer rate in the two components. The data from this and previous studies of multiple-concurrent performance were accurately predicted by our analysis and supported our contention that the allocation of behavior in multiple-schedule components depends on the relative values of concurrently-available reinforcers within each component.     

Delay and amount of reward in a concurrent chain

Eight pigeons responded under a concurrent-chain schedule for rewards differing in both delay and amount, the larger reward being associated with the longer delay. Preference was examined as the absolute durations of the terminal-link delays were increased at four different delay ratios. Difficulties with other experiments of this type were controlled for by the use of (a) a single-tape initial link to equalize terminal-link entries, (b) a blackout following the more immediate reward to equalize terminal-link length, and (c) a photocell to measure reinforcer duration more accurately. Preference for the larger reward changed systematically as delays increased in all conditions, decreasing for the 6:1, 3:1, and 3:2 ratios, and increasing for the 1:1 ratio. These results were similar to, but significantly different from, those of previous investigations. The implications of these results for various models of concurrent-chain behavior are discussed.     

Sensitivity to reinforcement in concurrent arithmetic and exponential schedules

The generalized matching law states that the logarithm of the ratio of responses emitted or time spent responding in concurrent variable-interval schedules is a linear function of the logarithm of the ratio of reinforcements obtained. The slope of this relation, sensitivity to reinforcement, varies about 1.0 but has been shown to be different when obtained in different laboratories. The present paper analyzed the results from 18 experiments on concurrent variable-interval schedule performance and showed that response-allocation sensitivity to reinforcement was significantly smaller when arithmetic, rather than exponential, progressions were used to produce variable-interval schedules. There were no differences in time-allocation sensitivity between the two methods of constructing variable-interval schedules. Since the two laboratories have consistently used different methods for constructing variable-interval schedules, the differences in obtained sensitivities to reinforcement are explained. The reanalysis suggests that animals may be sensitive to differences in the distribution of reinforcements in time.