Concurrent fixed-interval variable-ratio schedules and the matching relation

Five rats responded under concurrent fixed-interval variable-ratio schedules of food reinforcement. Fixed-interval values ranged from 50-seconds to 300-seconds and variable-ratio values ranged from 30 to 360; a five-second changeover delay was in effect throughout the experiment. The relations between reinforcement ratios obtained from the two schedules and the ratios of responses and time spent on the schedules were described by Baum's (1974) generalized matching equation. All subjects undermatched both response and time ratios to reinforcement ratios, and all subjects displayed systematic bias in favor of the variable-ratio schedules. Response ratios undermatched reinforcement ratios less than did time ratios, but response ratios produced greater bias than did time ratios for every subject and for the group as a whole. Local rates of responding were generally higher on the variable-ratio than on the fixed-interval schedules. When responding was maintained by both schedules, a period of no responding on either schedule immediately after fixed-interval reinforcement typically was followed by high-rate responding on the variable-ratio schedule. At short fixed-interval values, when a changeover to the fixed-interval schedule was made, responding usually continued until fixed-interval reinforcement was obtained; at longer values, a changeover back to the variable-ratio schedule usually occurred when fixed-interval reinforcement was not forthcoming within a few seconds, and responding then alternated between the two schedules every few seconds until fixed-interval reinforcement finally was obtained.     

Dynamic equilibrium on a cyclic-interval schedule with a ramp

Five human subjects pressed a panel for money on a cyclic-interval schedule that arranged recurring periods of linearly increasing reinforcement rates (ramps). Response rate versus time functions for all subjects showed recurring periods of linearly increasing response rates. The responding of four of the five subjects was in phase with the reinforcement input. The remaining subject showed a two-minute phase shift. These results suggest that organisms may act like simple amplifiers on cyclic-interval schedules, that is, the form of the input signal is not changed by the organism, but is returned with amplification. By analogy with the variable-interval case, the controlling variable on cyclic-interval schedules with rate ramps may be the constant reinforcement acceleration that is arranged by the schedule.     

Stimulus control of respondent and operant key pecking: A single key procedure

Pigeons' responses to a uniformly illuminated response key were either reinforced on a variable-interval one-minute schedule of reinforcement or extinguished for one-minute periods. When 1.5 second signals were presented at the beginning of each component, so as to differentially predict reinforcement, the pigeons pecked at the signals, at rates higher than rates during the remainder of the component. When the brief signals were not differentially predictive of reinforcement, pecking in their presence decreased to near zero levels. Similar results were obtained with signals based upon colors and upon line orientations. Changes in rates of (unreinforced) pecking occurred during the signal whether pigeons responded differentially during the remainder of the component or not. Experiment II demonstrated that the presence of the signal correlated with extinction was not necessary for pecking to develop at the signal which preceded the component in which responding was intermittently reinforced. The experiments demonstrated a clear dissociation of respondent control from operant control of a response. In addition, operant behavior was shown to be relatively insensitive to differing rates of reinforcement, as compared to the sensitivity of respondent behavior to differing rates of reinforcement produced by the very same operant behavior.     

Preference for mixed versus constant delays of reinforcement: Effect of probability of the short, mixed delay

Preference for mixed versus constant delays of reinforcement was studied with a concurrent-chain procedure. Lever pressing by rats in concurrently available variable-interval 60-second initial links occasionally produced mutually exclusive terminal-link reinforcement delays. A constant delay of reinforcement (either 15 seconds or 30 seconds) composed one terminal link and mixed delays (.2 second and twice the value of the constant delay) were arranged in the other terminal link. The proportion of .2-second delays in the mixed-delay terminal link took on values of 0, .1, .25, .5, .75, .9, and 1.0 over experimental conditions. Based on relative rates of responding in the initial links, preference for the mixed delays was a negatively accelerated function of the proportion of short, mixed delays. Three of five rats preferred the mixed delays to the constant delays when the proportion of short, mixed delays was .1 or higher, and all five rats preferred the mixed delays when the proportion of short, mixed delays was .25 or higher. Neither Squires and Fantino's (1971) delay-reduction model of choice nor a model based on the harmonic mean reinforcement delay provided a close estimate of choice proportions over the range of short-delay proportions studied. The delay-reduction model underestimated choice for the mixed delays at low and intermediate proportions of short delays, and the harmonic-mean-delay model overestimated choice for the mixed delays at intermediate and high proportions of short delays.     

Response rate, latency, and resistance to change

Pigeons were trained on a multiple variable-interval/variable-interval schedule with pacing contingencies that generated high response rates in one component and low response rates in the other. Timeout periods separated the schedule components. During resistance-to-change tests, response-independent food was presented during the timeout periods, and the duration of that food presentation was varied among test sessions. Response rates in the schedule components decreased and latencies to the first response increased as a function of the duration of food presentations during the timeout. Both dependent measures changed about the same amount relative to their own baseline levels. The conclusions are that baseline response rates controlled by pacing contingencies are equally resistant to change, given equal reinforcement densities, and latency is a sensitive measure of resistance to change.     

Hill-climbing by pigeons

Pigeons were exposed to two types of concurrent operant-reinforcement schedules in order to determine what choice rules determine behavior on these schedules. In the first set of experiments, concurrent variable-interval, variable-interval schedules, key-peck responses to either of two alternative schedules produced food reinforcement after a random time interval. The frequency of food-reinforcement availability for the two schedules was varied over different ranges for different birds. In the second series of experiments, concurrent variable-ratio, variable-interval schedules, key-peck responses to one schedule produced food reinforcement after a random time interval, whereas food reinforcement occurred for an alternative schedule only after a random number of responses. Results from both experiments showed that pigeons consistently follow a behavioral strategy in which the alternative schedule chosen at any time is the one which offers the highest momentary reinforcement probability (momentary maximizing). The quality of momentary maximizing was somewhat higher and more consistent when both alternative reinforcement schedules were time-based than when one schedule was time-based and the alternative response-count based. Previous attempts to provide evidence for the existence of momentary maximizing were shown to be based upon faulty assumptions about the behavior implied by momentary maximizing and resultant inappropriate measures of behavior.     

Concurrent schedules: Spatial separation of response alternatives

Four pigeons were exposed to independent concurrent variable-interval 20-second variable-interval 60-second schedules of reinforcement. A transparent partition was inserted midway between the two response keys. The length of the partition was systematically manipulated. Increasing partition length produced a decrease in changeover rate in Experiment 1. Over-matching was observed with a partition length of 20 centimeters. In Experiment 2 a four-second limited hold was added to the schedules. Increasing partition length produced a decrease in changeover rate that exceeded the decrease observed in Experiment 1. This manipulation produced nearly exclusive choice of the variable-interval 20-second component. The present results, together with results obtained in related research, suggest that deviation from matching is a function of procedural variables that determine the consequences of a changeover response.     

A simple BASIC program to generate values for variable-interval schedules of reinforcement

A BASIC program to generate values for variable-interval (VI) schedules of reinforcement is presented. A VI schedule should provide access to reinforcement with a constant probability over a time horizon. If the values in a VI schedule are calculated from an arithmetic progression, the probability of reinforcement is positively correlated with the time since the last reinforcer was delivered. Fleshler and Hoffman (1962) developed an iterative equation to calculate VI schedule values so that the probability of reinforcement remains constant. This easy-to-use program generates VI schedule values according to the Fleshler and Hoffman equation, randomizes the values, and saves the values in ASCII to a disk file.     

Tolerance to and residual effects of cocaine in squirrel monkeys depend on reinforcement-schedule parameter.

Lever pressing by 4 squirrel monkeys was maintained under a three-component multiple fixed-ratio schedule of food presentation; components differed with respect to ratio size. For each monkey, acute administration of cocaine (0.03 to 1.3 mg/kg, i.m.) produced dose-dependent decreases in overall response rate in each component. During repeated daily administration of 1.0 mg/kg of cocaine, tolerance developed to the rate-decreasing effects under each of the ratio contingencies, but developed to a greater extent and was evident in earlier parts of sessions for performance under the smaller ratios. Response rates of 2 monkeys increased above nondrug control levels despite the putative reinforcer not being consumed during the session. When saline or a smaller dose of cocaine was substituted for 1.0 mg/kg, response rates often were suppressed below nondrug control-level responding. This suppressive effect was observed in each monkey and was more likely to be observed and/or to be of greater magnitude in large-ratio components for 3 of the 4 monkeys. When saline was administered chronically at the end of the chronic-drug phase, response rates remained suppressed in the large-ratio component for 2 of the monkeys. There was, therefore, a schedule-dependent dissociation between behavioral tolerance and the residual effects: Tolerance was greater when small ratios were arranged, whereas the residual effects were more pronounced when larger ratios were arranged.     

Choice as a function of local versus molar reinforcement contingencies.

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.