Synthetic variable-interval schedules of reinforcement

Three pigeons pecked for food on a synthetic variable-interval schedule of reinforcement that had two independent parts: a variable-interval schedule that arranged a distribution of interreinforcement intervals, and a device that randomly assigned each reinforcement to one of 10 classes of interresponse times. The frequencies of reinforcement for the 10 classes of interresponse times were systematically varied, while the overall frequency of reinforcement was held within a comparatively narrow range. The 10 classes extended either from 0.1 to 0.6 sec in 0.05-sec intervals, or from 1.0 to 6.0 sec in 0.5-sec intervals. In the former case, some control by reinforcement was obtained, but it was weak and no simple relationships were discernible. In the latter case, the relative frequency of an interresponse time was a generally increasing function of its relative frequency of reinforcement, and two simple controlling relationships were found. First, the function relating interresponse times per opportunity to reinforcements per opportunity was, over a restricted range, approximately linear with a slope of unity. Second, when all 10 classes of interresponse times were reinforced equally often, the relative frequency of an interresponse time approximately equalled the relative reciprocal of its length.     

Aftereffects of reinforcement on variable-ratio schedules

On each of variable-ratio 10, 40, and 80 schedules of reinforcement, when rats' lever-pressing rates were stable, the concentration of a liquid reinforcer was varied within sessions. The duration of the postreinforcement pause was an increasing function of the reinforcer concentration, this effect being more marked the higher the schedule parameter. The running rate, calculated by excluding the postreinforcement pause, was unaffected by concentration. The duration of the postreinforcement pause increased with the schedule parameter, but the proportion of the interreinforcement interval taken up by the pause decreased. Consequently, the overall response rate was an increasing function of the schedule parameter; i.e., it was inversely related to reinforcement frequency, contrary to the law of effect. The running rate, however, decreased with the reinforcement frequency, in accord with the law of effect. When 50% of reinforcements were randomly omitted, the postomission pause was shorter than the postreinforcement pause, but the running rate of responses was not affected.     

Two-key concurrent paced variable-interval paced variable-interval schedules of reinforcement

Nine pigeons were used in two experiments in which a response was reinforced if a variable-interval schedule had assigned a reinforcement and if the response terminated an interresponse time within a certain interval, or class, of interresponse times. One such class was scheduled on one key, and a second class was scheduled on a second key. The procedure was, therefore, a two-key concurrent paced variable-interval paced variable-interval schedule. In Exp. I, the lengths of the two reinforced interresponse times were varied. The relative frequency of responding on a key approximately equalled the relative reciprocal of the length of the interresponse time reinforced on that key. In Exp. II, the relative frequency and relative magnitude of reinforcement were varied. The relative frequency of responding on the key for which the shorter interresponse time was reinforced was a monotonically increasing, negatively accelerated function of the relative frequency of reinforcement on that key. The relative frequency of responding depended on the relative magnitude of reinforcement in approximately the same way as it depended on the relative frequency of reinforcement. The relative frequency of responding on the key for which the shorter interresponse time was reinforced depended on the lengths of the two reinforced interresponse times and on the relative frequency and relative magnitude of reinforcement in the same way as the relative frequency of the shorter interresponse time depended on these variables in previous one-key concurrent schedules of reinforcement for two interresponse times.     

Response-rate differences in variable-interval and variable-ratio schedules: An old problem revisited

In Experiment 1, a variable-ratio 10 schedule became, successively, a variable-interval schedule with only the minimum interreinforcement intervals yoked to the variable ratio, or a variable-interval schedule with both interreinforcement intervals and reinforced interresponse times yoked to the variable ratio. Response rates in the variable-interval schedule with both interreinforcement interval and reinforced interresponse time yoking fell between the higher rates maintained by the variable-ratio schedule and the lower rates maintained by the variable-interval schedule with only interreinforcement interval yoking. In Experiment 2, a tandem variable-interval 15-s variable-ratio 5 schedule became a yoked tandem variable-ratio 5 variable-interval x-s schedule, and a tandem variable-interval 30-s variable-ratio 10 schedule became a yoked tandem variable-ratio 10 variable-interval x-s schedule. In the yoked tandem schedules, the minimum interreinforcement intervals in the variable-interval components were those that equated overall interreinforcement times in the two phases. Response rates did not decline in the yoked schedules even when the reinforced interresponse times became longer. Experiment 1 suggests that both reinforced interresponse times and response rate–reinforcement rate correlations determine response-rate differences in variable-ratio 10 and yoked variable-interval schedules in rats. Experiment 2 suggests a minimal role for the reinforced interresponse time in determining response rates on tandem variable-interval 30-s variable-ratio 10 and yoked tandem variable-ratio 10 variable-interval x-s schedules in rats.     

Unsignalled delay of reinforcement in variable-interval schedules

Three pigeons responded on several tandem variable-interval fixed-time schedules in which the value of the fixed-time component was varied to assess the effects of different unsignalled delays of reinforcement. Actual (obtained) delays between the last key peck in an interval and reinforcement were consistently shorter than the nominal (programmed) delay. When nominal delays were relatively short, response rates were higher during the delay condition than during the corresponding nondelay condition. At longer nominal delay intervals, response rates decreased monotonically with increasing delays. The results were consistent with those obtained from delay-of-reinforcement procedures that impose either a stimulus change (signal) or a no-response requirement during the delay interval.     

Concurrent variable-interval variable-ratio schedules can provide only weak evidence for matching

Herrnstein and Heyman (1979) showed that when pigeons' pecking is reinforced on concurrent variable-interval variable-ratio schedules, (1) their behavior ratios match the ratio of the schedules' reinforcer frequencies, and (2) there is more responding on the variable interval. Since maximizing the reinforcement rate would require responding more on the variable ratio, these results were presented as establishing the primacy of matching over maximizing. In the present report, different ratios of behavior were simulated on a computer to see how they would affect reinforcement rates on these concurrent schedules. Over a wide range of experimenter-specified choice ratios, matching obtained — a result suggesting that changes in choice allocation produced changes in reinforcer frequencies that correspond to the matching outcome. Matching also occurred at arbitrarily selected choice ratios when reinforcement rates were algebraically determined by each schedule's reinforcement-feedback function. Additionally, three birds were exposed to concurrent variable-interval variable-ratio schedules contingent on key pecking in which hopper durations were varied in some conditions to produce experimenter-specified choice ratios. Matching generally obtained between choice ratios and reinforcer-frequency ratios at these different choice ratios. By suggesting that reinforcer frequencies track choice on this procedure, instead of vice versa, this outcome questions whether matching-as-outcome was due to matching-as-process in the Herrnstein and Heyman study.     

Behavior of humans in variable-interval schedules of reinforcement

During Phase I, human subjects pressed a button for monetary reinforcement in five variable-interval schedules, each of which specified a different frequency of reinforcement. The rate of responding was an increasing, negatively accelerated function of reinforcement frequency; the data conformed closely to Herrnstein's equation. During Phase II, the same five schedules were in operation, but in addition a concurrent variable-interval schedule (B) was introduced, responses on which were always reinforced at the same frequency. Response rate in component A increased while the response rate in B decreased, as a function of the reinforcement frequency in component A. Relative response rates in the two component schedules matched the relative frequencies of reinforcement. Comparing the absolute response rates in component A during Phase I and Phase II it was found that introduction of the concurrent schedule did not affect the value of the theoretical maximum response rate, but did increase the value of the reinforcement frequency needed to obtain any particular submaximal response rate.     

Performance of humans in variable-interval avoidance schedules programmed singly, and concurrently with variable-interval schedules of positive reinforcement

Performance maintained under single variable-interval avoidance schedules, single variable-interval schedules of positive reinforcement, and concurrent schedules consisting of a variable-interval avoidance component and a variable-interval positive reinforcement component, was studied in three human subjects, using points exchangeable for money as the reinforcer. Response rate in the single variable-interval avoidance schedules was an increasing function of the frequency of monetary loss avoidance. Response rate in the single variable-interval positive reinforcement schedules was an increasing function of the frequency of obtained monetary reinforcement. In the concurrent avoidance/reinforcement schedules, the rate of responding in the avoidance component increased, and the rate of responding in the positive reinforcement schedule decreased (with one exception) as a function of the frequency of loss avoidance in the avoidance component. The logarithms of the ratios of the response rates in the two components, and the logarithms of the ratios of the times spent in the two components, were linearly related to the logarithms of the ratios of the frequency of loss avoidance in the avoidance component to the frequency of reinforcement in the positive reinforcement component. All three subjects exhibited marked undermatching of response rate ratios to reinforcement frequency ratios. The results are discussed in the context of Herrnstein's quantitative model of operant performance.     

Local response-rate constancy on concurrent variable-interval schedules of reinforcement

Concurrent variable-interval schedules were arranged with a main key that alternated in color and schedule assignment, along with a changeover key on which a small fixed ratio was required to changeover. Acceptable matching was observed with pigeons in two replications, but there was a tendency toward overmatching. Local response rates were found to differ for unequal schedules of a concurrent pair: local response rate was greater for the variable-interval schedule with the smaller average interreinforcement interval, but qualifications based on an interresponse-time analysis were discussed. In a second experiment, two 3-minute variable-interval schedules were arranged concurrently, and the experimental variable was the changeover procedure: either a changeover delay was incurred by each changeover or a small fixed ratio on a changeover key was required to complete a changeover. Changeover delays of 2 and 5 seconds were compared with a fixed-ratio changeover of five responses. The response output on the main key (associated with the variable-interval schedules) was greater when a changeover delay was arranged than when a fixed ratio was required to changeover. A detailed analysis of stripchart records showed that a 2-second delay generated an increased response rate for 3 seconds after a changeover, while the fixed-ratio requirement generated an increased rate during the first second only, followed by a depressed response rate for 2 seconds.     

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.     

Changeover behavior under pairs of fixed-ratio and variable-ratio schedules of reinforcement

Three pigeons were studied under a pair of equal fixed-ratio schedules and a pair of equal variable-ratio schedules. Each pair was arranged as independent, concurrent schedules and also in a non-independent relation where each peck in a schedule counted toward the response requirement of both schedules. The non-independent pair of variable-ratio schedules maintained much higher changeover rates than any of the other three arrangements. Thus, two factors seemed necessary for generating high changeover rates. Responding on a schedule had to count toward the response requirement of both schedules, and the component schedules had to be variable. These data are consistent with the hypothesis that changeovers are at least partly controlled by the probability of reinforcement following a changeover.     

Induced attack during multiple fixed-ratio, variable-ratio schedules of reinforcement

Two pigeons were exposed to a multiple schedule of reinforcement: in the presence of one discriminative stimulus, key pecks produced grain according to a fixed-ratio schedule; in the presence of a second discriminative stimulus, key pecks produced grain according to a variable-ratio schedule. The key-peck requirements in the two components were increased in successive stages from 50 to 125 responses. Live target pigeons were restrained at the rear of the chamber. Attacks against the targets were automatically recorded, and a variety of measures of attack behavior were taken. Attacks, when they occurred, always followed grain presentation. All measures revealed higher levels of attack during the fixed-ratio component at all parameter values. All measures generally increased with increases in fixed-ratio values with both birds, and with increases in variable-ratio values with one bird. With the other bird, only the per cent of reinforcements followed by attack increased with increases in variable-ratio value; all other measures first increased and then decreased. Both increasing and bitonic functions relating induced attack to schedule parameters have been reported in experiments usually employing a single measure of attack. The measures have varied widely among these experiments. It is suggested that further studies of induced attack examine a wider range of schedule parameters and that relationships among measures be studied.     

Some factors controlling preference between fixed-ratio and variable-ratio schedules of reinforcement

A multiple schedule of food reinforcement for key-pecking was arranged which consisted of nine fixed-ratios, each of which operated in the presence of a different stimulus. Pigeons could complete a given fixed-ratio within the multiple schedule or, by pecking a second key, could switch from the fixed-ratio schedule to a variable-ratio schedule consisting of the same nine ratios. Stable switching behavior was established which did not maximize simple probability or rate of reinforcement. Instead, the subjects showed a stable preference for the variable-ratio schedule of food reinforcement. Increasing the number of responses required to switch, and removing the occasions on which reinforcement was delivered after a single response in the variable schedule, decreased the number of switches to the variable schedule. Periods of delay interposed between a completed switch and the availability of reinforcement after one response in the variable schedule also decreased switching to the variable schedule, particularly at long delay intervals.     

Second-order schedules of token reinforcement: comparisons of performance under fixed-ratio and variable-ratio exchange schedules

Rats' lever pressing produced tokens according to a 20-response fixed-ratio schedule. Sequences of token schedules were reinforced under a second-order schedule by presentation of periods when tokens could be exchanged for food pellets. When the exchange period schedule was a six-response fixed ratio, patterns of completing the component token schedules were bivalued, with relatively long and frequent pauses marking the initiation of each new sequence. Altering the exchange period schedule to a six-response variable ratio resulted in sharp reductions in the frequency and duration of these initial pauses, and increases in overall rates of lever pressing. These results are comparable to those ordinarily obtained under simple fixed-ratio and variable-ratio schedules.     

Spatiotemporal patterns of behavior produced by variable-interval schedules of reinforcement

The spatiotemporal patterns of behavior exhibited by two pigeons during a variable-interval 15-second schedule of food reinforcement, a variable-interval 5-minute schedule, and then extinction of key pecking were recorded using an apparatus that continuously tracked the position of the bird in the experimental chamber. The variable-interval 15-second schedule produced a close-to-key pattern between reinforcements with two types of regular excursions from the region of the key frequently occurring after reinforcement. Subsequent exposure to the variable-interval 5-minute schedule produced more extended and extremely regular patterns between responses. Reinstatement of the variable-interval 15-second schedule reestablished the close-to-key pattern with regular excursions frequently occurring after reinforcement. During extinction the spatiotemporal patterns that had developed during the variable-interval 5-minute schedule reappeared and gradually dissipated. These patterns may have been a form of superstitious behavior.     

Matching with a trio of concurrent variable-interval schedules of reinforcement

A trio of concurrent variable-interval schedules of reinforcement was arranged according to a changeover-key procedure, including a changeover delay of 1.5 sec. The three schedules provided a combined maximum reinforcement rate of 45 reinforcements per hour. With that restriction, the nine experimental conditions included several combinations of variable-interval schedules, sometimes including extinction. The pigeons matched relative response rate and relative time to relative reinforcement rate. Relative time appeared to match some-what better than relative response rate. Performance adjusted rapidly from one experimental condition to the next, whether the change involved two or all three schedules of the concurrent trio.     

Performance of rats under concurrent variable-interval schedules of negative reinforcement

The behavior of rats under concurrent variable-interval schedules of negative reinforcement was examined. A single one-minute variable-interval programmer determined the availability of 30-second timeouts from electric shock. These were assigned to one or the other of the two component schedules with a probability of 0 to 1.0. The response requirement for the component schedules was standing to the right or left of the center of the experimental chamber. With a six-second changeover delay, the relative time spent under one component schedule varied directly and linearly with the relative number of timeouts earned under that component schedule. The absolute number of changeovers was highest when a similar number of timeouts was earned under each component schedule, and lowest when all or nearly all timeouts were earned under one component schedule. In general, these relations are similar to those reported with concurrent variable-interval schedules of positive reinforcement.     

Inhibiting function of reinforcement: magnitude effects on variable-interval schedules

In two experiments, the performance of rats under constant-probability and arithmetic variable-interval schedules respectively was compared when the concentration of a liquid reinforcer was varied within sessions; in other sessions, half of the reinforcers were randomly omitted. When the discriminative function of the reinforcer as a signal for a decrease in the probability of reinforcement was attenuated (the constant-probability schedule) the postreinforcement pause duration was nevertheless an increasing function of reinforcer magnitude. This relationship was also present, but more marked, when the temporal discriminative function of the reinforcer was enhanced (the arithmetic schedule). These results suggested that reinforcement has an unconditioned suppressive effect on the reinforced response distinct from any discriminative function it may acquire. The reinforcement-omission effect, where response rate accelerates following omission, was observed when the reinforcer functioned as an effective temporal discriminative stimulus, but not when such temporal control was absent.