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.     

Human choice on concurrent variable-interval variable-ratio schedules.

Each of 5 adult male humans sat in a 4 degrees C room where they could warm themselves by illuminating six heat lamps for 10-second periods according to a concurrent variable-interval variable-ratio schedule. Left-button presses on a response panel switched between the schedules and started a 2-second changeover delay. Right-button presses illuminated the heat lamps if assigned by the associated schedule and if the changeover delay had timed out. Panel lights identified the schedule in effect and each effective right-button press. A discrimination procedure--either a multiple variable-interval variable-ratio schedule or the presentation of each schedule individually on alternate days--preceded exposure to the choice procedure for some subjects. For subjects not exposed to a discrimination procedure prior to exposure to choice, or if such exposure failed to result in higher rates to the ratio than to the interval schedule, relative response rates matched relative reinforcement rates. However, if subjects responded at higher rates to the ratio schedule than to the interval schedule during a prior discrimination procedure, relative rates on a subsequent choice procedure deviated from matching in the direction of reinforcement-rate maximizing. In eight of 11 conditions, choice appeared to be governed by maximizing processes. In all cases, human concurrent ratio-interval performances differed from those of nonhumans in that matching was never obtained with local ratio-interval rate differences.     

Concurrent variable-ratio schedules: Implications for the generalized matching law

Rats' responses were reinforced on concurrent variable-ratio variable-ratio schedules in which responses on one lever incremented the ratio counter and responses on a second lever changed the schedule and correlated stimulus. The relative frequency of reinforcement was varied from .10 to .99. In one set of conditions, responding on the main lever incremented both ratio counters, but reinforcement required a response in the presence of the stimulus correlated with the ratio that had been completed. In a second set of conditions, responses on the main lever incremented only the ratio correlated with the stimulus that was currently present. When main-lever responses incremented both ratio counters, subjects distributed responding and time in a manner consistent with the generalized matching law. When responses on the main lever incremented only the schedule currently in effect, the rats responded almost exclusively on the schedule producing the higher frequency of reinforcement. These results extend the applicability of the generalized matching law to dependent ratio schedules.     

Matching in concurrent variable-interval avoidance schedules

After pretraining with multiple variable-interval avoidance schedules, two rats were exposed to a series of concurrent variable-interval avoidance schedules. Responses on two levers cancelled delivery of electric shocks arranged according to two independent variable-interval schedules. The ratio of responses and time spent on the two levers approximately matched the ratio of shocks avoided on each. Matching to the number of shocks received was not obtained. Concurrent variable-interval avoidance can therefore be added to the group of positive and negative reinforcement schedules that can be expressed in the quantitative framework of the matching law.     

Within-session changes in key and lever pressing for water during several multiple variable-interval schedules

Rats pressed keys or levers for water reinforcers delivered by several multiple variable-interval schedules. The programmed rate of reinforcement varied from 15 to 240 reinforcers per hour in different conditions. Responding usually increased and then decreased within experimental sessions. As for food reinforcers, the within-session changes in both lever and key pressing were smaller, peaked later, and were more symmetrical around the middle of the session for lower than for higher rates of reinforcement. When schedules provided high rates of reinforcement, some quantitative differences appeared in the within-session changes for lever and key pressing and for food and water. These results imply that basically similar factors produce within-session changes in responding for lever and key pressing and for food and water. The nature of the reinforcer and the choice of response can also influence the quantitative properties of within-session changes at high rates of reinforcement. Finally, the results show that the application of Herrnstein's (1970) equation to rates of responding averaged over the session requires careful consideration.     

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.     

Temporal control by signals of interval duration within variable-interval schedules

Rats' lever pressing produced sucrose reinforcers on a variable-interval schedule where, in different conditions, the duration of a stimulus presented immediately after reinforcement was either correlated or uncorrelated with the duration of the current interreinforcement interval. Under the baseline schedule, in which no stimulus was presented, the minimum interreinforcement interval was 8 s and the mean postreinforcement pause of each subject approximated this value. Response rates increased slowly over the first 10 to 15 s and then remained roughly constant throughout the remainder of the interval. In both the correlated and uncorrelated conditions, the added stimulus resulted in the postreinforcement pauses lengthening to values in excess of the duration of the preceding stimulus. This resulted in a poststimulus pause which was, in most cases, roughly constant irrespective of the duration of the preceding stimulus, or of the reinforcement contingencies prevailing immediately after stimulus offset. Local response-rate patterns in the uncorrelated conditions were similar to those obtained under the baseline schedule in which no stimulus was presented. However, in the correlated condition local response rates increased across the remainder of the interreinforcer interval. Further, the rate of acceleration was inversely related to the duration of the preceding stimulus. These results show that a correlation between stimulus duration and the ensuing time to reinforcement can control behavior—a type of temporal control not previously reported.     

Yoked variable-ratio and variable-interval responding in pigeons

Pigeons' key pecks were maintained by variable-ratio or variable-interval schedules of food reinforcement. For pairs of pigeons in one group, variable-ratio reinforcement was arranged for one pigeon's pecks; for the second pigeon, reinforcement was arranged according to a variable-interval schedule yoked to the interreinforcement times produced by the first pigeon. For pairs of pigeons in another group, variable-interval reinforcement was arranged for one pigeon's pecks; for the second pigeon, reinforcement was arranged according to a variable-ratio schedule yoked to the interreinforcement responses produced by the first pigeon. For each pair, the yoking procedure was maintained for four or five consecutive sessions of 50 reinforcements each. In more than three-quarters of the pairs, variable-ratio response rates were higher than variable-interval rates within two sessions; in all cases, the rate difference developed within four sessions.     

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.     

Interlocking schedules: the relationship between response and time requirements.

Rats were exposed to an interlocking fixed-ratio 150 fixed-interval 5-minute schedule of food reinforcement and then to yoked variable-ratio schedules in which individual ratios corresponded exactly to the ratios of responses to reinforcement obtained on the interlocking schedule. After additional training with the interlocking schedule, the rats were exposed to yoked variable-interval schedules in which intervals corresponded to the intervals between successive reinforcements obtained on the second interlocking schedule. Response rates were highest in the yoked VR condition and lowest in the yoked VI, while intermediate rates characterized the interlocking schedule. Break-run patterns of responding were generated by the interlocking schedule for all subjects, while both the yoked VR and VI schedules produced comparatively stable local rates of responding. These results indicate that responding is sensitive to the interlocking schedule's inverse relationship between reinforcement frequency and responses per reinforcement.     

Rats' performance on variable-interval schedules with a linear feedback loop between response rate and reinforcement rate

Three experiments investigated whether rats are sensitive to the molar properties of a variable-interval (VI) schedule with a positive relation between response rate and reinforcement rate (i.e., a VI+ schedule). In Experiment 1, rats responded faster on a variable ratio (VR) schedule than on a VI+ schedule with an equivalent feedback function. Reinforced interresponse times (IRTs) were shorter on the VR as compared to the VI+ schedule. In Experiments 2 and 3, there was no systematic difference in response rates maintained by a VI+ schedule and a VI schedule yoked in terms of reinforcement rate. This was found both when the yoking procedure was between-subject (Experiment 2) and within-subject (Experiment 3). Mean reinforced IRTs were similar on both the VI+ and yoked VI schedules, but these values were more variable on the VI+ schedule. These results provided no evidence that rats are sensitive to the feedback function relating response rate to reinforcement rate on a VI+ schedule.     

Molar And Molecular Control In Variable-interval And Variable-ratio Schedules

Response rates are typically higher under variable-ratio than under variable-interval schedules of reinforcement, perhaps because of differences in the dependence of reinforcement rate on response rate or because of differences in the reinforcement of long interresponse times. A variable-interval-with-added-linear-feedback schedule is a variable-interval schedule that provides a response rate/reinforcement rate correlation by permitting the minimum interfood interval to decrease with rapid responding. Four rats were exposed to variable-ratio 15, 30, and 60 food reinforcement schedules, variable-interval 15-, 30-, and 60-s food reinforcement schedules, and two versions of variable-interval-with-added-linear-feedback 15-, 30-, and 60-s food reinforcement schedules. Response rates on the variable-interval-with-added-linear-feedback schedule were similar to those on the variable-interval schedule; all three schedules led to lower response rates than those on the variable-ratio schedules, especially when the schedule values were 30. Also, reinforced interresponse times on the variable-interval-with-added-linear-feedback schedule were similar to those on variable interval and much longer than those produced by variable ratio. The results were interpreted as supporting the hypothesis that response rates on variable-interval schedules in rats are lower than those on comparable variable-ratio schedules, primarily because the former schedules reinforce long interresponse times.     

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.     

Effects of a variable-ratio conditioning history on sensitivity to fixed-interval contingencies in rats.

We investigated the possibility that human-like fixed-interval performances would appear in rats given a variable-ratio history (Wanchisen, Tatham, & Mooney, 1989). Nine rats were trained under single or compound variable-ratio schedules and then under a fixed-interval 30-s schedule. The histories produced high fixed-interval rates that declined slowly over 90 sessions; differences as a function of the particular history were absent. Nine control animals given only fixed-interval training responded at lower levels initially, but rates increased with training. Despite differences in absolute rates, rates within the intervals and postreinforcement pauses indicated equivalent development of the accelerated response patterns suggestive of sensitivity to fixed-interval contingencies. The finding that the histories elevated rates without retarding development of differentiated patterns suggests that the effective response unit was a burst of several lever presses and that the fixed-interval contingencies acted on these units in the same way as for single responses. Regardless of history, the rats did not manifest the persistent, undifferentiated responding reported for humans under comparable schedules. We concluded that the shortcomings of animal models of human fixed-interval performances cannot be easily remedied by including a variable-ratio conditioning history within the model.     

Matching under concurrent fixed-ratio variable-interval schedules of food presentation

Four pigeons were exposed to concurrent fixed-ratio, variable-interval schedules of food presentation. The fixed-ratio requirement was either 25, 50, 75, or 100 responses, with the variable-interval schedule parameter held constant at 4 minutes. A delay time was imposed between a changeover from one schedule to the other and subsequent food availability. The delay time was varied at each ratio requirement over four values; no delay, 0-second delay, 1.5-second delay, and 5.0-second delay. As the fixed-ratio requirement or the delay time increased, a greater proportion of the total responses and time spent responding occurred under the variable-interval schedule relative to the proportion of food deliveries under that schedule. Neither relative overall response rate nor relative time spent responding equalled the relative frequency of food presentation, as would be predicted by a linear “matching” model. Rather, these data were described by power functions with slopes of approximately 1.0 and intercepts greater than 1.0. In the terms of Baum's (1974) analysis, these deviations from linear matching represent bias in favor of responding under the interval schedule. Bias, as reflected in the intercept of the power function, was greater for the ratio of time than the ratio of responses.     

Temporal control by progressive-interval schedules of reinforcement.

Progressive-interval performances are described using measures that have proven to be successful in the analysis of fixed-interval responding. Five rats were trained with schedules in which the durations of consecutive intervals increased arithmetically as each interval was completed (either 6-s or 12-s steps for different subjects). The response patterns that emerged with extended training (90 sessions) indicated that performances had come under temporal control. Postreinforcement pausing increased as a function of the interval duration, the pauses were proportional to the prevailing duration, and the likelihood of the first response within an interval increased as the interval elapsed. To assess the resistance of these patterns to disruption, subjects were trained with a schedule that generated high response rates and short pauses (variable ratio). When the progressive-interval schedule was reinstated, pausing was attenuated and rates were elevated, but performances reverted to earlier patterns with continued exposure. The results indicated that temporal control by progressive-interval schedules, although slow to develop, is similar in many respects to that for fixed-interval schedules.     

In search of the feedback function for variable-interval schedules

Finding a theoretically sound feedback function for variable-interval schedules remains an important unsolved problem. It is important because interval schedules model a significant feature of the world: the dependence of reinforcement on factors beyond the organism's control. The problem remains unsolved because no feedback function yet proposed satisfies all the theoretical and empirical requirements. Previous suggestions that succeed in fitting data fail theoretically because they violate a newly recognized theoretical requirement: The slope of the function must approach or equal 1.0 at the origin. A function is presented that satisfies all requirements but lacks any theoretical justification. This function and two suggested by Prelec and Herrnstein (1978) and Nevin and Baum (1980) are evaluated against several sets of data. All three fitted the data well. The success of the two theoretically incorrect functions raises an empirical puzzle: Low rates of reinforcement are coupled with response rates that seem anomalously high. It remains to be discovered what this reflects about the temporal patterning of operant behavior at low reinforcement rates. A theoretically and empirically correct function derived from basic assumptions about operant behavior also remains to be discovered.     

Drug discrimination in rats under concurrent variable-interval variable-interval schedules

Eight rats were trained to discriminate pentobarbital from saline under a concurrent variable-interval (VI) VI schedule, on which responses on the pentobarbital-biased lever after pentobarbital were reinforced under VI 20 s and responses on the saline-biased lever were reinforced under VI 80 s. After saline, the reinforcement contingencies programmed on the two levers were reversed. The rats made 62.3% of their responses on the pentobarbital-biased lever after pentobarbital and 72.2% on the saline-biased lever after saline, both of which are lower than predicted by the matching law. When the schedule was changed to concurrent VI 50 s VI 50 s for test sessions with saline and the training dose of pentobarbital, responding on the pentobarbital-biased lever after the training dose of pentobarbital and on the saline-biased lever after saline became nearly equal, even during the first 2 min of the session, suggesting that the presence or absence of the training drug was exerting minimal control over responding and making the determination of dose-effect relations of drugs difficult to interpret. When the pentobarbital dose-response curve was determined under the concurrent VI 50-s VI 50-s schedule, responding was fairly evenly distributed on both levers for most rats. Therefore, 6 additional rats were trained to respond under a concurrent VI 60-s VI 240-s schedule. Under this schedule, the rats made 62.6% of their responses on the pentobarbital-biased lever after pentobarbital and 73.5% of their responses on the saline-biased lever after saline, which also is lower than the percentages predicted by perfect matching. When the schedule was changed to a concurrent VI 150-s VI 150-s schedule for 5-min test sessions with additional drugs, the presence or absence of pentobarbital continued to control responding in most rats, and it was possible to generate graded dose-response curves for pentobarbital and other drugs using the data from these 5-min sessions. The dose-response curves generated under these conditions were similar to the dose-response curves generated using other reinforcement schedules and other species.     

Pausing under variable-ratio schedules: Interaction of reinforcer magnitude, variable-ratio size, and lowest ratio

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Postreinforcement pausing and the rates of responding following the pause (run rates) in each component were measured as a function of variable-ratio size and the size of the lowest ratio in the configuration of ratios comprising each schedule. In one group of subjects, variable-ratio size was varied while the size of the lowest ratio was held constant. In a second group, the size of the lowest ratio was varied while variable-ratio size was held constant. For all subjects, the mean duration of postreinforcement pausing increased in the 2-s component but not in the 8-s component. Postreinforcement pauses increased with increases in variable-ratio size (Group 1) and with increases in the lowest ratio (Group 2). In both groups, run rates were slightly higher in the 8-s component than in the 2-s component. Run rates decreased slightly as variable-ratio size increased, but were unaffected by increases in the size of the lowest ratio. These results suggest that variable-ratio size, the size of the lowest ratio, and reinforcer magnitude interact to determine the duration of postreinforcement pauses.     

Within-session Response Patterns On Conjoint Variable-interval Variable-time Schedules

Operant responding often changes within sessions, even when factors such as rate of reinforcement remain constant. The present study was designed to determine whether within-session response patterns are determined by the total number of reinforcers delivered during the session or only by the reinforcers earned by the operant response. Four rats pressed a lever and 3 pigeons pecked a key for food reinforcers delivered by a conjoint variable-interval variable-time schedule. The overall rate of reinforcement of the conjoint schedule varied across conditions from 15 to 480 reinforcers per hour. When fewer than 120 reinforcers were delivered per hour, the within-session patterns of responding on conjoint schedules were similar to those previously observed when subjects received the same total number of reinforcers by responding on simple variable-interval schedules. Response patterns were less similar to those observed on simple variable-interval schedules when the overall rate of reinforcement exceeded 120 reinforcers per hour. These results suggest that response-independent reinforcers can affect the within-session pattern of responding on a response-dependent schedule. The results are incompatible with a response-based explanation of within-session changes in responding (e.g., fatigue), but are consistent with both reinforcer-based (e.g., satiation) and stimulus-based (e.g., habituation) explanations.