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.     

Preference for unsegmented interreinforcement intervals in concurrent chains

Five pigeons were trained under concurrent-chain schedules in which a pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link and either both variable-interval or both fixed-interval schedules were presented in the terminal link. Except for the baseline, one of the terminal-link schedules was always a two-component chained schedule and the other was either a simple or a tandem schedule of equal mean interreinforcement interval. The values of the fixed-interval schedules were either 15 s or 60 s; that of the variable-interval schedules was always 60 s. A 1.5-s changeover delay operated during the initial link in some conditions. The pigeons preferred a simple or a tandem schedule to a chain. For the fixed-interval schedules, this preference was greater when the fixed interval was 60 s than when it was 15 s. For the variable-interval schedules, the preferences were less pronounced and occurred only when the changeover delay was in effect. For a given type of schedule and interreinforcement interval, similar preferences were obtained whether the nonchained schedule was a tandem or simple schedule. The changeover delay generally inflated preference and lowered the changeover rate, especially when the terminal-link schedules were either short (15 s) or aperiodic (variable-interval). The results were consistent with the notion that segmenting the interreinforcement interval of a schedule into a chain lowers the preference for it.     

A comparison of ratio and interval reinforcement schedules with comparable interreinforcement times

Pigeons were trained to peck keys on fixed-ratio and fixed-interval schedules of food reinforcement. Both schedules produced a pattern of behavior characterized as pause and run, but the relation of pausing to time between reinforcers differed for the two schedules even when mean time between reinforcers was the same. Pausing in the fixed ratio occupied less of the time between reinforcers for shorter interreinforcer times. For two of three birds, the relation was reversed at longer interreinforcer times. As an interreinforcer time elapsed, there was an increasing tendency to return to responding for the fixed interval, but a roughly constant tendency to return to responding for the fixed-ratio schedule. In Experiment 1 these observations were made for both single-reinforcement schedules and multiple schedules of fixed-ratio and fixed-interval reinforcement. In Experiment 2 the observations were extended to a comparison of fixed-ratio versus variable-interval reinforcement schedules, where the distribution of interreinforcement times in the variable interval approximated that for the fixed ratio.     

The psychological distance to reward

Pigeons' responses in the presence of two concurrently available (initial-link) stimuli produced entry into one of two different and mutually exclusive terminal link stimuli according to identical but independent variable-interval schedules. In one experiment, a two-component chained fixed-interval schedule produced food in one terminal link while a simple fixed-interval schedule produced food in the other terminal link. When the interreinforcement intervals were equal in the two terminal links (i.e., the simple fixed-interval was twice the size of each of the components in the chained schedule) pigeons preferred the simple fixed-interval as measured by their relative rates of responding in the concurrently available initial links. This preference increased as the duration of the terminal links increased. The preference could be reversed by making the simple fixed-interval schedule sufficiently longer than the chained schedule. In the second experiment, the terminal links consisted of two- vs three-component chained fixed-intervals, again with equal interreinforcement intervals. Pigeons preferred the two-component chain to the three-component chain, although these results were less consistent and less dramatic than those in the first experiment. Again, preference increased as the duration of the terminal links increased. The results show that an organism's choice for a schedule will be substantially lowered by the chaining operation even when the interreinforcement interval remains constant.     

Separating the effects of interreinforcement time and number of interreinforcement responses

The relative importance of interreinforcement time and interreinforcement responses was evaluated by varying each independently. To do this, a blackout was presented after each nonreinforced response under both fixed-ratio and fixed-interval schedules of reinforcement. Manipulating the blackout duration under the fixed-ratio schedule caused interreinforcement time to vary without affecting the number of interreinforcement responses. Pigeons' post-reinforcement and post-blackout response latencies were found to increase linearly with interreinforcement time. Under the fixed-interval schedule, the same blackout manipulations changed the number of interreinforcement responses without affecting interreinforcement time. Post-reinforcement and post-blackout response latencies under this condition were approximately constant. These results suggest that responding is controlled by interreinforcement time and is not influenced by the number of responses emitted between reinforcements.     

Conjunctive schedules of reinforcement II: response requirements and stimulus effects

Responding of three pigeons was maintained under conjunctive fixed-ratio, fixed-interval schedules where a key peck produced food after both schedule requirements were completed. The individual schedule requirements were then successively removed and reinstated with responding maintained under the following conditions: conjunctive fixed-ratio, fixed-time; fixed-time; and fixed-interval schedules. Patterns of responding changed in accord with the successive removal of the schedule requirements. Compared to the conjunctive fixed-ratio, fixed-interval schedule, pause duration increased and response rate decreased under conjunctive fixed-ratio, fixed-time schedules and under fixed-time schedules alone. Overall mean rates of responding were highest and pause duration lowest under fixed-interval schedules. When changes in the keylight colors were correlated with completion of the fixed-ratio, the end of the fixed-interval, or both of these conditions, the pattern of responding was modified and indicated a greater degree of control by the individual schedules. Although two birds showed large increases in interreinforcement time when they were initially exposed to the conjunctive schedule, when responding stabilized this measure was largely invariant for all birds across most schedule conditions.     

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.     

Quantitative Analysis of IRT Variability During the First Training Stages of a Variable-Interval Schedule in Rats

Five rats were reinforced under variable-interval schedules with different average interreinforcement intervals (30 seC., 1 min, 2 min, and 4 min). Each animal was run only two sessions of each schedule. The interresponse times (IRTs) were recorded and analyzed. The autocorrelation function of the IRT series and of the IRT time series (number of responses per time interval) were calculated, and absence of periodicity in the subject’s behavior was demonstrated. Frequency distribution of IRTs showed in all cases a similar shape and could be fitted to a gamma probability density function in 60% of cases with a signification level of .01 (Kolmogorov-Smirnoff test). The frequency distributions of the IRT time series were distributed as a Poisson process with a .05 significance level. These results suggest that during variable-interval schedules the responses of the animal can be modeled as a random process characterized by a gamma distribution, as a first approximation.

     

The effects of number of responses on the postreinforcement pause in fixed-interval schedules

The present study manipulated the number of responses in a modified fixed-interval schedule by imposing a blackout after each unreinforced response during the interval. The blackout duration was varied, and the duration of the fixed interval was held constant. The subjects were initially exposed to a fixed-interval 300-sec schedule. Blackout durations of 0, 10, and 50 sec were used. Following this, a fixed-interval 30-sec schedule was used with blackout durations of 0, 1, and 5 sec. Under the fixed-interval 300-sec schedule, the number of interreinforcement responses varied over a wider range than occurred under the fixed-interval 30-sec schedule. The duration of the postreinforcement pause decreased as blackout durations were increased and number of responses decreased on the fixed-interval 300-sec schedule, but pause length did not vary with changes in blackout duration and number of responses for the fixed-interval 30-sec schedule. The differences in the effects of blackout duration and response manipulation on the two fixed-interval schedules were attributed to relatively greater changes in the number of interreinforcement responses for the fixed-interval 300-sec schedule.     

Tolerance to effects of cocaine on behavior under a response-initiated fixed-interval schedule

Tolerance to effects of cocaine can be modulated by schedules of reinforcement. With multiple ratio schedules, research has shown an inverse relationship between ratio requirement and amount of tolerance that resulted from daily administration of the drug. In contrast, tolerance to the effects of cocaine on behavior under multiple interval schedules generally has developed regardless of interval value. Under interval schedules reinforcement depends on the animal making one response following a time interval. Thus, as time to respond increases, the time to reinforcement decreases. On the other hand, fixed ratio schedules require a specified number of responses to be made prior to reinforcement. Therefore, delaying the initiation of responding does not coincide with a significant decrease in the time to reinforcement. In the current experiment, 6 pigeons were trained to respond under a three-component multiple schedule, with a different tandem fixed-ratio 1 fixed-interval schedule in each component. The multiple schedule required one response, which was followed by one of three fixed-interval values (5, 15, or 60 s). Thus, the multiple schedule was interval-like because after the fixed-ratio 1, only one more response was required for reinforcement, but it was also ratio-like because the length of the pause at the beginning of each interreinforcer interval affected the time until the next reinforcer. Acute administration of cocaine generally resulted in dose-dependent decreases in responding. Chronic (i.e., daily) administration of a rate-decreasing dose resulted in tolerance patterns similar to those usually obtained with multiple ratio schedules. That is, the magnitude of tolerance was related inversely to schedule size. These results suggest that delay to reinforcement from the initial response may play a role in the development of schedule-parameter-related tolerance.     

Dynamics in the fine structure of schedule-controlled behavior.

The variability in the behavioral equilibrium established by six basic schedules was characterized. The measures were the pause preceding the first response in each interreinforcement interval; the mean rate of responding in each interreinforcement interval; and the relative frequency of each interresponse time. The temporal windows ranged across the 780-session exposure, across a session, and across the interreinforcement interval. A display of individual interresponse times as a function of time in the interreinforcement interval indicated clear recurrent responding at somewhat less than 3 Hz in every bird, even after extended exposure to a schedule and regardless of the contingency. No strong sequential dependencies in the interresponse-time distributions were identified. A simulator, based on a simple recurrent pulser, was presented that produced output similar to the obtained data. An archival data base of the behavior chronically maintained by the simple schedules was also generated.     

The temporal organization of behavior on periodic food schedules.

Various theories of temporal control and schedule induction imply that periodic schedules temporally modulate an organism's motivational states within interreinforcement intervals. This speculation has been fueled by frequently observed multimodal activity distributions created by averaging across interreinforcement intervals. We tested this hypothesis by manipulating the cost associated with schedule-induced activities and the availability of other activities to determine the degree to which (a) the temporal distributions of activities within the interreinforcement interval are fixed or can be temporally displaced, (b) rats can reallocate activities across different interreinforcement intervals, and (c) noninduced activities can substitute for schedule-induced activities. Obtained multimodal activity distributions created by averaging across interreinforcement intervals were not representative of the transitions occurring within individual intervals, so the averaged multimodal distributions should not be assumed to represent changes in the subject's motivational states within the interval. Rather, the multimodal distributions often result from averaging across interreinforcement intervals in which only a single activity occurs. A direct influence of the periodic schedule on the motivational states implies that drinking and running should occur at different periods within the interval, but in three experiments the starting times of drinking and running within interreinforcement intervals were equal. Thus, the sequential pattern of drinking and running on periodic schedules does not result from temporal modulation of motivational states within interreinforcement intervals.     

Response suppression on DRL by rats with septal damage

The effectiveness of the differential reinforcement for low rates of responding (DRL) contingency in suppressing response rates of septal rats was investigated by using a Multi-DRL-yoked-VI (variable interval) schedule of reinforcement. The yoking procedure equated the interreinforcement times on the two schedules. Each schedule was in effect for half of each session, and the change in schedule was signaled by the presence or absence of a cue light. Schedule order and DRL delay requirement were varied. For both normal and septal rats, the response rates were higher in the VI component than the DRL component; this effect demonstrates that the responding of septals as well as normals is suppressed by the differential reinforcement of a particular class of IRTs. A sharp difference in the level of responding occurred at the point of transition from one component of the multiple schedule to the other, which provides evidence of a discrimination between the two schedules for both normals and septals. The conclusion is that the responding of septals is suppressed by the DRL contingency and not controlled solely by the density and distribution of reinforcement.     

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.     

The response-reinforcement dependency in fixed-interval schedules of reinforcement

Pigeons were exposed to four different schedules of food reinforcement that arranged a fixed minimum time interval between reinforcements (60 sec or 300 sec). The first was a standard fixed-interval schedule. The second was a schedule in which food was presented automatically at the end of the fixed time interval as long as a response had occurred earlier. The third and fourth schedules were identical to the first two except that the first response after reinforcement changed the color on the key. When the schedule required a peck after the interval elapsed, the response pattern consisted of a pause after reinforcement followed by responding at a high rate until reinforcement. When a response was not required after the termination of the interval, the pattern consisted of a pause after reinforcement, followed by responses and then by a subsequent pause until reinforcement. Having the first response after reinforcement change the color on the key had little effect on performance. Post-reinforcement pause duration varied with the minimum interreinforcement interval but was unaffected by whether or not a response was required after the interval elapsed.     

“Level of Aspiration”: Preference for Time Versus Response Feedback and History Effects on the Setting of Personal Performance Standards

Human subjects responded on a computer keyboard and accumulated points according to fixed-ratio (FR) reinforcement schedules. In Experiment 1, subjects responded under a FR 500 schedule. Under baseline conditions satisfying the schedule requirement resulted in counter points and session termination. Subsequently, subjects could (a) choose to have a clock appear on the screen during the interreinforcement interval (IRI) as well as to enter a target time which they would attempt to better during that session, (b) choose to enter a target time or respond under baseline conditions, and (c) enter a target time and choose between having a clock appear throughout or at the end of experimental sessions. In Experiment 2, subjects responded under a FR 500 schedule, entered a target time each session, and could respond during the session to briefly produce either (a) clock feedback, or (b) the number of responses emitted by the subject. In Experiment 3, subjects responded under FR 250, 500, 1000, and 2000 schedule parameters, entered target times and responded for either clock or response feedback. Subjects (a) preferred responding under conditions in which target times were entered to responding under baseline conditions, (b) preferred to have the clock illuminated throughout rather than at the end of experimental sessions, (c) preferred response to clock feedback under all schedule parameters, (d) responded to having equaled or bettered a target time by lowering target time for the subsequent session, and (e) responded to having missed a target time by maintaining the same time during the subsequent session. The results were interpreted within the context of behavior analytic as opposed to more traditional personality theory.

     

Choice between response rates

Three pigeons were required to peck a single key at a higher and a lower rate, corresponding to two classes of shorter and longer concurrently reinforced interresponse times. Food reinforcers arranged by a single variable-interval schedule were randomly allocated to the two reinforced interresponse times. The absolute durations of reinforced interresponse times were varied while the total reinforcements per hour was held constant and the relative duration, i.e., the relative reciprocal, of the shorter reinforcer class was held constant at 0.70. Preference for the higher rate of responding, as measured by the relative frequency of responses terminating interresponse times in the shorter reinforced class, depended on the absolute reinforced response rates. Preference for the higher reinforced rate increased from a level of near-indifference (0.50) at high reinforced response rates, through the matching level (0.70) at intermediate reinforced response rates, to a virtually exclusive preference (>0.90) at low reinforced response rates. These results resemble corresponding preference functions obtained with two-key concurrent-chains schedules and thereby provide another sense in which it may be said that interresponse-time distributions from interval schedules estimate preference functions for the component response rates corresponding to different classes of reinforced interresponse times.     

Schedule-induced locomotor activity in humans.

In two experiments, humans received tokens either on a fixed-interval schedule for plunger pulling or various response-nondependent fixed-time schedules ranging from 16 to 140 seconds. Locomotor activity such as walking, shifting weight, or pacing was recorded in quarters of the interreinforcement interval to examine the induced characteristics of that behavior in humans. While performance was variable, several characteristics were present that have counterparts in experiments with nonhumans during periodic schedules of food reinforcement: (a) first quarter rates, and sometimes overall rates, of locomotor activity were greater during intervals that terminated in a visual stimulus and token delivery than those without: (b) overall rates of locomotor activity were greater during fixed-time 16-second schedules than during fixed-time 80- or 140-second schedules; (c) rates of locomotor activity decreased during the interreinforcement intervals; (d) locomotor activity was induced by response-dependent and response-nondependent token delivery. These results showed that the rate and temporal pattern of locomotor activity can be schedule-induced in humans.     

Effects of cocaine on performance under fixed-interval schedules with a small tandem ratio requirement

Daily administration of cocaine often results in the development of tolerance to its effects on responding maintained by fixed-ratio schedules. Such effects have been observed to be greater when the ratio value is small, whereas less or no tolerance has been observed at large ratio values. Similar schedule-parameter-dependent tolerance, however, has not been observed with fixed-interval schedules arranging comparable interreinforcement intervals. This experiment examined the possibility that differences in rate and temporal patterning between the two types of schedule are responsible for the differences in observed patterns of tolerance. Five pigeons were trained to key peck on a three-component multiple (tandem fixed-interval fixed-ratio) schedule. The interval values were 10, 30, and 120 s; the tandem ratio was held constant at five responses. Performance appeared more like that observed under fixed-ratio schedules than fixed-interval schedules. Effects of various doses of cocaine given weekly were then determined for each pigeon. A dose that reduced responding was administered prior to each session for 50 days. A reassessment of effects of the range of doses revealed tolerance. The degree of tolerance was similar across components of the multiple schedule. Next, the saline vehicle was administered prior to each session for 50 days to assess the persistence of tolerance. Tolerance diminished in all subjects. Overall, the results suggested that schedule-parameter-dependent tolerance does not depend on the temporal pattern of responding engendered by fixed-ratio schedules.