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.     

Choice between delayed reinforcers and fixed-ratio schedules requiring forceful responding.

This experiment measured pigeons' choices between delayed reinforcers and fixed-ratio schedules in which a force of approximately 0.48 N was needed to operate the response key. In ratio-delay conditions, subjects chose between a fixed-ratio schedule and an adjusting delay. The delay was increased or decreased several times a session in order to estimate an indifference point--a delay duration at which the two alternatives were chosen about equally often. Each ratio-delay condition was followed by a delay-delay condition in which subjects chose between the adjusting delay and a variable-time schedule, with the components of this schedule selected to match the ratio completion times of the preceding ratio-delay condition. The adjusting delays at the indifference point were longer when the alternative was a fixed-ratio schedule than when it was a matched variable-time schedule, which indicated a preference for the matched variable-time schedules over the fixed-ratio schedules. This preference increased in a nonlinear manner with increasing ratio size. This nonlinearity was inconsistent with a theory that states that indifference points for both time and ratio schedules can be predicted by multiplying the choice response-reinforcer intervals of the two types of schedules by different multiplicative constants. Two other theories, which predict nonlinear increases in preference for the matched variable-time schedules, are discussed.     

A behavioral economic analysis of concurrently available money and cigarettes.

In economic terms, consumption of a reinforcer is determined by its price and the availability and price of other reinforcers. This study examined the effects of response-requirement (i.e., price) manipulations on the self-administration of two concurrently available reinforcers. Six cigarette smokers participated in 4-hr sessions in which money and puffs on a cigarette were concurrently available according to fixed-ratio schedules of reinforcement. Once stable responding was obtained with both reinforcers available at Fixed Ratio 100, the response requirement for one reinforcer was systematically varied (Fixed Ratio 1,000 and 2,500), while the other reinforcer remained scheduled at Fixed Ratio 100. Increasing the fixed-ratio size for a reinforcer decreased its consumption, with a greater decrease occurring for monetary reinforcement. This finding was quantified in economic terms as own-price elasticity, with elasticity coefficients greater for money than cigarettes. The effects of fixed-ratio size on response output also differed across the two reinforcers. Although greater responding occurred for money at Fixed Ratio 100, increases in fixed-ratio size (for money) decreased responding for money, whereas the same increase in fixed-ratio size (for puffs) increased responding for puffs. Finally, increasing the fixed-ratio size for one reinforcer had little effect on consumption of the other concurrently available reinforcer. This finding was quantified as cross-price elasticity, with elasticity coefficients near 0.0 for most subjects, indicating little or no reinforcer interaction. The results indicate that the reinforcing effects of cigarettes and money in the setting studied here differed, and that the effects produced by changing the price of one reinforcer did not interact with the consumption of the other concurrently available reinforcer.     

A comparison of delays and ratio requirements in self-control choice.

In a discrete-trial procedure, pigeons could choose between 2-s and 6-s access to grain by making a single key peck. In Phase 1, the pigeons obtained both reinforcers by responding on fixed-ratio schedules. In Phase 2, they received both reinforcers after simple delays, arranged by fixed-time schedules, during which no responses were required. In Phase 3, the 2-s reinforcer was available through a fixed-time schedule and the 6-s reinforcer was available through a fixed-ratio schedule. In all conditions, the size of the delay or ratio leading to the 6-s reinforcer was systematically increased or decreased several times each session, permitting estimation of an "indifference point," the schedule size at which a subject chose each alternative equally often. By varying the size of the schedule for the 2-s reinforcer across conditions, several such indifference points were obtained from both fixed-time conditions and fixed-ratio conditions. The resulting "indifference curves" from fixed-time conditions and from fixed-ratio conditions were similar in shape, and they suggested that a hyperbolic equation describes the relation between ratio size and reinforcement value as well as the relation between reinforcer delay and its reinforcement value. The results from Phase 3 showed that subjects chose fixed-time schedules over fixed-ratio schedules that generated the same average times between a choice response and reinforcement.     

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.     

Effects of methadone on alternative fixed-ratio fixed-interval performance: latent influences on schedule-controlled responding.

Effects of methadone on pigeons' key pecking were examined under four conditions selected to analyze the control of behavior under alternative fixed-ratio fixed-interval schedules. In Condition 1, pigeons pecked under one of three different alternative schedules (alternative fixed-ratio 50 fixed-interval 90 s, alternative fixed-ratio 75 fixed-interval 90 s and alternative fixed-ratio 200 fixed-interval 90 s) each week. In Condition 2, fixed-ratio 50 or fixed-ratio 75 schedules were in effect during baseline sessions, and alternative fixed-ratio 50 fixed-interval 90-s or alternative fixed-ratio 75 fixed-interval 90-s schedules were in effect during sessions in which methadone was administered. In Condition 3, effects of methadone on key pecking maintained under fixed-ratio 50 and fixed-ratio 75 schedules were examined, whereas in Condition 4 the effects of methadone on key pecking under a fixed-interval 90-s schedule as well as fixed-ratio 50 and fixed-ratio 75 schedules were investigated. Control by the fixed-interval contingency was assessed by computing the proportion of total session reinforcers delivered under the fixed-interval schedule. Methadone administration (0.5-4.0 mg/kg) shifted the predominant source of schedule control under the alternative schedule from the fixed-ratio schedule to the fixed-interval contingency. This shift was dependent on methadone dose and fixed-ratio size. Control by the fixed-interval contingency was greatest following extensive exposure to the interval component embedded within the alternative schedule (Condition 1), but was apparent to a lesser degree with even very limited exposure to the alternative fixed-ratio fixed-interval schedule (Condition 2). Interreinforcement intervals comparable to those under fixed-interval schedule were not observed under the fixed-ratio schedules presented alone (Condition 3). Repeated exposure to the fixed-interval contingency outside the context of the alternative fixed-ratio fixed-interval schedule did not engender performance changes under a fixed-ratio schedule which would mimic those of increased fixed-interval contingency control (Condition 4). These data suggest that drug administration can be used to unmask the influence of contingencies that are latent under baseline conditions and reveal influences of both past and present environmental variables.     

Ratio requirement and reinforcer effects in concurrent fixed-interval fixed-ratio schedules

The fixed-ratio requirement was varied in concurrent fixed-interval fixed-ratio schedules. Fixed-interval responding was reinforced by food. In different phases, fixed-ratio responding was reinforced by food or water. There was a direct relation between the ratio requirement and interval response rates when both responses were reinforced with food, but essentially no relation when the reinforcers were different. The role of reinforcers in concurrent schedules merits detailed study.     

The effects of number of responses on pause length with temporal variables controlled

A change in the size of a fixed-ratio schedule involves a simultaneous change in number of responses, in time to complete the ratio (work time), and in the interval between successive reinforcements (interreinforcement interval). Previous studies have suggested the importance of work time and the interreinforcement interval in controlling the length of the post-reinforcement pause. The present study sought to determine whether number of responses is also a significant factor. Pigeons were trained on a multiple fixed-ratio x fixed-ratio 2 plus timeout schedule in which the size of the fixed-ratio x was manipulated. When the work times (Experiment I) or interreinforcement intervals (Experiment II) were equated for the two components, the pause before the fixed-ratio x was longer than the pause before the fixed-ratio 2 plus timeout. As fixed-ratio x size increased, the relative difference in the lengths of the two types of pauses also increased. Because the fixed-ratio x component contained a larger number of responses than the fixed-ratio 2 plus timeout component, the relatively longer pause preceding the fixed-ratio x indicates that number of responses played a significant role in determining the length of the post-reinforcement pause.     

Pigeons' choices in situations of diminishing returns: fixed- versus progressive-ratio schedules.

In two different discrete-trial procedures, pigeons were faced with choices between fixed-ratio and progressive-ratio schedules. The latter schedules entail diminishing returns, a feature analogous to foraging situations in the wild. In the first condition (no reset), subjects chose between a progressive-ratio schedule that increased in increments of 20 throughout a session and a fixed-ratio schedule that was constant across blocks of sessions. The size of the fixed ratio was varied parametrically through an ascending and then a descending series. In the reset condition, the same fixed-ratio values were used, but each selection (and completion) of the fixed ratio reset the progressive-ratio schedule back to its minimal value. In the no-reset procedure, the pigeons tended to cease selecting the progressive ratio when it equaled or slightly exceeded the fixed-ratio value, whereas in reset, they chose the fixed ratio well in advance of that equality point. These results indicate sensitivity to molar as well as to molecular reinforcement rates, and those molar relationships are similar to predictions based on the marginal value theorem of optimal foraging theory (e.g., Charnov, 1976). However, although previous results with monkeys (Hineline & Sodetz, 1987) appeared to minimize responses per reinforcement, the present results corresponded more closely to predictions based on sums-of-reciprocals of distance from point of choice to each of the next four reinforcers. Results obtained by Hodos and Trumbule (1967) with chimpanzees in a similar procedure were intermediate between these two relationships. Variability of choices, as well as median choice points, differed between the reset and no-reset conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Concurrent nonindependent fixed‐ratio schedules of alcohol self‐administration: Effects of schedule size on choice

Choice behavior was studied under concurrent nonindependent fixed‐ratio fixed‐ratio (nFR) schedules of reinforcement, as these schedules result in frequent changeover responses. With these schedules, responses on either operandum count toward the completion of the ratio requirements of both schedules. Five monkeys were subjects, and two pairs of liquid reinforcers were concurrently available: 16% (w/v) and 0% ethanol or 16% and 8% ethanol. For each pair of reinforcers, the nFR sizes were systematically altered across sessions while keeping the schedule size equal for both liquids. Responding varied as a function of reinforcer pair and nFR size. With the 16% and 0% pair, higher response rates were maintained by 16% and were an inverted U‐shape function of nFR size. With 16% and 8%, a greater number of responses initially occurred on the schedule that delivered 8% ethanol. However, as nFR size increased, preference reversed such that responses that delivered 16% ethanol were greater. When the nFR size was subsequently decreased, preference reverted back to 8%. Number of responses emitted per delivery was a dependent variable and, in behavioral economic terms, was the price paid for each liquid delivery. With 16% and 0%, changeover responses initially increased and then decreased as schedule size became larger. In contrast, with the 16% and 8% pair, changeover responses increased directly with schedule size. Responding under nFR schedules is sensitive to differences in reinforcer magnitude and demonstrates that relative reinforcing effects can change as a function of schedule size.     

Preratio pausing: effects of an alternative reinforcer on fixed- and variable-ratio responding

Seven rats responding under fixed-ratio or variable-ratio schedules of food reinforcement had continuous access to a drinking tube inserted into the operant chamber. Under different conditions they could drink either tap water or one of two saccharin solutions. In a baseline condition, the drinking bottle was empty. Preratio pausing was observed with both schedules, more so with the fixed-ratio than the variable-ratio schedule, and increasing the concentration of the saccharin solution increased the duration of pausing. Comparisons with baseline performances revealed that the additional pausing was largely, but not entirely, spent drinking. The results support the view that pausing under ratio schedules is a consequence of competition between the scheduled reinforcer and alternative reinforcers that also are available within the experimental environment.     

Steady-state performance on fixed-, mixed-, and random-ratio schedules

Three groups of rats pressed a lever for milk reinforcers on various simple reinforcement schedules (one schedule per condition). In Group M, each pair of conditions included a mixed-ratio schedule and a fixed-ratio schedule with equal average response:reinforcer ratios. On mixed-ratio schedules, reinforcement occurred with equal probability after a small or a large response requirement was met. In Group R, fixed-ratio and random-ratio schedules were compared in each pair of conditions. For all subjects in these two groups, the frequency distributions of interresponse times of less than one second were very similar on all ratio schedules, exhibiting a peak at about .2 seconds. For comparison, subjects in Group V responded on variable-interval schedules, and few interresponse times as short as .2 seconds were recorded. The results suggest that the rate of continuous responding is the same on all ratio schedules, and what varies among ratio schedules is the frequency, location, and duration of pauses. Preratio pauses were longer on fixed-ratio schedules than on mixed-ratio or random-ratio schedules, but there was more within-ratio pausing on mixed-ratio and random-ratio schedules. Across a single trial, the probability of an interruption in responding decreased on fixed-ratio schedules, was roughly constant on random-ratio schedules, and often increased and then decreased on mixed-ratio schedules. These response patterns provided partial support for Mazur's (1982) theory that the probability of instrumental responding is directly related to the probability of reinforcement and the proximity of reinforcement.     

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.     

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.     

Effects of instructions and reinforcement-feedback on human operant behavior maintained by fixed-interval reinforcement

In three experiments, human subjects were trained on a five-component multiple schedule with different fixed intervals of monetary reinforcement scheduled in the different components. Subjects uninstructed about the fixed-interval schedules manifested high and generally equivalent rates regardless of the particular component. By comparison, subjects given instructions about the schedules showed orderly progressions of rates and temporal patterning as a function of the interreinforcement intervals, particularly when feedback about reinforcement was delivered but also when reinforcement-feedback was withheld. Administration of the instructions-reinforcement combination to subjects who had already developed poorly differentiated behavior, however, did not make their behavior substantially better differentiated. When cost was imposed for responding, both instructed and uninstructed subjects showed low and differentiated rates regardless of their prior histories. It was concluded that instructions can have major influences on the establishment and maintenance of human operant behavior.     

Second-order schedules of token reinforcement with pigeons: effects of fixed- and variable-ratio exchange schedules

Pigeons' key pecks produced food under second-order schedules of token reinforcement, with light-emitting diodes serving as token reinforcers. In Experiment 1, tokens were earned according to a fixed-ratio 50 schedule and were exchanged for food according to either fixed-ratio or variable-ratio exchange schedules, with schedule type varied across conditions. In Experiment 2, schedule type was varied within sessions using a multiple schedule. In one component, tokens were earned according to a fixed-ratio 50 schedule and exchanged according to a variable-ratio schedule. In the other component, tokens were earned according to a variable-ratio 50 schedule and exchanged according to a fixed-ratio schedule. In both experiments, the number of responses per exchange was varied parametrically across conditions, ranging from 50 to 400 responses. Response rates decreased systematically with increases in the fixed-ratio exchange schedules, but were much less affected by changes in the variable-ratio exchange schedules. Response rates were consistently higher under variable-ratio exchange schedules than tinder comparable fixed-ratio exchange schedules, especially at higher exchange ratios. These response-rate differences were due both to greater pre-ratio pausing and to lower local rates tinder the fixed-ratio exchange schedules. Local response rates increased with proximity to food under the higher fixed-ratio exchange schedules, indicative of discriminative control by the tokens.     

Choice for periodic schedules of reinforcement

Pigeons' responses in the presence of two concurrently available (initial-link) stimuli produced one of two different (terminal-link) stimuli according to identical but independent variable-interval schedules. Responding in the mutually exclusive terminal links was reinforced with food according to fixed-ratio schedules for six pigeons and according to fixed-interval schedules for two pigeons. None of the pigeons matched the proportion of (choice) responses in the initial links to the proportion of the rates of reinforcement obtained during the terminal links. Instead, as the values of each of the terminal-link schedules were increased by a constant amount, the choice proportions for the stimulus associated with the smaller of the two values increased, even though the relative rates of reinforcement during the terminal links decreased. These results are incompatible with those from previous studies with aperiodic (variable-interval or variable-ratio) schedules. The present results do suggest, however, that in transforming aperiodic schedules into their periodic equivalents, it may be necessary to consider the size of the smallest interreinforcement interval comprising the terminal-link schedules.     

Pentobarbital and d-amphetamine effects on concurrent performances.

The effects of pentobarbital and d-amphetamine were studied in pigeons responding under several concurrent fixed-ratio variable-interval and concurrent fixed-ratio fixed-interval schedules of food presentation. Drug effects were compared with different fixed ratios, fixed and variable intervals, changeover delays, and with the schedules operating singly. Doses of d-amphetamine that increased or did not affect responding under the interval schedules decreased responding under the fixed-ratio schedule, whereas doses of pentobarbital that increased responding under the fixed-ratio schedule decreased or eliminated responding under the interval schedules. These effects depended both on the schedule of food delivery and the parameters of schedules arranged concurrently. Pentobarbital increased responding under the fixed-ratio schedule with 4-minute and 10-minute interval schedules arranged concurrently, but not with 1.5-minute schedules. d-Amphetamine decreased concurrent ratio and interval responding with the 1.5-minute interval schedules, but either increased or did not affect responding with the longer intervals. Changes in the parameter of one schedule altered responding controlled by that schedule and also other concurrent performances. As a consequence, the effects of drugs on each behavior were altered.     

Instructions, multiple schedules, and extinction: Distinguishing rule-governed from schedule-controlled behavior

Schedule sensitivity has usually been examined either through a multiple schedule or through changes in schedules after steady-state responding has been established. This study compared the effects of these two procedures when various instructions were given. Fifty-five college students responded in two 32-min sessions under a multiple fixed-ratio 18/differential-reinforcement-of-low-rate 6-s schedule, followed by one session of extinction. Some subjects received no instructions regarding the appropriate rates of responding, whereas others received instructions to respond slowly, rapidly, or both. Relative to the schedule in operation, the instructions were minimal, partially inaccurate, or accurate. When there was little schedule sensitivity in the multiple schedule, there was little in extinction. When apparently schedule-sensitive responding occurred in the multiple schedule, however, sensitivity in extinction occurred only if differential responding in the multiple schedule could not be due to rules supplied by the experimenter. This evidence shows that rule-governed behavior that occurs in the form of schedule-sensitive behavior may not in fact become schedule-sensitive even though it makes contact with the scheduled reinforcers.