Conjunctive schedules of reinforcement: III. A fixed-interval adjusting fixed-ratio schedule

Key pecking of three pigeons was studied under a conjunctive schedule that specified both a fixed-interval and an adjusting fixed-ratio requirement. The fixed-interval schedule was 6 min for one pigeon and 3 min for the other two. The size of the ratio requirement was determined within each cycle of the fixed interval by the duration of the pause before responding began. The fixed-ratio value was at maximum at the start of each fixed interval and decreased linearly until the first response occurred (adjusting fixed-ratio schedule). A peck produced food when the number of responses remaining on the fixed-ratio schedule was completed and when the fixed interval had elapsed. If no response occurred during the interval, the fixed-ratio requirement decreased to one and a single response after the interval elapsed produced food. The initial value of the adjusting fixed-ratio schedule was studied over a range of 0 to 900. Increases in the adjusting fixed-ratio schedule to about 300 responses increased both pause duration and running response rate and also modified the pattern of responding from that obtained under the fixed-interval schedule. Higher values of the adjusting fixed ratio generally decreased pause duration and running response rate and also disrupted responding. Interreinforcement time under the conjunctive schedule was increased substantially when the adjusting fixed-ratio size exceeded 300 responses.     

Response persistence under ratio and interval reinforcement schedules

In Experiment 1, rats were exposed to progressive-ratio schedules of food reinforcement while other rats were exposed simultaneously to yoked-interval schedules that arranged equivalent interreinforcer intervals but required only a single response at the end of the interval for food delivery. In Experiment 2, a within-subject yoked-control procedure was employed in which pigeons were exposed to alternating sessions (one per day) of progressive-ratio schedules and yoked-interval schedules as described above. In both experiments, responding under the yoked-interval schedule persisted beyond the point at which responding under the progressive-ratio schedule had ceased. The progressive-ratio schedules controlled break-and-run distributions, and the yoked-interval schedules controlled more even distributions of responses in time. Response rates decreased and postreinforcement pauses increased over time within individual sessions under both schedules. The results suggest that responding maintained by interval schedules is more persistent than that maintained by ratio schedules. The limitations and implications of this conclusion are discussed in the context of other investigations of response strength and behavioral momentum.     

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.     

Signalled reinforcement and multiple schedules

The responses of four pigeons were first reinforced in the presence of two different wave-lengths (green and red) on a two-ply multiple schedule with identical variable-interval 3-min schedules of reinforcement associated with each component. While the constant-component reinforcement schedule remained unchanged during the experiment, the schedule associated with the variable component was changed to (1) signalled variable time, (2) unsignalled variable time, or (3) signalled variable interval. The probability with which the availability of the reinforcer was signalled in the variable-interval schedules was either 0.5 or 1.0. Positive contrast occurred in both signalled variable-interval and variable-time schedules, but only when the availability of all the variable-component reinforcers was signalled. Signalling the availability of only 50% of the reinforcers in signalled variable-interval schedules resulted in negative induction. The present data suggest that positive behavioral contrast resulting from signalled reinforcer availability is due to the presence of an extinction-correlated stimulus.     

Selective punishment early and late in fixed-ratio schedules of food reinforcement

Pigeons key pecked for grain on a fixed-ratio 100 schedule; electric shocks occurred intermittently at the fifteenth or eighty-fifth response in the ratio. In Experiment I, shock was at the fifteenth response for two birds, and at the eighty-fifth response for two others, in every sixth, twelfth, or eighteenth ratio. Rate of responding decreased as frequency of shock increased, and the pattern of responding included an increased initial pause and low rates or pause-run sequences that extended further into the ratio when shock was at the fifteenth response than when it was at the eighty-fifth response. Shock early in the ratio engendered longer initial pauses than shock late in the ratio. In Experiment II, four birds responded on a two-component multiple schedule in which shock occurred at the fifteenth response of the third ratio in the presence of a white keylight and at the eighty-fifth response of the third ratio in the presence of a green keylight. The overall rates of responding decreased as shock intensity increased. All four birds responded differentially to the white and green keylights, but with a pattern that varied between birds. In general, punishment reduced the probability of responses that preceded it, regardless of the ordinal position of those responses. Both studies confirm that the probability of responding is reduced less by aversive stimuli produced late in a fixed-ratio than by aversive stimuli produced early in a fixed-ratio.     

Determinants of pigeons' waiting time: Effects of interreinforcement interval and food delay

Four pigeons performed on three types of schedules at short (i.e., 10, 30, or 60 s) interreinforcement intervals: (a) a delay-dependent schedule where interreinforcement interval was held constant (i.e., increases in waiting time decreased food delay), (b) an interreinforcement-interval-dependent schedule where food delay was held constant (i.e., increases in waiting time increased interreinforcement interval), and (c) a both-dependent schedule where increases in waiting time produced increases in interreinforcement interval but decreases in food delay. Waiting times were typically longer under the delay-dependent schedules than under the interreinforcement-interval-dependent schedules. Those under both-dependent schedules for 1 subject were intermediate between those under the other two schedule types, whereas for the other subjects waiting times under the both-dependent procedure were similar either to those under the delay-dependent schedule or to those under the interreinforcement-interval-dependent schedule, depending both on the subject and the interreinforcement interval. These results indicate that neither the interreinforcement interval nor food delay is the primary variable controlling waiting time, but rather that the two interact in a complex manner to determine waiting times.     

Choice performance in several concurrent key-peck treadle-press reinforcement schedules

Five pigeons were exposed to several concurrent variable-interval food reinforcement schedules. For three subjects, one component of the schedule required a key-pecking response, the other a treadle-pressing response. For the other two subjects, both schedule components required treadle-pressing responses. The relative probability of reinforcement associated with the manipulanda was varied from 0 to 1.0 in 13 experimental conditions for the Key-Treadle subjects and nine conditions for the Treadle-Treadle subjects. The results indicated that the logarithms of relative time spent responding, and the logarithms of relative number of responses emitted on a manipulandum, approximated direct linear functions of logarithms of the relative frequencies of reinforcement associated with that manipulandum. No systematic bias in favor of time spent key pecking over time spent treadle pressing was apparent for the Key-Treadle subjects. All subjects exhibited undermatching, in that the ratios of time and response allocation at the alternatives systematically differed from the ratios of reinforcers obtained from the alternatives in the direction of indifference. Key pecking appeared to have no special link to food beyond treadle pressing or what would be expected on the basis of the reinforcement dependencies alone.     

Determinants of pausing under variable-ratio schedules: Reinforcer magnitude, ratio size, and schedule configuration

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Phase 1 assessed the effects of differences in reinforcer magnitude on postreinforcement pausing, as a function of ratio size. In Phase 2, postreinforcement pausing and the first five interresponse times in each ratio were measured as a function of differences in reinforcer magnitude under equal variable-ratio schedules consisting of different configurations of individual ratios. Rates were also calculated exclusive of postreinforcement pause times in both phases. The results from Phase 1 showed that as ratio size increased, the differences in pausing educed by unequal reinforcer magnitudes also increased. The results of Phase 2 showed that the effects of reinforcer magnitude on pausing and IRT durations were a function of schedule configuration. Under one configuration, in which the smallest ratio was a fixed-ratio 1, pauses were unaffected by magnitude but the first five interresponse times were affected. Under the other configuration, in which the smallest ratio was a fixed-ratio 7, pauses were affected by reinforcer magnitude but the first five interresponse times were not. The effect of each configuration seemed to be determined by the value of the smallest individual ratio. Rates calculated exclusive of postreinforcement pause times were, in general, directly related to reinforcer magnitude, and the relation was shown to be a function of schedule configuration.     

Contrast and induction in multiple schedules of discrete-trial concurrent reinforcement

Three pigeons were exposed to two-key discrete-trial concurrent schedules of reinforcement. Red and white key colors alternated irregularly and the assignment of reinforcers depended on key color. The red-key schedules were held constant, with the scheduled relative frequency of reinforcement for left-key pecks set at 0.75, while the white-key schedules varied. When the location of white-key reinforcement was changed from one side to the other, while its overall frequency was constant, red-key choices shifted in the same direction as white-key choices, an induction effect. When the overall frequency of white-key reinforcement was changed while its location remained constant, red key choices shifted in a direction opposite to white-key choices, a contrast effect. Both induction and contrast effects were clearer when the overall frequency of red-key reinforcement was reduced. These data demonstrate that the allocation of responding may exhibit schedule interaction effects similar to those commonly reported for response rate.     

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.     

A molar theory of reinforcement schedules

Behavior of subjects exposed to concurrent and individual interval and ratio schedules of reinforcement may be described in terms of a set of expressions relating the value of responses to their durations, a feedback equation relating reinforcement to response duration, and the assumption that subjects allocate their time among various responses so as to maximize value.     

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 dynamics in concurrent ratio schedules of reinforcement

The generalized matching law predicts performance on concurrent schedules when variable-interval schedules are programmed but is trivially applicable when independent ratio schedules are used. Responding usually is exclusive to the schedule with the lowest response requirement. Determining a method to program concurrent ratio schedules such that matching analyses can be usefully employed would extend the generality of matching research and lead to new avenues of research. In the present experiments, ratio schedules were programmed dependently such that responses to either of the two options progressed the requirement on both schedules. Responding is not exclusive because the probability of reinforcement increases on both schedules as responses are allocated to either schedule. In Experiment 1, performance on concurrent variable-ratio schedules was assessed, and reinforcer ratios were varied across conditions to investigate changes in sensitivity. Additionally, the length of a changeover delay was manipulated. In Experiment 2, performance was compared under concurrently available, dependently programmed variable-ratio and fixed-ratio schedules. Performance was well described by the generalized matching law. Increases in the changeover delay decreased sensitivity, whereas sensitivity was higher when variable-ratio schedules were employed, compared with fixed-ratio schedules. Concurrent ratio schedules can be a viable approach to studying functional differences between ratio and interval schedules.     

Concurrent schedules: Effects of time- and response-allocation constraints

Five pigeons were trained on concurrent variable-interval schedules arranged on two keys. In Part 1 of the experiment, the subjects responded under no constraints, and the ratios of reinforcers obtainable were varied over five levels. In Part 2, the conditions of the experiment were changed such that the time spent responding on the left key before a subsequent changeover to the right key determined the minimum time that must be spent responding on the right key before a changeover to the left key could occur. When the left key provided a higher reinforcer rate than the right key, this procedure ensured that the time allocated to the two keys was approximately equal. The data showed that such a time-allocation constraint only marginally constrained response allocation. In Part 3, the numbers of responses emitted on the left key before a changeover to the right key determined the minimum number of responses that had to be emitted on the right key before a changeover to the left key could occur. This response constraint completely constrained time allocation. These data are consistent with the view that response allocation is a fundamental process (and time allocation a derivative process), or that response and time allocation are independently controlled, in concurrent-schedule performance.     

Short-component multiple schedules: effects of relative reinforcement duration

Pigeons were exposed to multiple variable-interval 2-min variable-interval 2-min schedules of food presentation in which relative duration of food presentation was manipulated. When components alternated every 5 sec and were scheduled on separate response keys, relative response rates closely matched relative reinforcement duration in three of four pigeons. On the other hand, relative response rates were insensitive to relative reinforcement duration when components scheduled on a single response key alternated every 5 sec, and when components scheduled on separate response keys alternated every 2 min. Thus, both rapid alternation and spatial separation of components were necessary to produce approximate matching of relative responding to relative reinforcement duration. This finding contrasts with previous findings that only rapid component alternation is necessary for matching when relative rate of reinforcement is manipulated.     

Concurrent second-order schedules of reinforcement

Responses on one key (the main key) of a two-key chamber produced food according to a second-order variable-interval schedule with fixed-interval schedule components. A response on a second key (the changeover key) alternated colors on the main key and provided a second independent second-order variable-interval schedule with fixed-interval components. The fixed-interval component on one variable-interval schedule was held constant at 8 sec, while the fixed interval on the other variable-interval schedule was varied from 0 to 32 sec. Under some conditions, a brief stimulus terminated each fixed interval and generated fixed-interval patterns; in other conditions, the brief stimulus was omitted. Relative response rate and relative time deviated substantially from scheduled relative reinforcement rate and, to a lesser extent, from obtained relative reinforcement rate under both brief-stimulus and no-stimulus conditions. Matching was observed with equal components on both schedules; with unequal components, increasingly greater proportions of time and responses than the matching relation would predict were spent on the variable-interval schedule containing the shorter component. Preference for the shorter fixed interval was typically more extreme under brief-stimulus than under no-stimulus schedules. The results limit the extension of the matching relation typically observed under simple concurrent variable-interval schedules to concurrent second-order variable-interval schedules.     

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.     

Preference for simple interval schedules of reinforcement in concurrent chains: Effects of segmentation ratio

A concurrent-chains procedure was used to examine pigeons' preferences between segmented and unsegmented terminal-link schedules of reinforcement. During the initial link, a pair of independent, concurrent variable-interval 60-s schedules was in effect. In the terminal link, reinforcement was provided by a chain fixed-interval fixed-interval schedule on one key and by a simple fixed-interval schedule with an equal interreinforcement interval in the other. The relative duration between the first and second components (segmentation ratio) in the terminal-link chained schedule was systematically varied while the terminal-link duration was kept constant at either 15 s or 30 s in two sets of conditions. With few exceptions, the simple schedule was preferred to the chained schedule. Furthermore, this preference was inversely related to the size of the segmentation ratio in the segmented schedule. When the segmentation ratio was smaller than 1:1, preference was more extreme for a 30-s condition than for a 15-s condition. However, preference decreased more rapidly in conditions with the longer terminal-link duration when the ratio increased. Taken together, these results were consistent with previous findings concerning the effect of the terminal-link duration on choice between segmented and unsegmented schedules. In addition, the data suggested that segmentation ratio in a segmented schedule constitutes another potent factor influencing preference for the unsegmented schedule.