Concurrent schedules: a quantitative relation between changeover behavior and its consequences

Data from several published experiments on concurrent variable-interval schedules were analyzed with respect to the effects of changeover delay on the time spent responding on a schedule before changing to an alternate schedule: i.e., the interchangeover time. Interchangeover time increases as the duration of the changeover delay increases, and the present analysis shows that a power function describes the relation. The power relation applied in spite of numerous differences in the experiments: different variable-interval schedules for the concurrent pairs; equal or unequal reinforcement rates for the schedules of the concurrent pairs; different durations of the changeover delay; response-dependent or response-independent reinforcers; pigeons or rats as subjects; different reinforcers. A power function also described the data in experiments where the changeover incurred a timeout, where a fixed ratio was required to changeover, and also when asymmetrical changeover delays were used.     

Control rate of response or reinforcement and amphetamine's effect on behavior.

The roles of control response rate and reinforcement frequency in producing amphetamine's effect on operant behavior were evaluated independently in rats. Two multiple schedules were arranged in which one variable, either response rate or reinforcement frequency, was held constant and the other variable manipulated. A multiple differential-reinforcement-of-low-rate seven-second yoked variable-interval schedule was used to equate reinforcement frequencies at different control response rates between multiple-schedule components. Amphetamine increased responding under the variable-interval component. In contrast, amphetamine decreased responding equivalently between components of a multiple random-ratio schedule that produced similar control response rates at different reinforcement frequencies. The results provide experimental support to the rate-dependency principle that control rate of responding is an important determinant of amphetamine's effect on operant behavior.     

Stimulus Equivalence: Effects Of A Default-response Option On Emergence Of Untrained Stimulus Relations

Human subjects were exposed to a concurrent-chains schedule in which reinforcer amounts, delays, or both were varied in the terminal links, and consummatory responses were required to receive points that were later exchangeable for money. Two independent variable-interval 30-s schedules were in effect during the initial links, and delay periods were defined by fixed-time schedules. In Experiment 1, subjects were exposed to three different pairs of reinforcer amounts and delays, and sensitivity to reinforcer amount and delay was determined based on the generalized matching law. The relative responding (choice) of most subjects was more sensitive to reinforcer amount than to reinforcer delay. In Experiment 2, subjects chose between immediate smaller reinforcers and delayed larger reinforcers in five conditions with and without timeout periods that followed a shorter delay, in which reinforcer amounts and delays were combined to make different predictions based on local reinforcement density (i.e., points per delay) or overall reinforcement density (i.e., points per total time). In most conditions, subjects' choices were qualitatively in accord with the predictions from the overall reinforcement density calculated by the ratio of reinforcer amount and total time. Therefore, the overall reinforcement density appears to influence the preference of humans in the present self-control choice situation.     

Unsignaled delay of reinforcement, relative time, and resistance to change

Two experiments with pigeons examined the effects of unsignaled, nonresetting delays of reinforcement on responding maintained by different reinforcement rates. In Experiment 1, 3-s unsignaled delays were introduced into each component of a multiple variable-interval (VI) 15-s VI 90-s VI 540-s schedule. When considered as a proportion of the preceding immediate reinforcement baseline, responding was decreased similarly for the three multiple-schedule components in both the first six and last six sessions of exposure to the delay. In addition, the relation between response rates and reinforcement rates was altered such that both parameters of the single-response version of the matching law (i.e., k and Re) were decreased. Experiment 2 examined the effects of unsignaled delays ranging from 0.5 s to 8.0 s on responding maintained by a multiple VI 20-s VI 120-s schedule of reinforcement. Response rates in both components increased with brief unsignaled delays and decreased with longer delays. As in Experiment 1, response rates as a proportion of baseline were affected similarly for the two components in both the first six and last six sessions of exposure to the delay. Unlike delays imposed between two stimulus events, the effects of delays between responses and reinforcers do not appear to be attenuated when the average time between reinforcers is longer. In addition, the disruptions produced by unsignaled delays appear to be inconsistent with the general finding that responding maintained by higher rates of reinforcement is less resistant to change.     

Using progressive ratio schedules to evaluate tokens as generalized conditioned reinforcers

The properties of operant reinforcers are dynamic and dependent on a number of variables, such as schedule and effort. There has been sparse research on the generalized conditioned properties of token reinforcement. We evaluated leisure items, edible items, and tokens using a progressive ratio schedule with three children with diagnoses of ASD and developmental delays. The highest break points occurred during the token reinforcement condition for two out of three participants, but response rates tended to be higher with edibles. We then evaluated the effects of presession access to edibles on the break points of edible items and tokens with two participants. Break points decreased only in the edible reinforcement condition, and the participants chose to work for leisure items rather than edibles when presession access to edibles was in place. These findings suggest that the tokens functioned as generalized conditioned reinforcers.     

An invariant relation between changing over and reinforcement

Although concurrent schedules may arrange reinforcers irregularly, relatively large numbers of reinforcers are obtained when an animal changes from one schedule to the other. This paper proposes a quantitative relation that predicts the proportion of reinforcers obtained when an animal is working on a schedule and the proportion when the animal changes over to a schedule. Basically the relation states that the number of reinforcers obtained while an animal works on a schedule varies directly with the relative amount of time spent working on that schedule; and the number of reinforcers obtained when an animal changes to a schedule varies directly with the relative amount of time spent on the alternate schedule. An important aspect of this relation is that when relative reinforcement rates are less than .50, more reinforcers are obtained just after an animal changes to a schedule than at all other times when this schedule is engaged. Data obtained both from a stat-bird and a live pigeon were in close agreement with the quantitative predictions. The relation between changing over and reinforcement held across several procedural changes that included changes in relative reinforcement rate, changes from independent to interdependent scheduling procedures, and changes in the variable-interval reinforcement distributions. The results are discussed in terms of the effects of the local distribution of reinforcement on responding. The local reinforcement distribution can affect local response rates and affects the resulting matching relation. This arrangement has implications for explanations of choice.     

Choice between single and multiple delayed reinforcers.

Pigeons chose between alternatives that differed in the number of reinforcers and in the delay to each reinforcer. A peck on a red key produced the same consequences on every trial within a condition, but between conditions the number of reinforcers varied from one to three and the reinforcer delays varied between 5 s and 30 s. A peck on a green key produced a delay of adjustable duration and then a single reinforcer. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices, which permitted estimation of an indifference point, or a delay at which a subject chose each alternative about equally often. The indifference points decreased systematically with more red-key reinforcers and with shorter red-key delays. The results did not support the suggestion of Moore (1979) that multiple delayed reinforcers have no effect on preference unless they are closely grouped. The results were well described in quantitative detail by a simple model stating that each of a series of reinforcers increases preference, but that a reinforcer's effect is inversely related to its delay. The success of this model, which considers only delay of reinforcement, suggested that the overall rate of reinforcement for each alternative had no effect on choice between those alternatives.     

Operant and nonoperant vocal responding in the mynah: Complex schedule control and deprivation-induced responding

Several recent studies have been concerned with operant responses that are also affected by nonoperant factors, (e.g., biological constraints, innate behavior patterns, respondent processes). The major reason for studying mynah vocal responding concerned the special relation of avian vocalizations to nonoperant emotional and reflexive systems. The research strategy was to evaluate operant and nonoperant control by comparing the schedule control obtained with the vocal response to that characteristic of the motor responses of other animals. We selected single, multiple, and chain schedules that ordinarily produce disparate response rates at predictable times. In multiple schedules with one component where vocal responding (“Awk”) was reinforced with food (fixed-ratio or fixed-interval schedule) and one where the absence of vocal responding was reinforced (differential reinforcement of other behavior), response rates never exceeded 15 responses per minute, but clear schedule differences developed in response rate and pause time. Nonoperant vocal responding was evident when responding endured across 50 extinction sessions at 25% to 40% of the rate during reinforcement. The “enduring extinction responding” was largely deprivation induced, because the operant-level of naive mynahs under food deprivation was comparable in magnitude, but without deprivation the operant level was much lower. Food deprivation can induce vocal responding, but the relatively precise schedule control indicated that operant contingencies predominate when they are introduced.     

The measurement and reinforcement of behavior of psychotics

An attempt was made to strengthen behaviors of psychotics by applying operant reinforcement principles in a mental hospital ward. The behaviors studied were necessary and/or useful for the patient to function in the hospital environment. Reinforcement consisted of the opportunity to engage in activities that had a high level of occurrence when freely allowed. Tokens were used as conditioned reinforcers to bridge the delay between behavior and reinforcement. Emphasis was placed on objective definition and quantification of the responses and reinforcers and upon programming and recording procedures. Standardizing the objective criteria permitted ward attendants to administer the program. The procedures were found to be effective in maintaining the desired adaptive behaviors for as long as the procedures were in effect. In a series of six experiments, reinforced behaviors were considerably reduced when the reinforcement procedure was discontinued; the adaptive behaviors increased immediately when the reinforcement procedure was re-introduced.     

Reinforcement contingencies and signal detection.

Pigeons were trained to discriminate temporal stimuli in a discrete-trial signal-detection procedure. Pecks to one side key were reinforced intermittently after exposure to one duration, and pecks to the other side key were reinforced intermittently after exposure to a different duration. In Experiment I, the allocation of reinforcers was varied systematically for correct responses and for errors, using a procedure that controlled the obtained numbers of reinforcers. When reinforcers were allocated symmetrically, the level of discrimination decreased as the proportion of reinforcers for errors increased. When reinforcers were allocated asymmetrically, the decrease in discrimination was less systematic. Bias toward one or the other side key roughly matched the ratio of reinforcers obtained by pecks at those keys, independent of the level of discrimination. In Experiment II, the overall rate of reinforcement for correct responses was varied both within and between experimental conditions. The level of discrimination was positively related to the overall rate of reinforcement. The discrimination data of both experiments were interpreted in relation to the contingencies of reinforcement and nonreinforcement, characterized by the average difference in reinforcement probability for correct responses and errors.     

IMPULSIVITY IN STUDENTS WITH SERIOUS EMOTIONAL DISTURBANCE: THE INTERACTIVE EFFECTS OF REINFORCER RATE,DELAY, AND QUALITY

We conducted two studies extending basic matching research on self-control and impulsivity to the investigation of choices of students diagnosed as seriously emotionally disturbed. In Study 1 we examined the interaction between unequal rates of reinforcement and equal versus unequal delays to reinforcer access on performance of concurrently available sets of math problems. The results of a reversal design showed that when delays to reinforcer access were the same for both response alternatives, the time allocated to each was approximately proportional to obtained reinforcement. When the delays to reinforcer access differed between the response alternatives, there was a bias toward the response alternative and schedule with the lower delays, suggesting impulsivity (i.e., immediate reinforcer access overrode the effects of rate of reinforcement). In Study 2 we examined the interactive effects of reinforcer rate, quality, and delay. Conditions involving delayed access to the high-quality reinforcers on the rich schedule (with immediate access to low-quality reinforcers earned on the lean schedule) were alternated with immediate access to low-quality reinforcers on the rich schedule (with delayed access to high-quality reinforcers on the lean schedule) using a reversal design. With 1 student, reinforcer quality overrode the effects of both reinforcer rate and delay to reinforcer access. The other student tended to respond exclusively to the alternative associated with immediate access to reinforcers. The studies demonstrate a methodology based on matching theory for determining influential dimensions of reinforcers governing individuals' choices.     

Theories of probabilistic reinforcement.

In three experiments, pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck at a red key led to a delay of 5 s and then a possible reinforcer. A peck at a green key led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials so as to estimate an indifference point, or a duration at which the two alternatives were chosen about equally often. In Experiments 1 and 2, the intertrial interval was varied across conditions, and these variations had no systematic effects on choice. In Experiment 3, the stimuli that followed a choice of the red key differed across conditions. In some conditions, a red houselight was presented for 5 s after each choice of the red key. In other conditions, the red houselight was present on reinforced trials but not on nonreinforced trials. Subjects exhibited greater preference for the red key in the latter case. The results were used to evaluate four different theories of probabilistic reinforcement. The results were most consistent with the view that the value or effectiveness of a probabilistic reinforcer is determined by the total time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. According to this view, probabilistic reinforcers are analogous to reinforcers that are delivered after variable delays.     

Matching, contrast, and equalizing in the concurrent lever-press responding of rats

Five rats pressed levers for food reinforces delivered by several concurrent variable-interval variable-interval schedules. The rate of reinforcement available for responding on one component schedule was held constant at 60 reinforcers per hour. The rate of reinforcement available for responding on the other schedule varied from 30 to 240 reinforcers per hour. The behavior of the rats resembled the behavior of pigeons pecking keys for food reinforcers. The ratio of the overall rates of responding emitted under, and the ratio of the time spent responding under, the two components of each concurrent schedule were approximately equal to the ratio of the overall rates of reinforcement obtained from the components. The overall rate of responding emitted under, and the time spent responding under, the variable component schedule varied directly with the overall rate of reinforcement from that schedule. The overall rate of responding emitted under, and the time spent responding under, the constant component schedule varied inversely with the overall rate of reinforcement obtained from the variable component. The local rates of responding emitted under, and the local rates of reinforcement obtained from, the two components did not differ consistently across subjects. But they were not exactly equal either.     

Self-stimulatory behavior and perceptual reinforcement.

Self-stimulatory behavior is repetitive, stereotyped, functionally autonomous behavior seen in both normal and developmentally disabled populations, yet no satisfactory theory of its development and major characteristics has previously been offered. We present here a detailed hypothesis of the acquisition and maintenance of self-stimulatory behavior, proposing that the behaviors are operant responses whose reinforcers are automatically produced interoceptive and exteroceptive perceptual consequences. The concept of perceptual stimuli and reinforcers, the durability of self-stimulatory behaviors, the sensory extinction effect, the inverse relationship between self-stimulatory and other behaviors, the blocking effect of self-stimulatory behavior on new learning, and response substitution effects are discussed in terms of the hypothesis. Support for the hypothesis from the areas of sensory reinforcement and sensory deprivation is also reviewed. Limitations of major alternative theories are discussed, along with implications of the perceptual reinforcement hypothesis for the treatment of excessive self-stimulatory behavior and for theoretical conceptualizations of functionally related normal and pathological behaviors.     

A CLASSIFICATION SCHEME OF SOCIAL CONDITIONS OF REINFORCEMENT WITHIN GROUP OPERANT SYSTEMS1

Many different reinforcement contingencies are found in group operant systems, such as token economies and point systems. Some systems use group contingencies in which the reinforcement of any one participant may depend on the behavior of some other group member. Other programs are individual, in that participants earn reinforcers dependent only on their own behavior. The various possible arrangements of people and their response requirements are labelled “social conditions of reinforcement” in this paper. Previous attempts at classification have failed to categorize the variety of social conditions of reinforcement. In addition, some conditions that may produce behaviorally different effects have not been separated. The present paper classifies the social conditions of reinforcement found in applied programs in a three-dimensional scheme. The efficacy of the three major dimensions—reinforcing agent, recipient response requirement, and group response requirement—is supported by clinical and research data. The reinforcing agent dimension refers to the person(s) who dispenses reinforcers to group members. This major dimension is further subdivided: one or several agents may be either designated or nondesignated. Recipients are the group members who receive reinforcement. This dimension is also subdivided: one or several recipients in a social condition of reinforcement may obtain reinforcers either contingently or noncontingently. The group response requirement is a criterion that must be satisfied before any group participant is eligible for reinforcement. Some systems have no group requirement, and others have a group requirement that must be met by some designated or nondesignated participant(s). Supportive references and examples are given in the explanation of each dimension and subdimension. The behavioral impact of the various categories is emphasized. For all major dimensions, applied implications and research suggestions are discussed. Concluding remarks center on the utility of the present scheme, the classification of operant procedures other than positive reinforcement, and both theoretical and applied issues requiring further study (e.g., the long-term effects of participation in group contingencies).     

On the functions of the changeover delay

The function of changeover delays in producing matching was examined with pigeons responding on concurrent variable-interval variable-interval schedules. In Experiment 1, no changeover delay was compared to two different types of changeover delay. One type, designated generically as response-response but in the present example as peck-peck, was timed from the first response on the switched-to key; the other, designated generically as pause-response but in the present example as pause-peck, was timed from the last response on the switched-from key. High changeover rates occurred with no changeover delay. Peck-peck and pause-peck changeover delays produced low and intermediate changeover rates, respectively. In Experiment 2, pause-peck and peck-peck changeover delays were compared across a range of relative reinforcement rates. Similar matching relations developed despite differences in the changeover rates and local response patterns as a function of the type of changeover delay. In Experiment 3, both types of changeover delay yielded similar changeover rates when their obtained durations were equal via yoking. The results suggest that changeover delays function to separate responses on one key from reinforcers on the other or to delay reinforcement for changing over. In addition, the distribution of responding during and after the changeover delay may vary considerably without affecting matching.     

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.     

A comparison of signaled and unsignaled delay of reinforcement

Pigeons were trained on either a variable-interval 60-second schedule, or on a schedule that differentially reinforced responses that were spaced at least 20 seconds apart. The birds were then exposed to several durations of reinforcement delay, with comparisons between signaled and unsignaled delays. Although unsignaled delays of 5 and 10 seconds produced large decreases in response rate, signaled delays of up to 10 seconds produced only moderate decreases in response rates. In addition, some subjects responded more rapidly with a .5 or 1.0 second duration of unsignaled delay than with immediate reinforcement. These response rate changes occurred regardless of whether the rate of reinforcement concomitantly decreased or increased.     

Choice and number of reinforcers

Pigeons were exposed to the concurrent-chains procedure in two experiments designed to investigate the effects of unequal numbers of reinforcers on choice. In Experiment 1, the pigeons were indifferent between long and short durations of access to variable-interval schedules of equal reinforcement density, but preferred a short high-density terminal link over a longer, lower density terminal link, even though in both sets of comparisons there were many more reinforcers per cycle in the longer terminal link. In Experiment 2, the pigeons preferred five reinforcers, the first of which was available after 30 sec, over a single reinforcer available at 30 sec, but only when the local interval between successive reinforcers was short. The pigeons were indifferent when this local interval was sufficiently long. The pigeons' behavior appeared to be under the control of local terminal-link variables, such as the intervals to the first reinforcer and between successive reinforcers, and was not well described in terms of transformed delays of reinforcement or reductions in average delay to reinforcement.