Matching and maximizing with variable-time schedules.

Pigeons were offered choices between a variable-time schedule that arranged reinforcers throughout the session and a variable-time schedule that arranged reinforcers only when the pigeon was spending time on it. The subjects could maximize the overall rate of reinforcement in this situation by biasing their time allocation towards the latter schedule. This arrangement provides an alternative to concurrent variable-interval variable-ratio schedules for testing whether animals maximize overall rates or match relative rates, and has the advantage of being free of the asymmetrical response requirements present with those schedules. The results were contrary to those predicted by maximizing: The bias it predicts did not appear.     

Conditioned reinforcement and choice

In a series of three experiments, rats were exposed to successive schedule components arranged on two levers, in which lever pressing produced a light, and nose-key pressing produced water in 50% of the light periods. When one auditory signal was presented only during those light periods correlated with water on one lever, and a different signal was presented only during those light periods correlated with nonreinforcement on the other lever, the former lever was preferred in choice trials, and higher rates of responding were maintained on the former lever in nonchoice (forced) trials. Thus, the rats preferred a schedule component that included a conditioned reinforcer over one that did not, with the schedules of primary reinforcement and the information value of the signals equated. Preferences were maintained when one or the other of the auditory signals was deleted, but were not established in naive subjects when training began with either the positive or negative signal only. Discriminative control of nose-key pressing by the auditory signals was highly variable across subjects and was not correlated with choice.     

Reinforcement schedule thinning following treatment with functional communication training

We evaluated four methods for increasing the practicality of functional communication training (FCT) by decreasing the frequency of reinforcement for alternative behavior. Three participants whose problem behaviors were maintained by positive reinforcement were treated successfully with FCT in which reinforcement for alternative behavior was initially delivered on fixed-ratio (FR) 1 schedules. One participant was then exposed to increasing delays to reinforcement under FR 1, a graduated fixed-interval (FI) schedule, and a graduated multiple-schedule arrangement in which signaled periods of reinforcement and extinction were alternated. Results showed that (a) increasing delays resulted in extinction of the alternative behavior, (b) the FI schedule produced undesirably high rates of the alternative behavior, and (c) the multiple schedule resulted in moderate and stable levels of the alternative behavior as the duration of the extinction component was increased. The other 2 participants were exposed to graduated mixed-schedule (unsignaled alternation between reinforcement and extinction components) and multiple-schedule (signaled alternation between reinforcement and extinction components) arrangements in which the durations of the reinforcement and extinction components were modified. Results obtained for these 2 participants indicated that the use of discriminative stimuli in the multiple schedule facilitated reinforcement schedule thinning. Upon completion of treatment, problem behavior remained low (or at zero), whereas alternative behavior was maintained as well as differentiated during a multiple-schedule arrangement consisting of a 4-min extinction period followed by a 1-min reinforcement period.     

Multiple determinants of the effects of reinforcement magnitude on free-operant response rates

Four experiments examined the effects of increasing the number of food pellets given to hungry rats for a lever-press response. On a simple variable-interval 60-s schedule, increased number of pellets depressed response rates (Experiment 1). In Experiment 2, the decrease in response rate as a function of increased reinforcement magnitude was demonstrated on a variable-interval 30-s schedule, but enhanced rates of response were obtained with the same increase in reinforcement magnitude on a variable-ratio 30 schedule. In Experiment 3, higher rates of responding were maintained by the component of a concurrent variable-interval 60-s variable-interval 60-s schedule associated with a higher reinforcement magnitude. In Experiment 4, higher rates of response were produced in the component of a multiple variable-interval 60-s variable-interval 60-s schedule associated with the higher reinforcement magnitude. It is suggested that on simple schedules greater reinforcer magnitudes shape the reinforced pattern of responding more effectively than do smaller reinforcement magnitudes. This effect is, however, overridden by another process, such a contrast, when two magnitudes are presented within a single session on two-component schedules.     

Multiple and concurrent schedule performance: independence from concurrent and successive schedule contexts

Six pigeons were trained on multiple variable-interval schedules and performance was measured in the presence or absence of another variable-interval schedule (the common schedule) arranged concurrently with both components. Manipulations included varying the rate of reinforcement on the common schedule, leaving the common schedule unchanged while the components of the multiple schedule were varied, varying the multiple schedule components in the absence of the common schedule, and varying one component of the multiple schedule while the other component and the common schedule were unchanged. The normal rate-increasing and rate-decreasing effects of reinforcement rate increase were found, except that changing one multiple schedule component did not affect the response rate in the successively available common schedule component. Both concurrent and multiple schedule performance undermatched obtained reinforcement-rate ratios, but the degree of undermatching in multiple schedules was reliably greater. Allocation of responses between multiple schedule components was unaffected by the concurrent availability of reinforcement, and allocation of responses between concurrent schedules was unaffected by the successive availability of different reinforcement rates.     

Human performance on negative slope schedules of points exchangeable for money: a failure of molar maximization

Panel pressing was generated and maintained in 5 adult humans by schedules of points exchangeable for money. Following exposure to a variable-interval 30-s schedule and to a linear variable-interval 30-s schedule (which permitted points to accumulate in an unseen "store" in the absence of responding), subjects were exposed to a series of conditions with a point-subtraction contingency arranged conjointly with the linear variable-interval schedule. Specifically, points were added to the store according to the linear-variable interval 30-s schedule and were subtracted from the store according to a ratio schedule. Ratio value varied across conditions and was determined individually for each subject such that the subtraction contingency would result in an approximately 50% reduction in the rate of point delivery. Conditions that included the subtraction contingency were termed negative slope schedules because the feedback functions were negatively sloped across all response rates greater than the inverse of the variable-interval schedule, in this case, two per minute. Overall response rates varied inversely with the subtraction ratio, indicating sensitivity to the negative slope conditions, but were in excess of that required by accounts based on strict maximization of overall reinforcement rate. Performance was also not well described by a matching-based account. Detailed analyses of response patterning revealed a consistent two-state pattern in which bursts of high-rate responding alternated with periods of prolonged pausing, perhaps reflecting the joint influence of local and overall reinforcement rates.     

Interlocking schedules: the relationship between response and time requirements.

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

Conditioned reinforcement value and resistance to change

Three experiments examined the effects of conditioned reinforcement value and primary reinforcement rate on resistance to change using a multiple schedule of observing-response procedures with pigeons. In the absence of observing responses in both components, unsignaled periods of variable-interval (VI) schedule food reinforcement alternated with extinction. Observing responses in both components intermittently produced 15 s of a stimulus associated with the VI schedule (i.e., S+). In the first experiment, a lower-valued conditioned reinforcer and a higher rate of primary reinforcement were arranged in one component by adding response-independent food deliveries uncorrelated with S+. In the second experiment, one component arranged a lower valued conditioned reinforcer but a higher rate of primary reinforcement by increasing the probability of VI schedule periods relative to extinction periods. In the third experiment, the two observing-response components provided similar rates of primary reinforcement but arranged different valued conditioned reinforcers. Across the three experiments, observing-response rates were typically higher in the component associated with the higher valued conditioned reinforcer. Resistance to change was not affected by conditioned reinforcement value, but was an orderly function of the rate of primary reinforcement obtained in the two components. One interpretation of these results is that S+ value does not affect response strength and that S+ deliveries increase response rates through a mechanism other than reinforcement. Alternatively, because resistance to change depends on the discriminative stimulus-reinforcer relation, the failure of S+ value to impact resistance to change could have resulted from a lack of transfer of S+ value to the broader discriminative context.     

Alternative reinforcement effects on fixed-interval performance

Pigeons' key pecks were reinforced with food on a fixed-interval schedule. Food also was available at variable time periods either independently of responding or for not key pecking (a differential-reinforcement-of-other-behavior schedule). The latter condition arranged reinforcement following the first pause of t seconds after it became available according to a variable-time schedule. This schedule allowed separation of the effects of pause requirements ≤ five-seconds and reinforcement frequency. The time spent pausing increased as the duration of the pause required for reinforcement increased from 0 to 30 seconds and as the frequency of reinforcement for pausing increased from 0 to 2 reinforcers per minute. Key pecking was more evenly distributed within each fixed interval with shorter required pauses and with more frequent reinforcement for pausing. The results complement those obtained with other concurrent schedules in which the same operant response was reinforced in both components.     

The following schedule of reinforcement as a fundamental determinant of steady state contrast in multiple schedules

Two experiments investigated whether steady-state interactions in multiple schedules depend exclusively on the following schedule of reinforcement. Experiment 1 used a four-component multiple schedule in which two components were associated with the same constant schedule of reinforcement, and where rate of reinforcement was varied in the component that followed one of these. Contrast effects were reliable only in the component that preceded the point of reinforcement variation, although some contrast did occur otherwise. In those instances where contrast other than the following-schedule effect did occur, it was accounted for by the effect of the preceding schedule, an effect for which there were consistent individual differences among subjects, and which varied with component duration. Experiment 2 used a three-component schedule, in which reinforcement rate was varied in the middle component. The results were consistent with Experiment 1, as the following-schedule effect was the only consistent effect that occurred, although an effect of the preceding schedule did occur for some subjects under some conditions, and was especially evident early in training. The conclusion from both experiments is that there is no general effect of relative rate of reinforcement apart from the sum of the effects of the preceding and following schedules, and that the following-schedule effect is the fundamental cause of steady-state interactions.     

Behavior of humans in variable-interval schedules of reinforcement

During Phase I, human subjects pressed a button for monetary reinforcement in five variable-interval schedules, each of which specified a different frequency of reinforcement. The rate of responding was an increasing, negatively accelerated function of reinforcement frequency; the data conformed closely to Herrnstein's equation. During Phase II, the same five schedules were in operation, but in addition a concurrent variable-interval schedule (B) was introduced, responses on which were always reinforced at the same frequency. Response rate in component A increased while the response rate in B decreased, as a function of the reinforcement frequency in component A. Relative response rates in the two component schedules matched the relative frequencies of reinforcement. Comparing the absolute response rates in component A during Phase I and Phase II it was found that introduction of the concurrent schedule did not affect the value of the theoretical maximum response rate, but did increase the value of the reinforcement frequency needed to obtain any particular submaximal response rate.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

Yoked variable-ratio and variable-interval responding in pigeons

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

Behavior-dependent reinforcer-rate changes in concurrent schedules: A further analysis

Six pigeons were trained on concurrent variable-interval schedules in three different procedures. The first procedure was a standard concurrent schedule, and the relative reinforcer frequency for responding was varied. The second was a schedule in which a relative left-key response rate (over a fixed period of time) exceeding .75 produced, in the next identical time period a higher reinforcer rate on the right key. If this criterion was not exceeded, equal reinforcer rates were arranged on the two keys in this period. This was the dependent procedure. In the third (independent) procedure, the periods of higher right-key reinforcer rates occurred with the same probability as in the second procedure, but occurred independently of behavior. In the second and third procedures, the fixed-time period (window) was varied from 5 s to 60 s, and to 240 s in the second procedure only. Performance on the two keys was similar in the concurrent and independent procedures. The procedure used in the dependent conditions generally affected performance when the windows were shorter than about 30 s. Models of performance that assume that subjects do not discriminate changes in local relative reinforcer rates cannot account for the data. Moreover, existing models are inherently unable to account for the effects of contingencies of reinforcement between responding on one alternative and gaining reinforcers on another that are arranged or that emerge as a result of time allocated to alternative schedules. Undermatching on concurrent variable-interval schedules may result from such emergent contingencies.     

RESPONSE REDUCTION THROUGH THE SUPERIMPOSITION OF CONTINUOUS REINFORCEMENT: A SYSTEMATIC REPLICATION

Prior clinical research suggests that superimposition and subsequent removal of a schedule of continuous reinforcement (CRF) may be a viable rate-decreasing procedure in that an extinction-like condition is arranged. The arrangement of similar conditions in the laboratory, however, resulted in the quick recovery of baseline rates. Lever-pressing patterns of eight male rats maintained by different schedules of variable-ratio and variable-interval food reinforcement were examined in an A-B-A experimental design of CRF food superimposition and removal. Responding was substantially reduced during the superimposition of CRF. Upon removal of the superimposed schedule, responding quickly approached presuperimposition baseline rates.     

Performance in concurrent interval schedules: a systematic replication

Five pigeons were trained on a variety of concurrent interval schedules that arranged reinforcements at either fixed or variable times after the last reinforcement. Two measures were obtained: the number of responses on each schedule, and the time spent responding on each schedule. Ratios of response rates on the two schedules did not equal ratios of reinforcement rates when both schedules were variable nor when one was variable and the other fixed. Ratios of times spent responding approximately equalled ratios of reinforcement rates when both schedules were variable, but did not do so when one was fixed.     

Dependency, temporal contiguity, and response-independent reinforcement

A comparison was made of the effects of variable-interval, variable-time, and tandem variable-interval fixed-time schedules on key-peck responding of pigeons. The variable-interval component of the tandem schedule retained the response-reinforcement dependency; the fixed-time component allowed the temporal proximity between responding and reinforcement to vary, constrained only by the duration of the fixed-time interval. Response rates were highest during the variable-interval and lowest during the variable-time schedule. Intermediate response rates occurred during the tandem schedule. The results of a yoked control condition showed that the effects of the tandem schedule were not due simply to changes in reinforcement distribution or frequency. The results suggest that substantial reductions in responding occur when reinforcement is response-dependent but not necessarily contiguous with the response required to produce reinforcement.     

The role of discriminative stimuli in concurrent performances

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.     

Rate of conditioned reinforcement affects observing rate but not resistance to change

The effects of rate of conditioned reinforcement on the resistance to change of operant behavior have not been examined. In addition, the effects of rate of conditioned reinforcement on the rate of observing have not been adequately examined. In two experiments, a multiple schedule of observing-response procedures was used to examine the effects of rate of conditioned reinforcement on observing rates and resistance to change. In a rich component, observing responses produced a higher frequency of stimuli correlated with alternating periods of random-interval schedule primary reinforcement or extinction. In a lean component, observing responses produced similar schedule-correlated stimuli but at a lower frequency. The rate of primary reinforcement in both components was the same. In Experiment 1, a 4:1 ratio of stimulus production was arranged by the rich and lean components. In Experiment 2, the ratio of stimulus production rates was increased to 6:1. In both experiments, observing rates were higher in the rich component than in the lean component. Disruptions in observing produced by presession feeding, extinction of observing responses, and response-independent food deliveries during intercomponent intervals usually were similar in the rich and lean components. When differences in resistance to change did occur, observing tended to be more resistant to change in the lean component. If resistance to change is accepted as a more appropriate measure of response strength than absolute response rates, then the present results provide no evidence that higher rates of stimuli generally considered to function as conditioned reinforcers engender greater response strength.