Superimposition of response-independent reinforcement

Studies that have superimposed response-independent reinforcement (or reinforcers scheduled by contingencies placed on the absence of responding) upon conventional response-dependent schedules are reviewed. In general, providing alternative sources of reinforcement reduced response rates below the levels observed when alternative reinforcement was absent. However, response-rate elevation was sometimes found, particularly when rates of superimposed response-independent reinforcement were low. Superimposition of schedules providing reinforcers contingent on the absence of responding usually produced more severe response-rate decrements than superimposition of response-independent reinforcement. A variant of Herrnstein's equation, which assumes that some of the alternative reinforcers function as if they were delivered by baseline response-dependent source of reinforcement, is in qualitative agreement with the overall body of results obtained, and can predict both increases and decreases in response rate as resulting from superimposed reinforcers.     

The long-term effect of high- and low-rate responding histories on fixed-interval responding in rats

Tell rats were given extended lever-press training on a fixed-interval (FI) 30-s food reinforcement schedule from the outset or following exposure to one or two previous reinforcement schedules. For 4 rats the previots schedule was either fixed-ratio 20, which generated high response rates, or differential-reinforcement-of-low-rate 20 s, which produced low response rates. For 4 additional rats the extended training on FI 30 s was preceded by experience with two schedules: fixed-ratio 20 followed by differential-reinforcement-of-low-rate 20 s; or the same two schedules in the reverse order. Fixed-interval response rates were initially affected by the immediately preceding schedule, but after 80 to 100 sessions, all traces of prior schedule history had disappeared. The results also showed no long-term effect of schedule history on the interfood-interval patterns of responding on the FI 30-s schedule. These results support one of the most central tenets of the experimental analysis of behavior: control by the immediate consequences of behavior.     

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.     

Effects of reinforcer rate and reinforcer quality on time allocation: Extensions of matching theory to educational settings

We examined how 3 special education students allocated their responding across two concurrently available tasks associated with unequal rates and equal versus unequal qualities of reinforcement. The students completed math problems from two alternative sets on concurrent variable-interval (VI) 30-s VI 120-s schedules of reinforcement. During the equal-quality reinforcer condition, high-quality (nickels) and low-quality items ("program money" in the school's token economy) were alternated across sessions as the reinforcer for both sets of problems. During the unequal-quality reinforcer condition, the low-quality reinforcer was used for the set of problems on the VI 30-s schedule, and the high-quality reinforcer was used for the set of problems on the VI 120-s schedule. Equal- and unequal-quality reinforcer conditions were alternated using a reversal design. Results showed that sensitivity to the features of the VI reinforcement schedules developed only after the reinforcement intervals were signaled through countdown timers. Thereafter, when reinforcer quality was equal, the time allocated to concurrent response alternatives was approximately proportional to obtained reinforcement, as predicted by the matching law. However the matching relation was disrupted when, as occurs in most natural choice situations, the quality of the reinforcers differed across the response options.     

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.     

Temporal proximity and reinforcement sensitivity in multiple schedules

Distributions of reinforcers between two components of multiple variable-interval schedules were varied over a number of conditions. Sensitivity to reinforcement, measured by the exponent of the power function relating ratios of responses in the two components to ratios of reinforcers obtained in the components, did not differ between conditions with 15-s or 60-s component durations. The failure to demonstrate the “short-component effect,” where sensitivity is high for short components, was consistent with reanalysis of previous data. With 60-s components, sensitivity to reinforcement decreased systematically with time since component alternation, and was higher in the first 15-s subinterval of the 60-s component than for the component whose total duration was 15 s. Varying component duration and sampling behavior at different times since component transition may not be equivalent ways of examining the effects of average temporal distance between components.     

Reinforcement Probability and Delay as Determinants of Human Impulsiveness

In behavior theory, “impulsiveness” refers to the choice of an immediate, small reinforcer over a delayed, large reinforcer. Such behavior generally is attributed to a reduction in the value of the large reinforcer as a function of the duration of delay. In contrast, social learning theorists have suggested that human impulsiveness can result from a lowered “expectancy” (subjective probability) of reinforcement. Effects of probability and delay were assessed by asking adults to make repeated choices between reinforcement schedules in which the reinforcers were slides of entertainment figures. An immediate, 5-s reinforcer was consistently chosen over an immediate, 40-s reinforcer if the probability of receiving the large reinforcer had previously been low (.20), implying that impulsiveness can occur without time-based discounting. However, reinforcement delay was also influential: Choice between a certain, small reinforcer and an uncertain, large reinforcer varied according to which reinforcer was immediate and which delayed.

     

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

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

The momentum of human behavior in a natural setting

Adults with mental retardation in a group home received popcorn or coffee reinforcers for sorting plastic dinnerware. In Part 1 of the experiment, reinforcers were dispensed according to a variable-interval 60-s schedule for sorting dinnerware of one color and according to a variable-interval 240-s schedule for sorting dinnerware of a different color in successive components of a multiple schedule. Sorting rates were similar in baseline, but when a video program was shown concurrently, sorting of dinnerware was more resistant to distraction when correlated with a higher rate of reinforcement. In Part 2 of the experiment, popcorn or coffee reinforcers were contingent upon sorting both colors of dinnerware according to variable-interval 60-s schedules, but additional reinforcers were given independently of sorting according to a variable-time 30-s schedule during one dinnerware-color component. Baseline sorting rate was lower but resistance to distraction by the video program was greater in the component with additional variable-time reinforcers. These results demonstrate that resistance to distraction depends on the rate of reinforcers obtained in the presence of component stimuli but is independent of baseline response rates and response–reinforcer contingencies. Moreover, these results are similar to those obtained in laboratory studies with pigeons, demonstrating that the determination of resistance to change by stimulus–reinforcer relations is not confined to controlled laboratory settings or unique to the pigeon.     

Effects of reinforcement rate and delay on the acquisition of lever pressing by rats.

The acquisition of lever pressing by naive rats, in the absence of shaping, was studied as a function of different rates and unsignaled delays of reinforcement. Groups of 3 rats were each exposed to tandem schedules that differed in either the first or the second component. First-component schedules were either continuous reinforcement or random-interval 15, 30, 60 or 120 s; second-component schedules were fixed-time 0, 1, 3, 6, 12, or 24 s. Rate of responding was low under continuous immediate reinforcement and higher under random-interval 15 s. Random interval 30-s and 60-s schedules produced lower rates that were similar to each other. Random-interval 120 s controlled the lowest rate in the immediate-reinforcement condition. Adding a constant 12-s delay to each of the first-component schedule parameters controlled lower response rates that did not vary systematically with reinforcement rate. The continuous and random-interval 60-s schedules of immediate reinforcement controlled higher global and first-component response rates than did the same schedules combined with longer delays, and first-component rates showed some graded effects of delay duration. In addition, the same schedules controlled higher second-component response rates in combination with a 1-s delay than in combination with longer delays. These results were related to those from previous studies on acquisition with delayed reinforcement as well as to those from similar reinforcement procedures used during steady-state responding.     

Molar And Molecular Control In Variable-interval And Variable-ratio Schedules

Response rates are typically higher under variable-ratio than under variable-interval schedules of reinforcement, perhaps because of differences in the dependence of reinforcement rate on response rate or because of differences in the reinforcement of long interresponse times. A variable-interval-with-added-linear-feedback schedule is a variable-interval schedule that provides a response rate/reinforcement rate correlation by permitting the minimum interfood interval to decrease with rapid responding. Four rats were exposed to variable-ratio 15, 30, and 60 food reinforcement schedules, variable-interval 15-, 30-, and 60-s food reinforcement schedules, and two versions of variable-interval-with-added-linear-feedback 15-, 30-, and 60-s food reinforcement schedules. Response rates on the variable-interval-with-added-linear-feedback schedule were similar to those on the variable-interval schedule; all three schedules led to lower response rates than those on the variable-ratio schedules, especially when the schedule values were 30. Also, reinforced interresponse times on the variable-interval-with-added-linear-feedback schedule were similar to those on variable interval and much longer than those produced by variable ratio. The results were interpreted as supporting the hypothesis that response rates on variable-interval schedules in rats are lower than those on comparable variable-ratio schedules, primarily because the former schedules reinforce long interresponse times.     

Resistance to reinforcement change in multiple and concurrent schedules assessed in transition and at steady state

Behavioral momentum theory relates resistance to change of responding in a multiple-schedule component to the total reinforcement obtained in that component, regardless of how the reinforcers are produced. Four pigeons responded in a series of multiple-schedule conditions in which a variable-interval 40-s schedule arranged reinforcers for pecking in one component and a variable-interval 360-s schedule arranged them in the other. In addition, responses on a second key were reinforced according to variable-interval schedules that were equal in the two components. In different parts of the experiment, responding was disrupted by changing the rate of reinforcement on the second key or by delivering response-independent food during a blackout separating the two components. Consistent with momentum theory, responding on the first key in Part 1 changed more in the component with the lower reinforcement total when it was disrupted by changes in the rate of reinforcement on the second key. However, responding on the second key changed more in the component with the higher reinforcement total. In Parts 2 and 3, responding was disrupted with free food presented during intercomponent blackouts, with extinction (Part 2) or variable-interval 80-s reinforcement (Part 3) arranged on the second key. Here, resistance to change was greater for the component with greater overall reinforcement. Failures of momentum theory to predict short-term differences in resistance to change occurred with disruptors that caused greater change between steady states for the richer component. Consistency of effects across disruptors may yet be found if short-term effects of disruptors are assessed relative to the extent of change observed after prolonged exposure.     

Soft commitment: self-control achieved by response persistence.

With reinforcement contingent on a single peck on either of two available keys (concurrent continuous reinforcement schedules) 4 pigeons, at 80% of free-feeding weights, preferred a smaller-sooner reinforcer (2.5 s of mixed grain preceded by a 0.5-s delay) to a larger-later reinforcer (4.5 s of mixed grain preceded by a 3.5-s delay). However, when the smaller-sooner and larger-later reinforcers were contingent on a concurrent fixed-ratio 31 schedule (the first 30 pecks distributed in any way on the two keys), all pigeons obtained the larger-later reinforcer much more often than they did when only a single peck was required. This "self-control" was achieved by beginning to peck the key leading to the larger-later reinforcer and persisting on that key until reinforcement occurred. We call this persistence "soft commitment" to distinguish it from strict commitment, in which self-control is achieved by preventing changeovers. Soft commitment also effectively achieved self-control when a brief (1-s) signal was inserted between the 30th and 31st response of the ratio and with concurrent fixed-interval 30-s schedules (rather than ratio schedules) of reinforcement. In a second experiment with the same subjects, the fixed ratio was interrupted by darkening both keys and lighting a third (center) key on which pecking was required for various fractions of the fixed-ratio count. The interruption significantly reduced self-control. When interruption was complete (30 responses on the center key followed by a single choice response), pigeons chose the smaller-sooner reinforcer as frequently as they did when only a single choice response was required.     

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.     

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.     

Nonstable concurrent choice in pigeons

Six pigeons were trained on concurrent variable-interval schedules in which the arranged reinforcer ratios changed from session to session according to a 31-step pseudorandom binary sequence. This procedure allows a quantitative analysis of the degree to which performance in an experimental session is affected by conditions in previous sessions. Two experiments were carried out. In each, the size of the reinforcer ratios arranged between the two concurrent schedules was varied between 31-step conditions. In Experiment 1, the concurrent schedules were arranged independently, and in Experiment 2 they were arranged nonindependently. An extended form of the generalized matching law described the relative contribution of past and present events to present-session behavior. Total performance in sessions was mostly determined by the reinforcer ratio in that session and partially by reinforcers that had been obtained in previous sessions. However, the initial exposure to the random sequence produced a lower sensitivity to current-session reinforcers but no difference in overall sensitivity to reinforcement. There was no evidence that the size of the reinforcer ratios available on the concurrent schedules affected either overall sensitivity to reinforcement or the sensitivity to reinforcement in the current session. There was also no evidence of any different performance between independent and nonindependent scheduling. Because of these invariances, this experiment validates the use of the pseudorandom sequence for the fast determination of sensitivity to reinforcement.     

Response-independent milk delivery enhances persistence of pellet-reinforced lever pressing by rats

If, during training, one stimulus is correlated with a higher rate of reinforcement than another, responding will be more resistant to extinction in the presence of that higher rate signal, even if many of the reinforcers have been presented independently of responding. For the present study we asked if the response-independent reinforcers must be the same as the response-dependent reinforcers to enhance the response's persistence. Twelve Long-Evans hooded rats obtained 45-mg food pellets by lever pressing (variable-interval 100-s schedules) in the presence of two discriminative stimuli (blinking vs. steady lights) that alternated every minute during daily sessions. Also, in the presence of one of the stimuli (counterbalanced across rats), the rats received additional response-independent deliveries of sweetened condensed milk (a variable-time schedule). Extinction sessions were exactly like training sessions except that neither pellets nor milk were presented. Lever pressing was more resistant to extinction in the presence of the milk-correlated stimulus when (a) the size of the milk deliveries during training (under a variable-time 30 s schedule) was 0.04 ml (vs. 0.01 ml) and (b) 120-s or 240-s blackouts separated components. Response-independent reinforcers do not have to be the same as the response-dependent reinforcers to enhance persistence.     

Additional free reinforcers increase persistence of problem behavior in a clinical context: A partial replication of laboratory findings

Behavioral momentum theory is a quantitative framework used to characterize the persistence of behavior during response disruptors as a function of baseline stimulus–reinforcer relations. Results of several investigations have shown that alternative reinforcement can increase the resistance to change of a target response during extinction. In the present study, concomitant variable‐interval fixed‐time schedules of reinforcement for problem behavior were employed to simulate naturalistic situations involving the superimposition of response‐independent reinforcers on a baseline schedule of reinforcement for problem behavior, as in the common use of noncontingent reinforcement treatments. Resistance to change of problem behavior was assessed during postsession periods of extinction by comparing response rates in extinction following sessions with and without additional reinforcer deliveries arranged by fixed‐time schedules. For 2 out of 3 participants, problem behavior tended to be more resistant to extinction following periods in which additional fixed‐time reinforcers were delivered. These results are discussed in terms of potential effects of noncontingent reinforcement on problem behavior when the intervention is discontinued or implemented without good treatment integrity.