Income maximizing on concurrent ratio-interval schedules of reinforcement

Three experiments examined the effect of food availability on pigeons' choice behavior under concurrent schedules of reinforcement. In Experiment 1, 3 pigeons earned their daily food ration by choosing, in 30-min sessions, between concurrent variable-ratio 30 variable-interval 40-s schedules. Food presentations during both schedules lasted 2 or 12 s, depending upon the condition. Relative variable-ratio response rate was inversely related to hopper duration. In Experiment 2, 4 pigeons received their daily feeding by responding on the same schedule pair as in Experiment 1 (with 4-s food presentations) in sessions that varied in length from 10 to 30 min, depending on the condition. The length of a vertical slit projected on a response key increased with time so that “passage of time” might be more easily discriminable. As session duration decreased, relative variable-ratio response rate increased. In Experiment 3, 4 pigeons chose between two variable-interval 40-s schedules. One schedule operated without regard to the schedule selected, whereas the other operated only when the subject responded in its presence (dependent). Although these schedules had the same feedback function, preference for the dependent variable interval increased as session duration decreased from 30 to 10 min. The preference changes in these studies reveal the operation of an income-maximizing process in choice.     

The Probability of Small Schedule Values and Preference for Random-Interval Schedules

Preference for working on variable schedules and temporal discrimination were simultaneously examined in two experiments using a discrete-trial, concurrent-chains arrangement with fixed interval (FI) and random interval (RI) terminal links. The random schedule was generated by first sampling a probability distribution after the programmed delay to reinforcement on the FI schedule had elapsed, and thus the RI never produced a component schedule value shorter than the FI and maintained a rate of reinforcement half that of the FI. Despite these features, the FI was not strongly preferred. The probability of obtaining the smallest programmed delay to reinforcement on the RI schedule was manipulated in Experiment 1, and the interaction of this probability and initial link length was examined in Experiment 2. As the probability of obtaining small values in the RI increased, preference for the schedule increased while the discriminated time of reinforcer availability in the terminal link decreased. Both of these effects were attenuated by lengthening the initial links. The results support the view that in addition to the delay to reinforcement, the probability of obtaining a short delay is an important choice-affecting variable that likely contributes to the robust preferences for variable, as opposed to fixed, schedules of reinforcement.     

DISCRIMINATION OF VARIABLE SCHEDULES IS CONTROLLED BY INTERRESPONSE TIMES PROXIMAL TO REINFORCEMENT

In Experiment 1, food‐deprived rats responded to one of two schedules that were, with equal probability, associated with a sample lever. One schedule was always variable ratio, while the other schedule, depending on the trial within a session, was: (a) a variable‐interval schedule; (b) a tandem variable‐interval, differential‐reinforcement‐of‐low‐rate schedule; or (c) a tandem variable‐interval, differential‐reinforcement‐of‐high‐rate schedule. Completion of a sample‐lever schedule, which took approximately the same time regardless of schedule, presented two comparison levers, one associated with each sample‐lever schedule. Pressing the comparison lever associated with the schedule just presented produced food, while pressing the other produced a blackout. Conditional‐discrimination accuracy was related to the size of the difference in reinforced interresponse times and those that preceded it (predecessor interresponse times) between the variable‐ratio and other comparison schedules. In Experiment 2, control by predecessor interresponse times was accentuated by requiring rats to discriminate between a variable‐ratio schedule and a tandem schedule that required emission of a sequence of a long, then a short interresponse time in the tandem's terminal schedule. These discrimination data are compatible with the copyist model from Tanno and Silberberg (2012) in which response rates are determined by the succession of interresponse times between reinforcers weighted so that each interresponse time's role in rate determination diminishes exponentially as a function of its distance from reinforcement.     

Free-operant performance on variable interval schedules with a linear feedback loop: no evidence for molar sensitivities in rats

Four experiments examined rats' sensitivity to molar and molecular factors on instrumental schedules of reinforcement. Rats were exposed to a variable interval schedule with a positive feedback loop (VI+), such that faster responding led to a shorter interreinforcement interval. In Experiments 1 and 2, rats responded faster on a variable response (VR) schedule than on either a VI schedule matched for reinforcement rate or a VI+ schedule matched for the feedback function. In Experiment 3, rats responded no differently on a VI schedule than they did on a VI+ schedule with equated rates of reinforcement. In Experiment 4, rats responded faster on a VI+ schedule with an interresponse time requirement yoked to that experienced on a VR schedule, than on a VI+ schedule with the same feedback function as the VR schedule. Taken together these results suggest that rats are more sensitive to the molecular than the molar properties of the schedules.     

Human sensitivity to reinforcement feedback functions

Two experiments investigated human sensitivity to the temporally extended aspects of reinforcement schedules. Experiment 1 investigated human sensitivity to the extended and local aspects of three reinforcement schedules: variable ratio (VR), variable interval (VI), and variable-interval-plus-linear-feedback (VI+) schedules. Experiment 2 investigated this sensitivity on two reinforcement schedules: VI and VI+ schedules. In both experiments, there was evidence of sensitivity to the temporally extended aspects of the schedule: There were differences between the response rate on the VI+ and yoked-VI schedules, but no statistical difference in rates of response between the VR and VI+ schedules. The VI+ versus VI difference was much more pronounced when a lower response force needed to depress a lever was used. These results suggest that human subjects do show some sensitivity to temporally extended aspects of schedules of reinforcement.     

Punished and Nonpunished Responding in A Multiple Schedule in Humans: A Brief Report

Four male subjects responded on a multiple schedule in which responding was maintained by a random interval 20-sec (RI20) schedule of point presentation. Responding was suppressed in alternating components by an added variable ratio 30 (VR30) schedule of point subtractions. Each component was accompanied by distinctive stimulus lights. Subjects were exposed to the multiple schedule from the initial session. Two subjects experienced four 50-min sessions daily (Experiment 1) and the other two subjects participated in one 50-min session daily (Experiment 2). Once responding in the punished components had stabilized, responding in the nonpunished components continued to increase across sessions. Nonpunished responding did not stabilize even after as many as 36 sessions. These results are discussed in the context of previous studies using animals which employed multiple schedules with punished and nonpunished response contingencies.

     

Variable-ratio versus variable-interval schedules: response rate, resistance to change, and preference

Two experiments asked whether resistance to change depended on variable-ratio as opposed to variable-interval contingencies of reinforcement and the different response rates they establish. In Experiment 1, pigeons were trained on multiple random-ratio random-interval schedules with equated reinforcer rates. Baseline response rates were disrupted by intercomponent food, extinction, and prefeeding. Resistance to change relative to baseline was greater in the interval component, and the difference was correlated with the extent to which baseline response rates were higher in the ratio component. In Experiment 2, pigeons were trained on multiple variable-ratio variable-interval schedules in one half of each session and on concurrent chains in the other half in which the terminal links corresponded to the multiple-schedule components. The schedules were varied over six conditions, including two with equated reinforcer rates. In concurrent chains, preference strongly overmatched the ratio of obtained reinforcer rates. In multiple schedules, relative resistance to response-independent food during intercomponent intervals, extinction, and intercomponent food plus extinction depended on the ratio of obtained reinforcer rates but was less sensitive than was preference. When reinforcer rates were similar, both preference and relative resistance were greater for the variable-interval schedule, and the differences were correlated with the extent to which baseline response rates were higher on the variable-ratio schedule, confirming the results of Experiment 1. These results demonstrate that resistance to change and preference depend in part on response rate as well as obtained reinforcer rate, and challenge the independence of resistance to change and preference with respect to response rate proposed by behavioral momentum theory.     

Directed forgetting of a single item

In two experiments, we investigated directed forgetting of a single item. We presented participants with two phone numbers to remember and instructed half of the participants to forget the first phone number. The first number was either learned on a single trial (Experiment 1) or on three trials (Experiment 2). In Experiment 1, there was evidence of directed forgetting as a result of differential encoding; the forget instruction affected recall and recognition for both phone numbers. In Experiment 2, the evidence favored differential rehearsal because the forget instruction affected recall but not recognition. These results indicate that instructions to forget can affect memory of single items.     

Waiting in pigeons: the effects of daily intercalation on temporal discrimination.

Pigeons trained on cyclic-interval schedules adjust their postfood pause from interval to interval within each experimental session. But on regular fixed-interval schedules, many sessions at a given parameter value are usually necessary before the typical fixed-interval "scallop" appears. In the first case, temporal control appears to act from one interfood interval to the next; in the second, it appears to act over hundreds of interfood intervals. The present experiments look at the intermediate case: daily variation in schedule parameters. In Experiments 1 and 2 we show that pauses proportional to interfood interval develop on short-valued response-initiated-delay schedules when parameters are changed daily, that additional experience under this regimen leads to little further improvement, and that pauses usually change as soon as the schedule parameter is changed. Experiment 3 demonstrates identical waiting behavior on fixed-interval and response-initiated-delay schedules when the food delays are short (less than 20 s) and conditions are changed daily. In Experiment 4 we show that daily intercalation prevents temporal control when interfood intervals are longer (25 to 60 s). The results of Experiment 5 suggest that downshifts in interfood interval produce more rapid waiting-time adjustments than upshifts. These and other results suggest that the effects of short interfood intervals seem to be more persistent than those of long intervals.     

Development and maintenance of attack in pigeons during variable-interval reinforcement of key pecking

Key-peck responses of two pigeons were maintained on variable-interval schedules of food reinforcement in the presence of a stuffed pigeon to study the characteristics of attack induced by that schedule. The mean interval of the schedule was increased from 15 sec to 600 sec in eight steps before an intermediate interval was reintroduced. The principal characteristics of attack were: (1) substantial attack first occurred on a variable-interval schedule of 90 sec in one pigeon and at 180 sec in the other, (2) the highest attack rates occurred on variable-interval schedules of 300 sec and 600 sec, (3) attack rate generally increased to a maximum and then decreased to a lower level across sessions at each schedule, (4) attacks developed a postreinforcement locus across the initial sessions on all schedules and, except on variable-interval schedules of 300 and 600 sec, occurred primarily in the postreinforcement period during extended training, (5) attack rates and key-peck rates were not recovered when the intermediate-length schedules were reintroduced, and (6) attack rate and key-peck rates were negatively correlated. Except for the fact that the maximum attack rates occurred at interfood intervals of 300 and 600 sec, and that attack and key-peck rates were negatively correlated, these findings have counter-parts in experiments with other reinforcement schedules.     

Variable-time reinforcement in multiple and concurrent schedules

Experiment I examined the role of a reduced rate of responding in the occurrence of behavioral contrast. Four rats and a pigeon were exposed to a two-component multiple schedule in which one component was always a variable-interval schedule. The second component was, at different times, either a variable-time schedule in which food was delivered independently of responding, or extinction. Both extinction and the variable-time schedule reduced the rate of responding in the second component. Behavioral contrast was observed, however, only when extinction was scheduled in the second component. Experiment II examined preference, as measured by time allocation in concurrent schedules for a variable-interval schedule relative to a variable-time schedule. Two rats displayed a lack of preference between the two schedules. The results of these experiments support a preference interpretation of behavioral contrast, which holds that behavioral contrast is the result of the introduction of a less-preferred condition in one component of a multiple schedule.     

SINGLE‐SAMPLE DISCRIMINATION OF DIFFERENT SCHEDULES' REINFORCED INTERRESPONSE TIMES

Food‐deprived rats in Experiment 1 responded to one of two tandem schedules that were, with equal probability, associated with a sample lever. The tandem schedules' initial links were different random‐interval schedules. Their values were adjusted to approximate equality in time to completing each tandem schedule's response requirements. The tandem schedules differed in their terminal links: One reinforced short interresponse times; the other reinforced long ones. Tandem‐schedule completion presented two comparison levers, one of which was associated with each tandem schedule. Pressing the lever associated with the sample‐lever tandem schedule produced a food pellet. Pressing the other produced a blackout. The difference between terminal‐link reinforced interresponse times varied across 10‐trial blocks within a session. Conditional‐discrimination accuracy increased with the size of the temporal difference between terminal‐link reinforced interresponse times. In Experiment 2, one tandem schedule was replaced by a random ratio, while the comparison schedule was either a tandem schedule that only reinforced long interresponse times or a random‐interval schedule. Again, conditional‐discrimination accuracy increased with the temporal difference between the two schedules' reinforced interresponse times. Most rats mastered the discrimination between random ratio and random interval, showing that the interresponse times reinforced by these schedules can serve to discriminate between these schedules.     

The schedule dependency of the signaled reinforcement effect

In Experiment 1, rats leverpressed for food reinforcement on either a variable ratio (VR) 30 schedule or a variable interval (VI) 15-s schedule. One group in each condition received a signal filling a 500-ms delay of reinforcement. This treatment enhanced rates on the VR schedule, and attenuated rates on the VI schedule, relative to the rate seen in an unsignaled control condition. In Experiment 2 there was no delay of reinforcement and the signal and food were presented simultaneously. Attenuated rates of responding were observed on VI schedules with a range of mean interval values (15 to 300 s). Experiment 3 used a range of VR schedules (10 to 150) with simultaneous presentations of signal and food. A signal-induced enhancement of response rate was found at all VR values. In Experiment 4, a signal elevated response rates on a tandem VI VR schedule, but depressed rates on a tandem VR VI schedule, compared to control conditions receiving unsignaled delayed reinforcement. These results are taken to show that the effect of a signal accompanying reinforcement depends upon the nature of the behavior that is reinforced during exposure to a given schedule.     

Response–reinforcer dependency and resistance to change

The effects of the response–reinforcer dependency on resistance to change were studied in three experiments with rats. In Experiment 1, lever pressing produced reinforcers at similar rates after variable interreinforcer intervals in each component of a two‐component multiple schedule. Across conditions, in the fixed component, all reinforcers were response‐dependent; in the alternative component, the percentage of response‐dependent reinforcers was 100, 50 (i.e., 50% response‐dependent and 50% response‐independent) or 10% (i.e., 10% response‐dependent and 90% response‐independent). Resistance to extinction was greater in the alternative than in the fixed component when the dependency in the former was 10%, but was similar between components when this dependency was 100 or 50%. In Experiment 2, a three‐component multiple schedule was used. The dependency was 100% in one component and 10% in the other two. The 10% components differed on how reinforcers were programmed. In one component, as in Experiment 1, a reinforcer had to be collected before the scheduling of other response‐dependent or independent reinforcers. In the other component, response‐dependent and ‐independent reinforcers were programmed by superimposing a variable‐time schedule on an independent variable‐interval schedule. Regardless of the procedure used to program the dependency, resistance to extinction was greater in the 10% components than in the 100% component. These results were replicated in Experiment 3 in which, instead of extinction, VT schedules replaced the baseline schedules in each multiple‐schedule component during the test. We argue that the relative change in dependency from Baseline to Test, which is greater when baseline dependencies are high rather than low, could account for the differential resistance to change in the present experiments. The inconsistencies in results across the present and previous experiments suggest that the effects of dependency on resistance to change are not well understood. Additional systematic analyses are important to further understand the effects of the response–reinforcer relation on resistance to change and to the development of a more comprehensive theory of behavioral persistence.     

Influence of the cost of responding

In three experiments, the effect of costs associated with responding on judgments of the causal effectiveness of the response was examined. In Experiment 1, the temporal interval between outcomes was matched on a variable interval (VI) and a variable ratio (VR) schedule. When each response was made at some “cost,” and outcomes represented some “gain” for the subject, the rating of causal effectiveness for responses was higher on the VR than on the VI schedule. This relationship was absent when the outcome was a triangle Hash. In Experiment 2, the number of responses required per outcome on a VI and a VR schedule were matched, and responses on the VR schedule were rated as more causally effective. In Experiment 3, a VI-to-VR yoking procedure was used. With minimal response costs, judgments were similar on the VI and VR schedules, but with greater response costs, responses performed on the VR schedule were rated as more causally effective than those emitted on the VI schedule.     

Destructive effects of “forget” instructions

In two experiments, participants were given three lists of words to study and were told to (1) remember all three lists, (2) forget the first list immediately after studying it but try to remember the other two lists, or (3) forget the middle list immediately after studying it but try to remember the first and the last lists. In Experiment 1, unrelated word lists were used, whereas Experiment 2 replicated Experiment 1 with categorical lists. The results from both experiments showed that forgetting the middle list leads also to recall decrement for the first list, which was not intended for forgetting. The results are discussed in terms of the contextual change hypothesis of directed forgetting.     

Similar consumption and responding across single and multiple sources of drug

Two experiments were conducted to assess whether total response output and total consumption would be similar when drugs are available from single and multiple sources of reinforcement, as predicted by behavioral economics. In Experiment 1, cigarette-deprived smokers were exposed to a concurrent-chains schedule in which equal fixed-ratio schedules served as the initial links, and different reinforcer magnitudes (i.e., number of cigarette puffs) were arranged across alternatives. After the session, obtained unit price was calculated and imposed in the next session when a different number of puffs was available according to a single fixed-ratio schedule. Thus, the unit price at which cigarette puffs could be earned was yoked within subjects across the single and concurrent-chains schedules. When plotted as a function of unit price, similar consumption and response rates were usually obtained across these schedules. Experiment 2 addressed a weakness of Experiment 1, namely, that responding was allocated exclusively to the larger reinforcer magnitude in concurrent-chains conditions, and therefore this schedule may have functioned as a single schedule. In Experiment 2, subjects were instructed to alternate responding between the two alternative schedules. Instructions produced approximately equal response allocation between the two alternatives. Again, similar consumption and response rates were observed across the single and instructed concurrent-chains schedules. These findings are discussed in the context of direct effects and behavioral economics perspectives of drug self-administration.     

Response-rate differences in variable-interval and variable-ratio schedules: An old problem revisited

In Experiment 1, a variable-ratio 10 schedule became, successively, a variable-interval schedule with only the minimum interreinforcement intervals yoked to the variable ratio, or a variable-interval schedule with both interreinforcement intervals and reinforced interresponse times yoked to the variable ratio. Response rates in the variable-interval schedule with both interreinforcement interval and reinforced interresponse time yoking fell between the higher rates maintained by the variable-ratio schedule and the lower rates maintained by the variable-interval schedule with only interreinforcement interval yoking. In Experiment 2, a tandem variable-interval 15-s variable-ratio 5 schedule became a yoked tandem variable-ratio 5 variable-interval x-s schedule, and a tandem variable-interval 30-s variable-ratio 10 schedule became a yoked tandem variable-ratio 10 variable-interval x-s schedule. In the yoked tandem schedules, the minimum interreinforcement intervals in the variable-interval components were those that equated overall interreinforcement times in the two phases. Response rates did not decline in the yoked schedules even when the reinforced interresponse times became longer. Experiment 1 suggests that both reinforced interresponse times and response rate–reinforcement rate correlations determine response-rate differences in variable-ratio 10 and yoked variable-interval schedules in rats. Experiment 2 suggests a minimal role for the reinforced interresponse time in determining response rates on tandem variable-interval 30-s variable-ratio 10 and yoked tandem variable-ratio 10 variable-interval x-s schedules in rats.     

Baseline response rates affect resistance to change

The effect of response rates on resistance to change, measured as resistance to extinction, was examined in two experiments. In Experiment 1, responding in transition from a variable‐ratio schedule and its yoked‐interval counterpart to extinction was compared with pigeons. Following training on a multiple variable‐ratio yoked‐interval schedule of reinforcement, in which response rates were higher in the former component, reinforcement was removed from both components during a single extended extinction session. Resistance to extinction in the yoked‐interval component was always either greater or equal to that in the variable‐ratio component. In Experiment 2, resistance to extinction was compared for two groups of rats that exhibited either high or low response rates when maintained on identical variable‐interval schedules. Resistance to extinction was greater for the lower‐response‐rate group. These results suggest that baseline response rate can contribute to resistance to change. Such effects, however, can only be revealed when baseline response rate and reinforcement rate are disentangled (Experiments 1 and 2) from the more usual circumstance where the two covary. Furthermore, they are more cleanly revealed when the programmed contingencies controlling high and low response rates are identical, as in Experiment 2.     

A COMPARISON OF TWO PROCEDURES FOR PROGRAMMING THE DIFFERENTIAL REINFORCEMENT OF OTHER BEHAVIORS

The relative effectiveness of two methods of programming DRO schedules of reinforcement was examined in two experiments. In these two methods, reinforcement is delivered if inappropriate responding is not occurring (a) at the end of an interval (momentary DRO), or (b) throughout the entire interval (whole-interval DRO). In Experiment 1, the effects of these schedules on disruptive responding of three retarded students were assessed in a multiple-baseline design. For two students, the momentary schedule occurred first and was ineffective, whereas the whole interval that followed was effective; for the third student, the whole-interval schedule occurred first and was effective, and reduced responding was maintained under the momentary schedule. In Experiment 2, baseline and the two DRO schedules were each presented in random order each day to one student in an alternating treatments design. The momentary DRO schedule reduced responding, but the whole-interval schedule was more effective.