Brief-stimulus presentations on multiform tandem schedules

Three experiments examined the influence of a brief stimulus (a light) on the behavior of food-deprived rats whose lever pressing on tandem schedules comprising components of different schedule types resulted in food presentation. In Experiment 1, either a tandem variable-ratio variable-interval or a tandem variable-interval variable-ratio schedule was used. The variable-interval requirement in the tandem variable-ratio variable-interval schedule was yoked to the time taken to complete the variable-ratio component in the tandem variable-interval variable-ratio schedule, and the length of the variable-interval component in the latter schedule was yoked to the variable-ratio component in the former schedule. If a brief stimulus occurred following completion of the first component, then behavior was differentiated in the two components; subjects responded more quickly in the variable-ratio than in the variable-interval component. If the stimulus was removed, then response rate was determined by the nature of the final component. Similar results were obtained in Experiments 2 and 3 with the use of a three-component tandem variable-ratio variable-interval variable-ratio schedule or tandem variable-interval variable-ratio variable-interval schedule. Thus, a brief stimulus that was not explicitly paired with reinforcement engendered behavior typical of the component schedule preceding its presentation.     

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.     

Bouts of responding from variable-interval reinforcement of lever pressing by rats

Four rats obtained food pellets by lever pressing. A variable-interval reinforcement schedule assigned reinforcers on average every 2 min during one block of 20 sessions and on average every 8 min during another block. Also, at each variable-interval duration, a block of sessions was conducted with a schedule that imposed a variable-ratio 4 response requirement after each variable interval (i.e., a tandem variable-time variable-ratio 4 schedule). The total rate of lever pressing increased as a function of the rate of reinforcement and as a result of imposing the variable-ratio requirement. Analysis of log survivor plots of interresponse times indicated that lever pressing occurred in bouts that were separated by pauses. Increasing the rate of reinforcement increased total response rate by increasing the rate of initiating bouts and, less reliably, by lengthening bouts. Imposing the variable-ratio component increased response rate mainly by lengthening bouts. This pattern of results is similar to that reported previously with key poking as the response. Also, response rates within bouts were relatively insensitive to either variable.     

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.     

Concurrent schedules of primary and conditioned reinforcement in rats

Rats responded on a fixed-interval schedule during which a 3-sec stimulus preceded each water reinforcement. The stimulus was then scheduled concurrently for responses on the same lever according to either a variable ratio. Although water reinforcement continued on a fixed-interval schedule, the pattern of responding became typical of a variable-interval or variable-ratio schedule. When the 3-sec stimulus was presented on a variable-interval or variable-ratio schedule, but was omitted on the fixed-interval schedule, the response rate decreased. When the stimulus occurred after the same time periods as those of the variable-interval schedule, but at least 7-sec after the last response, the rate decreased. The rate became higher when the fixed-interval schedule was discontinued and each presentation of the 3-sec stimulus was followed by water on a variable-interval schedule. When both water and the 3-sec stimulus were discontinued for a period of time, resulting in extinction of the lever response, and the 3-sec stimulus alone then presented on a variable-interval or variable-ratio schedule after lever responses, rate increased and then gradually decreased.     

The linear system theory's account of behavior maintained by variable-ratio schedules.

The mathematical theory of linear systems, which has been used successfully to describe behavior maintained by variable-interval schedules, is extended to describe behavior maintained by variable-ratio schedules. The result of the analysis is a pair of equations, one of which expresses response rate on a variable-ratio schedule as a function of the mean ratio requirement (n) that the schedule arranges. The other equation expresses response rate on a variable-ratio schedule as a function of reinforcement rate. Both equations accurately describe existing data from variable-ratio schedules. The theory accounts for two additional characteristics of behavior maintained by variable-ratio schedules; namely, the appearance of strained, two-valued (i.e., zero or very rapid) responding at large ns, and the abrupt cessation of responding at a boundary n. The theory also accounts for differences between behavior on variable-interval and variable-ratio schedules, including (a) the occurrence of strained responding on variable-ratio but not on variable-interval schedules, (b) the abrupt cessation of responding on occurrence of higher response rates on variable-ratio than on variable-interval schedules. Furthermore, given data from a series of variable-interval schedules and from a series of concurrent variable-ratio variable-interval schedules, the theory permits quantitative prediction of many properties of behavior on single-alternative variable-ratio schedules. The linear system theory's combined account of behavior on variable-interval and variable-ratio schedules is superior to existing versions of six other mathematical theories of variable-interval and variable-ratio responding.     

Matching and maximizing with concurrent ratio-interval schedules.

Animals exposed to standard concurrent variable-ratio variable-interval schedules could maximize overall reinforcement rate if, in responding, they showed a strong response bias toward the variable-ratio schedule. Tests with the standard schedules have failed to find such a bias and have been widely cited as evidence against maximization as an explanation of animal choice behavior. However, those experiments were confounded in that the value of leisure (behavior other than the instrumental response) partially offsets the value of reinforcement. The present experiment provides another such test using a concurrent procedure in which the confounding effects of leisure were mostly eliminated while the critical aspects of the concurrent variable-ratio variable-interval contingency were maintained: Responding in one component advanced only its ratio schedule while responding in the other component advanced both ratio schedules. The bias toward the latter component predicted by maximization theory was found.     

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.     

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.     

Bouts of responding: the relation between bout rate and the rate of variable-interval reinforcement

By nose poking a lighted key, rats obtained food pellets on either a variable-interval schedule of reinforcement or a schedule that required an average of four additional responses after the end of tile variable-interval component (a tandem variable-interval variable-ratio 4 schedule). With both schedule types, the mean variable interval was varied between blocks of sessions from 16 min to 0.25 min. Total rate of key poking increased similarly as a function of the reinforcer rate for the two schedule types, but response rate was higher with than without the four-response requirement. Analysis of log survivor plots of interresponse times showed that key poking occurred in bouts. The rate of initiating bouts increased as a function of reinforcer rate but was either unaffected or was decreased by adding the four-response requirement. Within-bout response rate was insensitive to reinforcer rate and only inconsistently affected by the four-response requirement. For both kinds of schedule, the ratio of bout time to between-bout pause time was approximately a power function of reinforcer rate, with exponents above and below 1.0.     

Matching under nonindependent variable-ratio schedules of drug reinforcement.

Response-contingent deliveries of oral pentobarbital maintained responding of 3 rhesus monkeys during daily 3-hr sessions. Deliveries of pentobarbital were arranged under nonindependent concurrent variable-ratio variable-ratio schedules. Responses to either schedule counted toward completion of both variable-ratio schedule requirements. This schedule is similar in some respects to conventional concurrent variable-interval variable-interval schedules, in which passage of time counts toward completion of the interval value on both schedules. Restricted nonindependent concurrent variable-ratio variable-ratio schedules were also studied. On that schedule, when a drug delivery was assigned to one spout, it had to be collected before responses on the opposite spout again counted toward completion of the schedule requirements. Relative reinforcer magnitude was varied by changing the drug concentration on one schedule while keeping the drug concentration constant on the other variable-ratio schedule. Under both types of concurrent variable-ratio schedules, the relative rate of responding corresponded to the relative drug intake. Unlike earlier studies of concurrent variable-interval variable-interval intravenous cocaine reinforcement, preference was proportionate to concentration, and exclusive preferences did not develop. The relationship between relative rate of responding and relative drug intake was well described by the generalized matching law.     

Intermittent punishment of human responding maintained by intermittent reinforcement

To determine the effects of variable-interval shock punishment on behavior maintained by variable-interval and variable-ratio reinforcement, human subjects' key-pressing behavior was reinforced with money on a four-component multiple schedule. Components 1 and 2 were variable-interval 30-sec, and Components 3 and 4 were variable-ratio 210. After responding was stabilized, response-contingent electric shock was scheduled on a variable-interval 10-sec schedule during the second and fourth components of each cycle. Subjects instructed as to the reinforcement contingencies showed gradually increasing suppression of variable-interval responding at increasing shock intensities and either very high or very low rates of variable-ratio responding at higher intensities. Minimally instructed subjects showed suppression at higher shock intensities, but no clear differential suppression as a function of reinforcement schedule. Recovery from initial suppression was observed within sessions.     

Effect of variable-interval punishment on the behavior of humans in variable-interval schedules of monetary reinforcement

One male and three female human subjects pressed a button for monetary reinforcement under a range of variable-interval schedules specifying different frequencies of reinforcement. On alternate days, responding was also punished (by subtraction of money) according to a variable-interval 170-second schedule. In the absence of punishment, the rate of responding was an increasing negatively accelerated function of reinforcement frequency, as predicted by Herrnstein's equation. The effect of the punishment schedule was to suppress responding under lower frequencies of reinforcement; responding under higher reinforcement frequencies was much less affected. This was reflected in an increase in the value of K_H (the constant expressing the reinforcement frequency corresponding to the half-maximal response rate), whereas there was no significant change in the value of R_max (the constant expressing the maximum response rate). Previous results had shown that variable-ratio punishment resulted in a change in the values of both constants (Bradshaw, Szabadi, and Bevan, 1977). The results of the present study were consistent with the concept that the suppressive effects of punishment on responding depend on the nature of the punishment schedule.     

Interaction of procedural factors in human performance on yoked schedules

The differential effects of reinforcement contingencies and contextual variables on human performance were investigated in two experiments. In Experiment 1, adult human subjects operated a joystick in a video game in which the destruction of targets was arranged according to a yoked variable-ratio variable-interval schedule of reinforcement. Three variables were examined across 12 conditions: verbal instructions, shaping, and the use of a consummatory response following reinforcement (i.e., depositing a coin into a bank). Behavior was most responsive to the reinforcement contingencies when the consummatory response was available, responding was established by shaping, and subjects received minimal verbal instructions about their task. The responsiveness of variable-interval subjects' behavior varied more than that of variable-ratio subjects when these contextual factors were altered. Experiment 2 examined resistance to instructional control under the same yoked-schedules design. Conditions varied in terms of the validity of instructions. Performance on variable-ratio schedules was more resistant to instructional control than that on variable-interval schedules.     

The effect of punishment shock intensity upon responding under multiple schedules

In the first of two experiments, responses of two pigeons were maintained by multiple variable-interval, variable-ratio schedules of food reinforcement. Concurrent punishment was introduced, which consisted of a brief electric shock after each tenth response. The initial punishment intensities had no lasting effect upon responding. Then, as shock intensity increased, variable-ratio response rates were suppressed more quickly than variable-interval response rates. When shock intensity decreased, variable-interval responding recovered more quickly, but the rates under both schedules eventually returned to their pre-punishment levels. In the second experiment, the following conditions were studied in three additional pigeons: (1) With each shock intensity in effect for a number of sessions, punishment shock intensity was gradually increased and decreased and responding was maintained by multiple variable-ratio, fixed-ratio schedules of food reinforcement; (2) Changes in punishment shock intensity as described above with responding maintained by either a variable-ratio or a fixed-ratio schedule, which were presented on alternate days; (3) Session-to-session changes in shock intensity with responding maintained by multiple variable-ratio, fixed-ratio schedules. Responding under the two schedules was suppressed to approximately the same extent by a particular shock intensity. Also, post-reinforcement pauses under the fixed-ratio schedule increased as response suppression increased.     

On the primacy of molecular processes in determining response rates under variable-ratio and variable-interval schedules

This study focused on variables that may account for response-rate differences under variable-ratio (VR) and variable-interval (VI) schedules of reinforcement. Four rats were exposed to VR, VI, tandem VI differential-reinforcement-of-high-rate, regulated-probability-interval, and negative-feedback schedules of reinforcement that provided the same rate of reinforcement. Response rates were higher under the VR schedule than the VI schedule, and the rates on all other schedules approximated those under the VR schedule. The median reinforced interresponse time (IRT) under the VI schedule was longer than for the other schedules. Thus, differences in reinforced IRTs correlated with differences in response rate, an outcome suggestive of the molecular control of response rate. This conclusion was complemented by the additional finding that the differences in molar reinforcement-feedback functions had little discernible impact on responding.     

IS THERE A DECISIVE TEST BETWEEN MATCHING AND MAXIMIZING?

Reinforcers under typical concurrent variable-interval, variable-ratio schedules may be (a) earned and obtained during the variable-interval component, (b) earned and obtained during the variable-ratio component, or (c) earned during the variable-ratio component and obtained during the variable-interval component. Categories a and b, which have no bearing on matching versus maximizing accounts of choice, were set at zero. The rate of Category c reinforcers and the duration of a changeover delay were varied. Simple matching, which predicts exclusive choice of the variable-interval component, and strict maximizing of overall reinforcement rate, which predicts a bias towards the variable-ratio component, were both disconfirmed: Subjects spent approximately 25% of their time in the variable-ratio component, contrary to the matching prediction, but earned only about one third of the reinforcers predicted by strict maximizing. However, maximizing describes the findings functionally in terms of discounting of delayed reinforcers; matching may describe the data in terms of a restructuring of the alternatives. Matching and maximizing are not competing theories about the fundamental nature of choice, but compatible points of view that may reveal environmental function and behavioral structure.     

Resistance to the response-decrementing effects of response-independent reinforcement produced by delay and non-delay schedules of reinforcement

In two experiments, animals were initially exposed to response-dependent schedules of food before exposure to response-independent reinforcement matched for overall rate and temporal distribution of reinforcers to the preceding condition. In Experiment I, response decrements during the response-independent phase were smaller after delayed reinforcement training than after a comparable immediate reinforcement schedule, for both doves and rats. In Experiment II variable-interval and variable-ratio schedules, both with either immediate or delayed reinforcement, were used with rats. Both the delayed reinforcement schedules produced resistance to subsequent response-independent reinforcement, but response decrements were larger after either of the immediate reinforcement conditions. It was concluded that the critical factor in response maintenance under response-independent reinforcement was the type of response-reinforcer contiguities permitted under the response-dependent schedule rather than perception of response-reinforcer “contingencies”. If the response-dependent schedule was arranged so that behaviours other than a designated operant (key pecking or lever pressing) could be contiguous with food, responding was maintained well under response-independent schedules.     

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.     

The effect of punishment on free-operant choice behavior in humans

During Phase I, three female human subjects pressed a button for monetary reinforcement in five variable-interval schedules specifying different frequencies of reinforcement. On alternate days, responding was also punished (by subtracting money) according to a variable-ratio 34 schedule. In the absence of punishment, response rates conformed to Herrnstein's equation for single variable-interval schedules. Punishment suppressed responding at all frequencies of reinforcement. This was reflected in a change in the values of both constants in Herrnstein's equation: the value of the theoretical maximum response-rate parameter was reduced, and the parameter describing the reinforcement frequency corresponding to the half-maximal response rate was elevated. During Phase II, the same five schedules (A) were in operation (without punishment), but in addition, a concurrent variable-interval schedule (B) of standard reinforcement frequency was introduced. On alternate days, responding in Component B was punished according to a variable-ratio 34 schedule. In the absence of punishment, absolute response rates conformed to equations proposed by Herrnstein to describe performance in concurrent schedules; the ratios of the response rates in the two components and the ratios of the times spent in the two components conformed to the Matching Law. When responding in Component B was punished, response rates in Component B were reduced and those in Component A were elevated, these changes being reflected in distortions of the matching relationship.