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.     

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.     

The law of effect and avoidance: a quantitative relationship between response rate and shock-frequency reduction

Two experiments were conducted to investigate the quantitative relationship between response rate and reinforcement frequency in single and multiple variable-interval avoidance schedules. Responses cancelled delivery of shocks that were scheduled by variable-interval schedules. When shock-frequency reduction was taken as the measure of reinforcement, the relationship between response rate and reinforcement frequency on single variable-interval avoidance schedules was accurately described by Herrnstein's (1970) equation for responding on single variable-interval schedules of positive reinforcement. On multiple variable-interval avoidance schedules with brief components, asymptotic relative response rate matched relative shock-frequency reduction. The results suggest that many interactions between response rates and shock-frequency reduction in avoidance can be understood within the framework of the generalized matching relation, as applied by Herrnstein (1970) to positive reinforcement.     

Independence of response force and reinforcement rate on concurrent variable-interval schedule performance

Five pigeons were trained over 43 experimental conditions on a variety of concurrent variable-interval schedules on which the forces required on the response keys were varied. The results were well described by the generalized matching law with log reinforcement ratios and log force ratios exerting independent (noninteractive) effects on preference. A further analysis using the Akaike criterion, an information-theoretic measure of the efficiency of a model, showed that overall reinforcement rate and overall force requirement did not affect preference. Unlike reinforcement rate changes, force requirement increases did not change the response rate on the alternate key, and an extension of Herrnstein's absolute response rate function for force variation on a single variable-interval schedule is suggested.     

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.     

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.     

Relative reinforcer magnitude under a nonindependent concurrent schedule of cocaine reinforcement in rhesus monkeys.

Lever pressing by three rhesus monkeys was maintained under a two-lever concurrent schedule of cocaine reinforcement. Responding on one lever (constant-dose lever) produced a constant dose of 0.05 or 0.1 mg/kg/injection arranged according to a variable-interval 1-min schedule. Responding on the other lever (variable-dose lever) produced a comparison dose of cocaine (0.013 to 0.8 mg/kg/injection), also under a variable-interval 1-min schedule. The two variable-interval schedules were made nonindependent by arranging that the assignment of a reinforcer by one schedule inactivated the second schedule until the assigned reinforcer had been obtained. This modification ensured that the two cocaine doses were obtained with approximately equal frequency, regardless of the distribution of the subject's responding. Preference, indicated by relative response frequency on the variable-dose lever, was almost always for the larger of the doses and was a monotonic function of the comparison dose, except at the highest doses. Preferences at the highest comparison doses may have resulted from the low overall response rates exhibited at these doses. Relative response frequencies on the variable-dose lever roughly matched relative reinforcer magnitude (mg/kg/injection available on the variable-dose lever divided by the sum of mg/kg/injections available on each lever).     

The effect of signaled reinforcement availability on concurrent performances in humans

During Phase I, three female human subjects pressed a button for monetary reinforcement in two-component concurrent variable-interval schedules. Five different reinforcement frequencies were used in component A, whereas the reinforcement frequency in component B was held constant. Absolute rates of responding conformed to equations proposed by Herrnstein to describe concurent performances, and the ratios of the response rates and the times spent in the two components conformed to the matching law. During Phase II, the availability of reinforcement in component A was signaled by the illumination of a lamp. This resulted in suppression of response rates in component A and elevation of response rates in component B, these changes being reflected in a distortion of the matching relationship which took the form of a bias in favor of component B.     

Schedule-induced licking during multiple schedules

Schedule-induced polydipsia was studied in rats bar pressing under two-component multiple schedules of food reinforcement. The first component of the multiple schedule was a variable-interval 1-min schedule throughout the experiment. The schedule comprising the second component was varied over blocks of sessions in terms of rate and magnitude of reinforcement, and was either variable-interval 3-min (one pellet), variable-interval 3-min (three pellets), variable-interval 1-min (one pellet), or extinction. Water intake per session varied with the rate of reinforcement in the schedule comprising the second component and was highest when the schedule was variable-interval 1-min. Both bar-pressing behavior and licking behavior showed behavioral interactions between the two components of the multiple schedules. With magnitude of reinforcement held constant, a matching relationship was observed between lick rate and reinforcement rate; the relative frequency of licks in the constant component matched the relative frequency of reinforcement in that component. Bar pressing, however, showed only a moderate degree of relativity matching. During the schedule-induced licking, a burst of licking followed each delivery of a pellet (post-prandial drinking). The duration of these bursts of licking was observed to be a function of the inter-reinforcement interval.     

Choice behavior and the accessibility of the reinforcer

In Experiment 1, matching of relative response rates to relative rates of reinforcement was obtained in concurrent variable-interval schedules when the absolute values of the two concurrent variable-interval schedules varied from 6 sec and 12 sec to 600 sec and 1200 sec. Increases in the duration of the changeover delay, however, produced decreases in the relative response rates and, consequently, some deviation from matching. In Experiment 2, matching of relative response rates to the relative duration of the reinforcer failed to occur when the equal variable-interval schedules arranging access to the two different reinforcer durations (1.5 and 6 sec) were varied in size from concurrent variable-interval 10-sec schedules to concurrent variable-interval 600-sec schedules.     

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

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

Concurrent second-order schedules of reinforcement

Responses on one key (the main key) of a two-key chamber produced food according to a second-order variable-interval schedule with fixed-interval schedule components. A response on a second key (the changeover key) alternated colors on the main key and provided a second independent second-order variable-interval schedule with fixed-interval components. The fixed-interval component on one variable-interval schedule was held constant at 8 sec, while the fixed interval on the other variable-interval schedule was varied from 0 to 32 sec. Under some conditions, a brief stimulus terminated each fixed interval and generated fixed-interval patterns; in other conditions, the brief stimulus was omitted. Relative response rate and relative time deviated substantially from scheduled relative reinforcement rate and, to a lesser extent, from obtained relative reinforcement rate under both brief-stimulus and no-stimulus conditions. Matching was observed with equal components on both schedules; with unequal components, increasingly greater proportions of time and responses than the matching relation would predict were spent on the variable-interval schedule containing the shorter component. Preference for the shorter fixed interval was typically more extreme under brief-stimulus than under no-stimulus schedules. The results limit the extension of the matching relation typically observed under simple concurrent variable-interval schedules to concurrent second-order variable-interval schedules.     

Duration and rate of reinforcement as determinants of concurrent responding

The duration and frequency of food presentation were varied in concurrent variable-interval variable-interval schedules of reinforcement. In the first experiment, in which pigeons were exposed to a succession of eight different schedules, neither relative duration nor relative frequency of reinforcement had as great an effect on response distribution as they have when they are manipulated separately. These results supported those previously reported by Todorov (1973) and Schneider (1973). In a second experiment, each of seven pigeons was exposed to only one concurrent schedule in which the frequency and/or duration of reinforcement differed on the two keys. Under these conditions, each pigeon's relative rate of response closely matched the relative total access to food that each schedule provided. This result suggests that previous failures to obtain matching may be due to factors such as an insufficient length of exposure to each schedule or to the pigeons' repeated exposure to different concurrent schedules.     

Force and rate relations in responding during variable-interval reinforcement

Four rats responded on one-minute variable-interval schedules with several variations in peak-force of response required for food reinforcement. Measures of peak force and rate were taken for the responses, which were the downward exertions of force against a static force-transducing operandum. The analysis distinguished responses, a generic class of measured behavior, from criterion responses, an operationally specified subclass required for reinforcement. Absolute rate of response showed no systematic change, but the rate of responses meeting a newly required criterion of peak-force invariably increased through changes in the absolute rate of response, the relative-frequency distributions of peak force, or some combination of both. The relative frequency of responses meeting an elevated force criterion during variable-interval reinforcement exceeded that maintained with the same criterion with continuous reinforcement. The requirement of more effortful responding for reinforcement does not necessarily reduce response rate. Conformity of the behavior to the requirement for reinforcement is the salient effect.     

The generality of selective observing

Four rats obtained food pellets by poking a key and 5-s presentations of the discriminative stimuli by pressing a lever. Every 1 or 2 min, the prevailing schedule of reinforcement for key poking alternated between rich (either variable-interval [VI] 30 s or VI 60 s) and lean (either VI 240 s, VI 480 s, or extinction) components. While the key was dark (mixed-schedule stimulus), no exteroceptive stimulus indicated the prevailing schedule. A lever press (i.e., an observing response), however, illuminated the key for 5 s with either a steady light (S+), signaling the rich reinforcement schedule, or a blinking light (S-), signaling the lean reinforcement schedule. One goal was to determine whether rats would engage in selective observing (i.e., a pattern of responding that maintains contact with S+ and decreases contact with S-). Such a pattern was found, in that a 5-s presentation of S+ was followed relatively quickly by another observing response (which likely produced another 5-s period of S+), whereas exposure to S- resulted in extended breaks from observing. Additional conditions demonstrated that the rate of observing remained high when lever presses were effective only when the rich reinforcement schedule was in effect (S+ only condition), but decreased to a low level when lever presses were effective only during the lean reinforcement component (S- only condition) or when lever presses had no effect (in removing the mixed stimulus or presenting the multiple-schedule stimuli). These findings are consistent with relativistic conceptualizations of conditioned reinforcement and extend the generality of selective observing to procedures in which the experimenter controls the duration of stimulus presentations, the schedule components both offer intermittent food reinforcement, and rats serve as subjects.     

Performance of humans in variable-interval avoidance schedules programmed singly, and concurrently with variable-interval schedules of positive reinforcement

Performance maintained under single variable-interval avoidance schedules, single variable-interval schedules of positive reinforcement, and concurrent schedules consisting of a variable-interval avoidance component and a variable-interval positive reinforcement component, was studied in three human subjects, using points exchangeable for money as the reinforcer. Response rate in the single variable-interval avoidance schedules was an increasing function of the frequency of monetary loss avoidance. Response rate in the single variable-interval positive reinforcement schedules was an increasing function of the frequency of obtained monetary reinforcement. In the concurrent avoidance/reinforcement schedules, the rate of responding in the avoidance component increased, and the rate of responding in the positive reinforcement schedule decreased (with one exception) as a function of the frequency of loss avoidance in the avoidance component. The logarithms of the ratios of the response rates in the two components, and the logarithms of the ratios of the times spent in the two components, were linearly related to the logarithms of the ratios of the frequency of loss avoidance in the avoidance component to the frequency of reinforcement in the positive reinforcement component. All three subjects exhibited marked undermatching of response rate ratios to reinforcement frequency ratios. The results are discussed in the context of Herrnstein's quantitative model of operant performance.     

Performances on ratio and interval schedules of reinforcement: Data and theory

Two differences between ratio and interval performance are well known: (a) Higher rates occur on ratio schedules, and (b) ratio schedules are unable to maintain responding at low rates of reinforcement (ratio “strain”). A third phenomenon, a downturn in response rate at the highest rates of reinforcement, is well documented for ratio schedules and is predicted for interval schedules. Pigeons were exposed to multiple variable-ratio variable-interval schedules in which the intervals generated in the variable-ratio component were programmed in the variable-interval component, thereby “yoking” or approximately matching reinforcement in the two components. The full range of ratio performances was studied, from strained to continuous reinforcement. In addition to the expected phenomena, a new phenomenon was observed: an upturn in variable-interval response rate in the midrange of rates of reinforcement that brought response rates on the two schedules to equality before the downturn at the highest rates of reinforcement. When the average response rate was corrected by eliminating pausing after reinforcement, the downturn in response rate vanished, leaving a strictly monotonic performance curve. This apparent functional independence of the postreinforcement pause and the qualitative shift in response implied by the upturn in variable-interval response rate suggest that theoretical accounts will require thinking of behavior as partitioned among at least three categories, and probably four: postreinforcement activity, other unprogrammed activity, ratio-typical operant behavior, and interval-typical operant behavior.     

Run length, visit duration, and reinforcers per visit in concurrent performance

The contingencies in each alternative of concurrent procedures consist of reinforcement for staying and reinforcement for switching. For the stay contingency, behavior directed at one alternative earns and obtains reinforcers. For the switch contingency, behavior directed at one alternative earns reinforcers but behavior directed at the other alternative obtains them. In Experiment 1, responses on the main lever, in S1, incremented stay and switch schedules and obtained a stay reinforcer when it became available. Responses on the switch lever changed S1 to S2 and obtained switch reinforcers when available. In S2, neither responses on the main lever nor on the switch lever were reinforced, but a switch response changed S2 to S1. Run lengths and visit durations were a function of the ratio of the scheduled probabilities of reinforcement (staying/switching). From run lengths and visit durations, traditional concurrent performance was synthesized, and that synthesized performance was consistent with the generalized matching law. Experiment 2 replicated and extended this analysis to concurrent variable-interval schedules. The synthesized results challenge any theory of matching that requires a comparison among the alternatives.     

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.     

Time-based and count-based measurement of preference

Rats' pressing on two levers was reinforced according to two independent variable-interval schedules that were varied during the experiment. Since the levers were connected directly to the programming equipment, bypassing the standard pulseformers, reinforcement could occur while a lever was held down. Although the time a lever was pressed might, therefore, have varied independently of number of presses, these two measures covaried substantially, because the average duration of the presses remained roughly constant. This rough invariance may have resulted from the rats' tendency to make bursts of brief presses (i.e., to jiggle the levers), even though the contingencies encouraged holding. When duration did vary, presses on the two levers tended to vary together. As a result, relative time spent pressing corresponded closely to relative number of presses. Both of these measures conformed well to the matching law. Absolute behavioral frequency at a lever, measured either way, varied directly with proportion of reinforcement for that lever, in accordance with the generalized version of the matching law. Number of presses seemed, on balance, to be a slightly more reliable measure than pressing time. The substantial interchangeability may prove more significant than the slight disparity, however, because it supports the notion that all behavior can be measured on a common scale of time.