Rats' performance on variable-interval schedules with a linear feedback loop between response rate and reinforcement rate

Three experiments investigated whether rats are sensitive to the molar properties of a variable-interval (VI) schedule with a positive relation between response rate and reinforcement rate (i.e., a VI+ schedule). In Experiment 1, rats responded faster on a variable ratio (VR) schedule than on a VI+ schedule with an equivalent feedback function. Reinforced interresponse times (IRTs) were shorter on the VR as compared to the VI+ schedule. In Experiments 2 and 3, there was no systematic difference in response rates maintained by a VI+ schedule and a VI schedule yoked in terms of reinforcement rate. This was found both when the yoking procedure was between-subject (Experiment 2) and within-subject (Experiment 3). Mean reinforced IRTs were similar on both the VI+ and yoked VI schedules, but these values were more variable on the VI+ schedule. These results provided no evidence that rats are sensitive to the feedback function relating response rate to reinforcement rate on a VI+ schedule.     

Temporally spaced responding by pigeons: development and effects of deprivation and extinction

In the first five or six sessions on a DRL 20-sec schedule of reinforcement there developed a stable performance characterized by a relatively constant conditional probability of occurrence (IRTs/op) of interresponse times (IRTs) of durations greater than 5 or 6 sec. Extinction and the level of deprivation changed both the overall rate of responding and the form of the function relating the duration of an IRT to its value of IRTs/op. The value of IRTs/op decreased more rapidly for short than for longer IRTs, resulting in the emergence of a finer discrimination of IRT duration.     

Differential reinforcement of interresponse times with controlled probability of reinforcement per response

Pigeons were presented food after interresponse times (IRTs) longer or shorter than a fixed percentage of their most recent IRTs. This procedure controlled probability of reinforcement per response while still allowing different classes of IRTs to be reinforced differentially. Support was found for IRT-reinforcement theory in that response rates were determined by the degree and direction of differential reinforcement of IRTs, but were relatively independent of probability of reinforcement per response and of the length of the control system's IRT memory. Stimulus control of these differential response rates was also demonstrated.     

Briefly delayed reinforcement: An interresponse time analysis

Key-peck responding of pigeons was compared under VI or DRL schedules arranging immediate reinforcement and briefly (.5 sec) delayed reinforcement. Delays were either signaled by a blackout in the chamber, unsignaled, or unsignaled with an additional requirement that responding not occur during the .5 sec interval immediately preceding reinforcement (response delay). Relative to the immediate reinforcement condition, response rates increased during the unsignaled delay, decreased during the signaled delay, and were inconsistent during the response delay condition. An analysis of interresponse times (IRTs) under the different conditions revealed a substantial increase in the frequency of short (0 to .5 sec) IRTs during the unsignaled condition and generally during the response delay conditions compared to that during the immediate reinforcement baseline. Signaled delays decreased the frequency of short (0 to .5 sec) IRTs relative to the immediate reinforcement condition. The results suggest that brief unsignaled delays and, in many instances, response delays increase the frequency of short IRTs by eliminating constraints on responding.     

Frequency distribution of interresponse times during VI and VR reinforcement

A detailed analysis was made of the interresponse times (IRTs) of two rats under both a VI 40-sec and a VR 15-sec schedule. Except for the latency of the first response after a reinforcement, the mean IRTs of all further responses differed little. Similarly, the frequency distributions of the successive IRTs did not vary greatly, but were of no simple form. Sequential dependencies between successive IRTs were small, never accounting for more than 1% of the variance.     

The Isolation of Motivational, Motoric, and Schedule Effects on Operant Performance: A Modeling Approach

Dissociating motoric and motivational effects of pharmacological manipulations on operant behavior is a substantial challenge. To address this problem, we applied a response‐bout analysis to data from rats trained to lever press for sucrose on variable‐interval (VI) schedules of reinforcement. Motoric, motivational, and schedule factors (effort requirement, deprivation level, and schedule requirements, respectively) were manipulated. Bout analysis found that interresponse times (IRTs) were described by a mixture of two exponential distributions, one characterizing IRTs within response bouts, another characterizing intervals between bouts. Increasing effort requirement lengthened the shortest IRT (the refractory period between responses). Adding a ratio requirement increased the length and density of response bouts. Both manipulations also decreased the bout‐initiation rate. In contrast, food deprivation only increased the bout‐initiation rate. Changes in the distribution of IRTs over time showed that responses during extinction were also emitted in bouts, and that the decrease in response rate was primarily due to progressively longer intervals between bouts. Taken together, these results suggest that changes in the refractory period indicate motoric effects, whereas selective alterations in bout initiation rate indicate incentive‐motivational effects. These findings support the use of response‐bout analyses to identify the influence of pharmacological manipulations on processes underlying operant performance.     

The microanalysis of fixed-interval responding

The fixed-interval schedule of reinforcement is one of the more widely studied schedules in the experimental analysis of behavior and is also a common baseline for behavior pharmacology. Despite many intensive studies, the controlling variables and the pattern of behavior engendered are not well understood. The present study examined the microstructure and superstructure of the behavior engendered by a fixed-interval 5- and a fixed-interval 15-minute schedule of food reinforcement in the pigeon. Analysis of performance typical of fixed-interval responding indicated that the scalloped pattern does not result from smooth acceleration in responding, but, rather, from renewed pausing early in the interval. Individual interresponse-time (IRT) analyses provided no evidence of acceleration. There was a strong indication of alternation in shorter-longer IRTs, but these shorter-longer IRTs did not occur at random, reflecting instead a sequential dependency in successive IRTs. Furthermore, early in the interval there was a high relative frequency of short IRTs. Such a pattern of early pauses and short IRTs does not suggest behavior typical of reinforced responding as exemplified by the pattern found near the end of the interval. Thus, behavior from clearly scalloped performance can be classified into three states: postreinforcement pause, interim behavior, and terminal behavior.     

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.     

Response rate viewed as engagement bouts: effects of relative reinforcement and schedule type.

The rate of a reinforced response is conceptualized as a composite of engagement bouts (visits) and responding during visits. Part I of this paper describes a method for estimating the rate of visit initiations and the average number of responses per visit from log survivor plots: the proportion) of interresponse times (IRTs) longer than some elapsed time (log scale) plotted as a function of elapsed time. In Part 2 the method is applied to IRT distributions from rats that obtained food pellets by nose poking a lighted key under various multiple schedules of reinforcement. As expected, total response rate increased as a function of (a) increasing the rate of reinforcement (i.e., variable-interval [VI] 4 min vs. VI 1 mi), (b) increasing the amount of the reinforcer (one food pellet vs. four pellets), (c) increasing the percentage of reinforcers that were contingent on nose poking (25% vs. 100%), and (d) requiring additional responses after the end of the VI schedule (i.e., adding a tandem variable-ratio [VR] 9 requirement). The first three of these variables (relative reinforcement) increased the visit-initiation rate. The tandem VR, in contrast, increased the number of responses per visit. Thus, variables that have similar effects on total response rate can be differentiated based on their effects on the componemts of response rate.     

Discrimination and emission of temporal intervals by pigeons

Because the frequency distribution of IRTs showed little or no control by a DRL schedule, the schedule was modified so that the pigeon's behavior after each IRT would indicate whether or not it had discriminated the duration of the IRT. After every two pecks on a red key, the key changed to blue for 30 sec. Then it automatically became red again. Pecks on the blue key were reinforced with food on a VI schedule only when the preceding IRT on the red key had been longer than 18 sec. The birds did not selectively emit longer IRTs on the red key: the value of IRTs/op did not increase with IRT duration. However, they did discriminate the duration of the IRT emitted on the red key: the rate of pecking on the blue key was an increasing function of the duration of the preceding IRT on the red key.     

IRT-stimulus contingencies in chained schedules: implications for the concept of conditioned reinforcement

Two experiments with pigeons investigated the effects of contingencies between interresponse times (IRTs) and the transitions between the components of 2- and 4-component chained schedules (Experiments 1 and 2, respectively). The probability of component transitions varied directly with the most recent (Lag 0) IRT in some experimental conditions and with the 4th (Lag 4) IRT preceding the most recent one in others. Mean component durations were constant across conditions, so the reinforcing effect of stimulus change was dissociated from that of delay to food. IRTs were longer in the Lag-0 than in the Lag-4 conditions of both experiments, thus demonstrating that stimulus change functioned as a reinforcer. In the Lag-0 conditions of Experiment 2, the Component-1 IRTs increased more than the Component-2 IRTs, which in turn increased more than the Component-3 IRTs. This finding runs counter to the conditioned-positive-reinforcement account of chained-schedule responding, which holds that the reinforcing effect of stimulus change should vary in strength as an inverse function of the delay to the unconditioned reinforcer at the end of the chain because conditioned reinforcement is due to first- or higher-order classical conditioning. Therefore, we present other possible explanations for this effect.     

Performance on ratio and interval schedules with matched reinforcement rates

In the first study, rats were trained to pull a chain on a schedule (RPI) that regulates the probability of reinforcement to maintain a constant average reinforcement rate without differentially reinforcing long inter-response times (IRTs). Although the response rate was sensitive to the overall rate of reinforcement, performance was unaffected by variations between 1 and 50 in the IRT memory size used in programming the schedule. In the second study, two groups of animals performed on either a random-interval (RI) schedule or a RPI schedule, with reinforcement rates determined by those generated by a third group performing on a random ratio (RR) 20 schedule. The RI group responded at a lower rate than the RPI group, which, in turn, responded at a lower rate than the RR group, even though the three groups experienced comparable rates of reinforcement. The fact that the RPI group responded at a lower rate than the RR group suggests that the standard response rate difference observed between ratio and interval schedules, which have been matched for reinforcement rate, cannot be attributed solely to the fact that conventional interval schedules differentially reinforce long IRTs.     

Reinforcement rate and interresponse time differentiation

Reinforcement rate and differential reinforcement of IRTs were independently manipulated to assess their relative contribution to the control of interresponse times (IRTs). Modified percentile reinforcement schedules (Platt, 1973) allowed control of reinforcement rate while longest or shortest IRTs were selectively reinforced. In the absence of differential IRT reinforcement, mean IRT decreased with increasing reinforcement rate. Compared to this small effect of reinforcement rate, reinforcement of long IRTs produced large changes in mean IRT at constant reinforcement rates. No interaction of reinforcement rate and IRT reinforcement was detected. The demonstration of large IRT changes in the absence of reinforcement-rate changes indicates the precedence of IRT reinforcement over molar reinforcement-rate correlations in the determination of IRTs in these procedures.     

Effects of hunger and VI value on VI pacing

In two experiments, each involving four rats, responses preceded by an inter-response time between 8 and 10 sec in duration were intermittently reinforced. In Experiment I, final performance was compared under two hunger levels, while the frequency of reinforcement was held constant by a VI 5 schedule. In Experiment II, hunger was held constant and VI 3 was compared with VI 8. Both hunger and frequency of reinforcement increased the over-all rate of response, but the exact effects of these operations on temporal discrimination were different for different rats. Usually, a peak “response probability” (IRTs/Op ratio) was obtained 8 to 10 sec after the preceding response, indicating adaptation to the reinforcement contingency, but in some cases this peak was about 2 sec earlier. One rat exhibited unusually pronounced bursting which seemed to alternate with adaptive temporally spaced responding. Prolonged pauses, observable in the cumulative records, particularly following reinforcement, were attributed to the fact that inter-response times greater than 10 sec were not reinforced, so that as the interval of time since the preceding response became discriminably greater than 10 sec, the probability of a response became small.     

Response rate and sensitivity to the molar feedback function relating response and reinforcement rate on VI+ schedules of reinforcement

In 5 experiments, the author examined rats' sensitivity to the molar feedback function relating response rate to reinforcement rate on schedules of reinforcement. These studies demonstrated that, at lower rates of responding, rats' performance on variable ratio (VR), variable interval (VI), and variable interval with linear feedback loop (VI+) schedules was determined largely by reinforcement of interresponse times; response rates were faster on VR than on both VI and VI+ schedules. In contrast, when procedures were adopted to maintain high rates of response, rats showed sensitivity to the molar characteristics of the schedules; they responded as fast on a VI+ schedule as on a VR schedule and faster on both of these schedules than on a yoked VI schedule. When the variance of response rate was manipulated, this factor was noted as an important element in determining sensitivity to the molar characteristics of the schedule.     

The distribution of interresponse times in the pigeon during variable-interval reinforcement

Three pigeons' pecks were reinforced on 1- and 2-min variable-interval schedules, and frequency distributions of their interresponse times (IRTs) were recorded. The conditional probability that a response would fall into any IRT category was estimated by the interresponse-times-per-opportunity transformation (IRTs/op). The resulting functions were notable chiefly for the relatively low probability of IRTs in the 0.2- to 0.3-sec range; in other respects they varied within and between subjects. The overall level of the curves generally rose over the course of 32 experimental hours, but their shapes changed unsystematically. The shape of the IRT distribution was much the same for VI 1-min and VI 2-min. The variability of these distributions supports the notion that the VI schedule only loosely controls response rate, permitting wide latitude to adventitious effects. There was no systematic evidence that curves changed over sessions to conform to the distribution of reinforcements by IRT.     

A comparison of procedures for programming noncontingent reinforcement schedules

We compared two methods for programming and thinning noncontingent reinforcement (NCR) schedules during the treatment of self-injurious behavior (SIB). The participants were 3 individuals who had been diagnosed with mental retardation. Results of functional analyses indicated that all participants' SIB was maintained by positive reinforcement (i.e., access to attention or food). Following baseline, the effects of two NCR schedule-thinning procedures were compared in multielement designs. One schedule (fixed increment) was initially set at fixed-time 10-s reinforcer deliveries and was also thinned according to fixed-time intervals. The other schedule (adjusting IRT) was initially determined by participants' baseline interresponse times (IRTs) for SIB and was thinned based on IRTs observed during subsequent treatment sessions. Results indicated that both schedules were effective in initially reducing SIB and in maintaining response suppression as the schedules were thinned.     

Some properties of spaced responding in pigeons

Pigeons exposed to a schedule which reinforces interresponse times (IRTs) longer than a given value (DRL schedule) eventually reach a stable pattern of responding which is shown to be a function both of the DRL value and of previous experience with other DRL values. On any given DRL schedule, the stable performance of most pigeons which have been previously exposed to a variety of such schedules, shows an IRT distribution with median equal to the DRL value. For DRL values longer than about 30 sec, however, the median IRT falls short of the DRL value; this failure of adjustment to longer values appears to be a species characteristic of pigeons. The function relating reinforcement rate to 1/DRL value is also shown to be approximately linear over the same range, with variable slope (less than 45°) and a downturn in the vicinity of DRL 30.     

Resurgence and downshifts in alternative reinforcement rate

Resurgence refers to an increase in a previously suppressed target behavior with a relative worsening of conditions for a more recently reinforced alternative behavior. This experiment examined the relation between resurgence and the magnitude of a reduction in the rate of reinforcement for the alternative behavior. Groups of both male and female rats initially pressed a target lever for food on a variable-interval (VI) 30-s schedule. In a second phase, responding to the target lever was extinguished for all groups and pressing an alternative lever was reinforced on a VI 10-s schedule. Next, the rate of reinforcement for alternative behavior was reduced differentially across groups by arranging extinction, VI 80-s, VI 40-s, VI 20-s, or continued VI 10-s reinforcement. Target responding increased as an exponential function of the magnitude of the reduction in alternative reinforcement rates. With the exception that males appeared to show higher rates of target responding in baseline and higher rates of alternative responding in other phases, the overall pattern of responding across phases was not meaningfully different between sexes. The pattern of both target and alternative response rates across sessions and phases was well described quantitatively by the Resurgence as Choice in Context model.     

Interresponse-time sensitivity during discrete-trial and free-operant concurrent variable-interval schedules

Two experiments investigated the sensitivity of pigeons' choice to elapsed time since the last response (i.e., to inter-response time [IRT]) during concurrent variable-interval variable-interval schedules. Experiment 1 used a two-key discrete-trial procedure with variable intertrial intervals. Experiment 2 employed a three-key free-operant procedure. In both experiments choice was found to be a function of the active-schedule IRT, defined as the time since the most recent response. Monte Carlo simulations show how this finding permits the joining of several seemingly incompatible data sets held to both support and contradict a kind of choice strategy, termed momentary maximizing, which attempts to maximize momentary reinforcement probabilities. The studies suggest that only two variables are needed to describe the static molecular structure of concurrent variable-interval choice: active-schedule IRTs and "response states" consisting of the last one or two schedule choices.