Alternative fixed-ratio fixed-interval schedules of reinforcement

Five rats were trained under alternative fixed-ratio fixed-interval schedules, in which food reinforcement was provided for the completion of either a fixed-ratio or a fixed-interval requirement, whichever was met first. Overall response rate and running rate (the rate of responding after the postreinforcement pause) decreased for all subjects as the fixed-ratio value increased. As the proportion of reinforcements obtained from the fixed-ratio component increased and the alternative schedule approached a simple fixed ratio, overall response rate and running rate both increased; conversely, as the proportion of reinforcements obtained from the fixed-interval component increased and the alternative schedule approached a simple fixed interval, response rates decreased. Postreinforcement pause length increased linearly as the average time between reinforcements increased, regardless of the schedule parameters. A break-run pattern of responding was predominant at low- and medium-valued fixed ratios. All subjects displayed at least occasional positively accelerated responding within interreinforcement intervals at higher fixed-ratio values.     

Determinants of pausing under variable-ratio schedules: Reinforcer magnitude, ratio size, and schedule configuration

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Phase 1 assessed the effects of differences in reinforcer magnitude on postreinforcement pausing, as a function of ratio size. In Phase 2, postreinforcement pausing and the first five interresponse times in each ratio were measured as a function of differences in reinforcer magnitude under equal variable-ratio schedules consisting of different configurations of individual ratios. Rates were also calculated exclusive of postreinforcement pause times in both phases. The results from Phase 1 showed that as ratio size increased, the differences in pausing educed by unequal reinforcer magnitudes also increased. The results of Phase 2 showed that the effects of reinforcer magnitude on pausing and IRT durations were a function of schedule configuration. Under one configuration, in which the smallest ratio was a fixed-ratio 1, pauses were unaffected by magnitude but the first five interresponse times were affected. Under the other configuration, in which the smallest ratio was a fixed-ratio 7, pauses were affected by reinforcer magnitude but the first five interresponse times were not. The effect of each configuration seemed to be determined by the value of the smallest individual ratio. Rates calculated exclusive of postreinforcement pause times were, in general, directly related to reinforcer magnitude, and the relation was shown to be a function of schedule configuration.     

Aftereffects of reinforcement on variable-ratio schedules

On each of variable-ratio 10, 40, and 80 schedules of reinforcement, when rats' lever-pressing rates were stable, the concentration of a liquid reinforcer was varied within sessions. The duration of the postreinforcement pause was an increasing function of the reinforcer concentration, this effect being more marked the higher the schedule parameter. The running rate, calculated by excluding the postreinforcement pause, was unaffected by concentration. The duration of the postreinforcement pause increased with the schedule parameter, but the proportion of the interreinforcement interval taken up by the pause decreased. Consequently, the overall response rate was an increasing function of the schedule parameter; i.e., it was inversely related to reinforcement frequency, contrary to the law of effect. The running rate, however, decreased with the reinforcement frequency, in accord with the law of effect. When 50% of reinforcements were randomly omitted, the postomission pause was shorter than the postreinforcement pause, but the running rate of responses was not affected.     

Effects of ethanol on multiple fixed-interval fixed-ratio schedule performances: dynamic interactions at different fixed-ratio values.

Key pecking by three pigeons was maintained under a multiple fixed-interval fixed-ratio schedule of food presentation. The fixed-interval value remained at 3 minutes, while the fixed-ratio size was increased systematically in 30-response increments from 30 to either 120 (two pigeons) or 150 (one pigeon). At least two lower fixed-ratio values were also redetermined. The effects of ethanol (5 to 2.5 g/kg) were assessed at each of the different schedule parameters. Both overall and running response rates under the fixed-ratio schedule decreased with increases in the size of the fixed-ratio schedule; pause duration under the fixed-ratio schedule was directly related to increases in fixed-ratio size. Overall and running rates of responding under the fixed-interval schedule changed little with increases in the size of the fixed-ratio schedule. Despite the relative invariance of fixed-interval responding across the different fixed-ratio values, the effects of ethanol on responding under the fixed-interval schedule differed depending on the size of the fixed-ratio schedule. Greater increases occurred in both overall and in lower local rates of responding under the fixed-interval schedule when the fixed-ratio value was 120 or 150. The effects of ethanol on responding under the fixed-ratio schedule also depended on the size of the fixed ratio. Increases in responding under the fixed-ratio schedule were typically greater at the higher fixed-ratio values where response rates were lower. When the effects of ethanol were redetermined at the lower fixed-ratio parameter values, rates and patterns of responding were comparable to those obtained initially. However, the dose-effect curves for responding under both fixed-ratio and fixed-interval schedules were shifted up and to the right of those determined during the ascending series. The effects of ethanol can depend on rate or responding, behavioral history, and the context in which behavior occurs.     

EFFECT OF REINFORCER MAGNITUDE ON PERFORMANCE MAINTAINED BY PROGRESSIVE‐RATIO SCHEDULES

This experiment examined the relationship between reinforcer magnitude and quantitative measures of performance on progressive‐ratio schedules. Fifteen rats were trained under a progressive‐ratio schedule in seven phases of the experiment in which the volume of a 0.6‐M sucrose solution reinforcer was varied within the range 6–300 μl. Overall response rates in successive ratios conformed to a bitonic equation derived from Killeen's (1994) Mathematical Principles of Reinforcement. The “specific activation” parameter, a, which is presumed to reflect the incentive value of the reinforcer, was a monotonically increasing function of reinforcer volume; the “response time” parameter, δ, which defines the minimum response time, increased as a function of reinforcer volume; the “currency” parameter, b, which is presumed to reflect the coupling of responses to the reinforcer, declined as a function of volume. Running response rate (response rate calculated after exclusion of the postreinforcement pause) decayed monotonically as a function of ratio size; the index of curvature of this function increased as a function of reinforcer volume. Postreinforcement pause increased as a function of ratio size. Estimates of a derived from overall response rates and postreinforcement pauses showed a modest positive correlation across conditions and between animals. Implications of the results for the quantification of reinforcer value and for the use of progressive‐ratio schedules in behavioral neuroscience are discussed.     

The role of verbal behavior in human learning: infant performance on fixed-interval schedules

The performances of two infants less than one year old were investigated on fixed-interval schedules. When the infants touched a cylinder either music or food was presented according to fixed-interval schedules ranging in value from 10 to 50 seconds. With respect to two principal criteria, namely, pattern of responding and sensitivity to the schedule parameter, the subjects' behavior closely resembled that of animals but differed markedly from that of older children and adults. Negatively accelerated responding in the course of the fixed interval in the early sessions gave way to a scalloped pattern, consisting of a pause after reinforcement followed by an accelerated response rate. This scalloped pattern was the final form of responding on all schedule values. Analysis of data after performance had stabilized showed that postreinforcement pause was a negatively accelerated increasing function, and running rate (calculated after excluding the postreinforcement pause) was a declining function, of schedule value. On each schedule, the durations of mean successive interresponse times declined in the course of the fixed interval and were directly related to schedule value. The results supported Lowe's (1979) suggestion that verbal behavior may be responsible for major differences in the schedule performance of older humans and animals.     

Food deliveries during the pause on fixed-interval schedules

Pigeons were trained on fixed-interval schedules of food delivery. In Experiments I and II, the fixed interval was initiated by the previous fixed-interval reinforcer; in Experiment III, the fixed interval was initiated by the first key peck following the preceding fixed-interval reinforcer (a chain fixed-ratio one, fixed-interval schedule). During the postreinforcement pause, variable-time schedules delivered food independent of any specific response. Rate of food delivery during the pause had only small effects on pause duration in Experiments I and II. In Experiment III, however, pause duration increased systematically with the rate of food delivery during the pause. These data suggest that the momentary proximity to reinforcement delivered via the fixed-interval schedule exerts potent control over pause termination. Additional analysis revealed that pause termination was unaffected by the intermittent delivery of food during the pause. Such data suggest that the temporal control by fixed-interval schedules is highly resistant to interference.     

Progressive-ratio schedules: effects of later schedule requirements on earlier performances

Four rats were studied with variants of a progressive-ratio schedule with a step size of 6 in which different terminal components followed completion of the 20th ratio: (a) a reversal of the progression, (b) a fixed-ratio 6 schedule, or (c) extinction. Responding in the progressive-ratio components of these schedules was compared to performances under conventional progressive-ratio baselines. Under baseline conditions, postreinforcement pauses increased exponentially as a function of increasing ratio size, whereas running rates showed modest declines. The procedure of linking the progressive-ratio schedule to the reversed progression or to the fixed-ratio component resulted in decreased pausing. Linking the progressive-ratio schedule to the extinction component had the opposite effect, that of producing weakened progressive-ratio performances as evidenced by increased pausing. Subjects whose responses were reinforced on half of the ratios also showed exponential increases; however, pauses were substantially shorter following ratios on which the reinforcer was omitted. The results suggested that progressive-ratio pausing reflects the influence of remote as well as local contingencies.     

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.     

Temporal patterns of responding in small fixed-ratio schedules

Pigeons were exposed to an ascending series of small fixed-ratio schedules from fixed-ratio 1 to 7. Two of those pigeons were later placed on a fixed-ratio 30 schedule. The two primary dependent variables were the postreinforcement pause and the interresponse time. Changes in these variables under small fixed ratios were sometimes opposite to changes reported with large fixed ratios. For example, postreinforcement pauses decreased in length as the fixed-ratio requirement increased from fixed-ratio 1 to fixed-ratio 3. Also, the interresponse times early in the small fixed-ratio schedule were shorter than those immediately preceding reinforcement. These findings question the role of interresponse-time reinforcement in determining temporal patterns of responding under small fixed-ratio schedules. They also suggest that there may be a limited region in which the independent variable, fixed-ratio size, does not operate as previously described.     

The contribution of an added counter to a fixed-ratio schedule

Although previous research showed that a visual counter increased the rate of responding on a large fixed-ratio schedule, a theoretical analysis of the factors responsible for fixed-ratio performance suggests that the primary control by number of responses since reinforcement is to weaken the performance. The present experiment employed a multiple schedule in which the same fixed-ratio value alternated with and without an added counter. It tested the hypothesis that the differential reinforcement of high-rate responding masked the attenuation of the fixed-ratio performance from the unoptimal discriminative control produced by the fixed relation between number of responses and reinforcement. In the present experiment the postreinforcement pause was consistently longer in the components with the added counter, while running rates remained comparable between the components of the multiple schedule. Both components of the multiple schedule involved differential reinforcement of high-rate responding while only the components with the added counter amplified the discriminative control by number of pecks since reinforcement.     

Conjunctive schedules of reinforcement: III. A fixed-interval adjusting fixed-ratio schedule

Key pecking of three pigeons was studied under a conjunctive schedule that specified both a fixed-interval and an adjusting fixed-ratio requirement. The fixed-interval schedule was 6 min for one pigeon and 3 min for the other two. The size of the ratio requirement was determined within each cycle of the fixed interval by the duration of the pause before responding began. The fixed-ratio value was at maximum at the start of each fixed interval and decreased linearly until the first response occurred (adjusting fixed-ratio schedule). A peck produced food when the number of responses remaining on the fixed-ratio schedule was completed and when the fixed interval had elapsed. If no response occurred during the interval, the fixed-ratio requirement decreased to one and a single response after the interval elapsed produced food. The initial value of the adjusting fixed-ratio schedule was studied over a range of 0 to 900. Increases in the adjusting fixed-ratio schedule to about 300 responses increased both pause duration and running response rate and also modified the pattern of responding from that obtained under the fixed-interval schedule. Higher values of the adjusting fixed ratio generally decreased pause duration and running response rate and also disrupted responding. Interreinforcement time under the conjunctive schedule was increased substantially when the adjusting fixed-ratio size exceeded 300 responses.     

Effects of reinforcement magnitude on interval and ratio schedules

Rats' lever pressing was studied on three schedules of reinforcement: fixed interval, response-initiated fixed interval, and fixed ratio. In testing, concentration of the milk reinforcer was varied within each session. On all schedules, duration of the postreinforcement pause was an increasing function of the concentration of the preceding reinforcer. The running rate (response rate calculated by excluding the postreinforcement pauses) increased linearly as a function of the preceding magnitude of reinforcement on fixed interval, showed slight increases for two of the three animals on response-initiated fixed interval, and did not change systematically on fixed ratio. In all cases, the overall response rate either declined or showed no effect of concentration. The major effect of increasing the reinforcement magnitude was in determining the duration of the following postreinforcement pause, and changes in the response rate reflected this main effect.     

Species differences in temporal control of behavior II: human performance

Human subjects responded on two panels. A differential-reinforcement-of-low-rate schedule with a limited-hold contingency operated on Panel A. In Condition 1, responses on Panel B produced a stimulus on the panel that signalled whether reinforcement was available on Panel A. In Condition 2, responses on Panel B briefly illuminated a digital clock. In both conditions, performance on Panel A was very efficient; with few exceptions, Panel A was pressed only when reinforcement was available. Thus, in effect, a fixed-interval schedule operated on Panel B. In Condition 1, a “break-and-run” response pattern occurred on Panel B; with increasing temporal parameters, the duration of the postreinforcement pause on Panel B increased linearly while overall response rate and running rate (calculated by excluding the postreinforcement pauses) remained approximately constant. In Condition 2, the response pattern on Panel B was scalloped; the postreinforcement pause was a negatively accelerated increasing function of schedule value, while overall response rate and running rate were negatively accelerated decreasing functions of schedule value. The performance of subjects in Condition 2, but not in Condition 1, was highly sensitive to the contingencies in operation, and resembled that of other species on the fixed-interval schedule.     

Effects of magnitude of food reinforcement on free-operant response rates

In Experiment 1 rats were trained to press a lever on a variable-ratio schedule of food presentation and were then exposed to progressively increasing magnitudes of food reinforcement. Response running rates (rates exclusive of the postreinforcement pause) were found to increase as a function of increasing reinforcement magnitudes. The effect of reinforcement magnitude on response rates inclusive of the postreinforcement pause, however, was less pronounced. Increases in the magnitude of reinforcement were also found to increase the length of the postreinforcement pause. Rats in Experiment 2 were trained to respond on a chained differential-reinforcement-of-low-rate variable-ratio schedule, and were exposed to increasing magnitudes of reinforcement as in Experiment 1. Response running rates increased in the variable-ratio component but decreased in the other component of the schedule. The results are discussed with reference to incentive accounts of reinforcement and the action of reinforcement on the response units generated by the operative contingencies.     

Changing the response unit from a single peck to a fixed number of pecks in fixed-interval schedules

Each of three pigeons was studied first under a standard fixed-interval schedule. With the fixed interval held constant, the schedule was changed to a second-order schedule in which the response unit was the behavior on a small fixed-ratio schedule (first a fixed-ratio 10 and then a fixed-ratio 20 schedule). That is, every completion of the fixed-ratio schedule produced a 0.7-sec darkening of the key and reset the response count to zero for the next ratio. The first fixed-ratio completed after the fixed-interval schedule elapsed produced the 0.7-sec blackout followed immediately by food. These manipulations were carried out under two different fixed-interval durations for each bird ranging from 3 min to 12 min. The standard fixed-interval schedules produced the typical pause after reinforcement followed by responding at a moderate rate until the next reinforcement. The second-order schedules also engendered a pause after reinforcement, but responding occurred in bursts separated by brief pauses after each blackout. For a particular fixed-interval duration, post-reinforcement pauses increased slightly as the number of pecks in the response unit increased despite large differences in the rate and pattern of key pecking. Post-reinforcement pause increased with the fixed-interval duration under all response units. These data confirm that the allocation of time between pausing and responding is relatively independent of the rate and topography of responding after the pause.     

Responding under chained and tandem fixed-ratio schedules

The role of stimuli in chained fixed-ratio schedules of reinforcement was examined. At various ratio values, responding on schedules consisting of three or five equal components, with a different colored light in each component (“block counter”) was compared with responding on tandem or simple fixed-ratio schedules having the same color present throughout the entire ratio. At all ratio values except the smallest, the chain stimuli resulted in longer pauses after reinforcement. The magnitude of this effect became greater as the size of the ratio was increased. Post-reinforcement pause durations were longer under five-component schedules than under three-component schedules. Running rates in the first component were lower on the chained schedules than on the tandem schedules; on both kinds of schedule, rates were lower in the first component than in the rest of the ratio. When the sequence of stimuli was reversed, the duration of the post-reinforcement pause dropped markedly and the running rate in the initial component increased, but these effects gradually disappeared after the first reversal session. When the final chain stimulus was substituted for the first component stimulus but continued to appear in the final chain component as well, the pause duration dropped and remained at this lower level during subsequent sessions.     

What 50 years of research tell us about pausing under ratio schedules of reinforcement

Textbooks in learning and behavior commonly describe performance on fixed-ratio schedules as “break and run,” indicating that after reinforcement subjects typically pause and then respond quickly to the next reinforcement. Performance on variable-ratio schedules, on the other hand, is described as steady and fast, with few long pauses. Beginning with Ferster and Skinner''s magnum opus, Schedules of Reinforcement (1957), the literature on pausing under ratio schedules has identified the influences on pausing of numerous important variables, in particular ratio size and reinforcement magnitude. As a result, some previously held assumptions have been called into question. For example, research has shown that the length of the pause is controlled not only by the preceding ratio, as Ferster and Skinner and others had assumed (and as implied by the phrase postreinforcement pause), but by the upcoming ratio as well. Similarly, despite the commonly held belief that ratio pausing is unique to the fixed-ratio schedule, there is evidence that pausing also occurs under variable-ratio schedules. If such widely held beliefs are incorrect, then what about other assumptions? This article selectively examines the literature on pausing under ratio schedules over the past 50 years and concludes that although there may indeed be some common patterns, there are also inconsistencies that await future resolution. Several accounts of pausing under ratio schedules are discussed along with the implications of the literature for human performances, most notably the behaviors termed procrastination.     

Behavior controlled by scheduled injections of cocaine in squirrel and rhesus monkeys.

Rates and patterns of key-press responding maintained under schedules in which responding resulted in intravenous injections of cocaine were studied in squirrel monkeys and rhesus monkeys. Each injection was followed by a 60- or 100-sec timeout period. Schedule-controlled behavior was obtained at appropriate cocaine doses in each species. Under FR 10 or FR 30 schedules, performance was characterized by high rates of responding (usually more than one response per second) in each ratio. Under FI 5-min schedules, performance was characterized by an initial pause, followed by acceleration of responding to a final rate that was maintained until the end of the interval. Under multiple fixed-ratio fixed-interval schedules, rates and patterns of responding appropriate to each schedule component were maintained. Responding seldom occurred during timeout periods under any schedule studied. At doses of cocaine above or below those that maintained characteristic schedule-controlled behavior, rates of responding were relatively low and patterns of responding were irregular. Characteristic fixed-interval responding was maintained over a wider range of cocaine doses than characteristic fixed-ratio responding. Complex patterns of responding controlled by discriminative stimuli under fixed-ratio or fixed-interval schedules can be maintained by cocaine injections in squirrel monkeys and rhesus monkeys.     

Responding under fixed-ratio and multiple fixed-interval fixed-ratio schedules of electric shock presentation

Squirrel monkeys, initially trained under a schedule of electric shock postponement and then under fixed-interval schedules of electric shock presentation, were studied under multiple fixed-interval fixed-ratio and under fixed-ratio schedules of shock presentation. Under the fixed-interval (10-min) component of the multiple schedule, a pause was followed by a gradual increase in responding to a rate maintained until shock presentation; under the fixed-ratio (3-, 10-, or 30-response) component of the multiple schedule, a brief pause was typically followed by a relatively high and uniform rate of responding until shock was presented. When the 60-sec timeout periods, which usually followed shock presentation, were eliminated from the multiple schedule for one monkey, responding was only transiently affected. In the one monkey studied, responding was maintained under a fixed-ratio schedule alone (with timeout periods), but rates of responding were lower than under the fixed-ratio component of the multiple schedule. Characteristic patterns of responding, similar to those engendered under schedules of food presentation or shock termination, can be maintained under fixed-ratio schedules of shock presentation; further, patterns of responding can be controlled by discriminative stimuli in multiple schedules.