Varying reinforcement magnitude on interval schedules

In Experiment 1, rats were trained on either a random-interval or a variable-interval 60-sec schedule of reinforcement, and reinforcement magnitude was varied across conditions between one and four pellets. Although the two schedules maintained different patterns of behaviour, patterns and rates of responding were not systematically affected by the variation in reinforcement magnitude. In Experiment 2, a regulated probability interval schedule that generated similar rates of reinforcement to those of the schedules of Experiment 1 was used, with the pattern of behaviour generated resembling that typical of a random-interval schedule. Changing reinforcement magnitude again produced few systematic changes in behaviour. In Experiment 3, a variable-ratio schedule was used within a procedure that otherwise resembled that of Experiments 1 and 2. Increasing the reinforcement magnitude now decreased the rates of responding, and examination of the patterns of responding showed that this came about because rates of responding were higher early in the interreinforcer interval in the one-pellet condition. These experiments demonstrate the insensitivity of behaviour under interval schedules to changes in reinforcement magnitude and suggest the operation of mechanisms different from those engaged by ratio schedules and discretetrial learning procedures.     

Fixed interval schedules and delay of reinforcement

In a fixed interval schedule of reinforcement the only responses to be reinforced are those made when a certain time interval has elapsed since the previous reinforcement. The behaviour of three rats on such a schedule was compared with their behaviour on a schedule where a response made at any time during the interval was reinforced by setting up a reward which was delivered when the interval had elapsed. Response rates were higher in the ordinary fixed interval schedule than in its modified version, and it is argued that this rules out attempts to explain the maintenance of fixed interval performance by delayed reinforcement. Despite the clear difference in response rates, there was considerable similarity between the post-reinforcement pauses developed in the two schedules, and this suggests that pausing is influenced more by temporal than by response contingencies.     

Properties of behavior under random interval reinforcement schedules

In a temporally defined system of reinforcement schedules, the fixed interval case is defined when reinforcement probability, P, is equal to unity for the first response in any cycle length, T; when P is less than 1.0, random interval schedules emerge wherein T/P specifies the expected interval between reinforcements. Key-pecking rates were found to be: (a) inversely related to T/P; (b) higher at T=1.0 second than at other T parameter values; (c) low and linear at several T and T/P values. The mean post-reinforcement pause, if initially small, increased, and if initially large, decreased, as T/P increased.     

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.     

Independence of concurrent responding maintained by interval schedules of reinforcement

A pigeon's responses were reinforced on a variable-interval schedule on one key; and, concurrently, either a multiple or a fixed-interval schedule of reinforcement was in effect on a second key. These concurrent schedules, conc VI 3 (mult VI 3 EXT) or conc VI 3 FI 6, were programmed with or without a changeover delay (COD). Because the COD provided that responses on one key could not be followed by reinforced responses on the other key, responding on one key was not likely to accidentally come under the control of the reinforcement schedule on the other. When the COD was used, the performances on each key were comparable to the performances maintained when these interval schedules are programmed separately. The VI schedule maintained a relatively constant rate of responding, even though the rate of responding on the second key varied in a manner appropriate to the schedule on the second key. The mult VI 3 EXT schedule maintained two separate rates of responding: a relatively high rate during the VI 3 component, and almost no responding during the EXT component. The FI schedule maintained the gradually increasing rate of responding within each interval that is characteristic of the performance maintained by this schedule. The concurrent performances, however, did include certain interactions involving the local characteristics of responding and the over-all rates of responding maintained by the various schedules. The relevance of the present findings to an inter-response time analysis of VI responding, a chaining account of FI responding, and the concept of the reflex reserve was discussed.     

The conditions for temporal tracking under interval schedules of reinforcement

On many cyclic-interval schedules, animals adjust their postreinforcement pause to follow the interval duration (temporal tracking). Six pigeons were trained on a series of square-wave (2-valued) interval schedules (e.g., 12 fixed-interval [FI] 60, 4 FI 180). Experiment 1 showed that pigeons track square-wave schedules, except those with a single long interval per cycle. Experiments 2 and 3 established that tracking and nontracking are learned and both can transfer from one cyclic schedule to another. Experiment 4 demonstrated that pigeons track a schedule with a single short interval per cycle, suggesting that a dual process--cuing and tracking--is necessary to explain behavior on these schedules. These findings suggest a potential explanation for earlier results that reported a failure to track square-wave schedules.     

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.     

A quantitative analysis of the responding maintained by interval schedules of reinforcement

Interval schedules of reinforcement maintained pigeons' key-pecking in six experiments. Each schedule was specified in terms of mean interval, which determined the maximum rate of reinforcement possible, and distribution of intervals, which ranged from many-valued (variable-interval) to single-valued (fixed-interval). In Exp. 1, the relative durations of a sequence of intervals from an arithmetic progression were held constant while the mean interval was varied. Rate of responding was a monotonically increasing, negatively accelerated function of rate of reinforcement over a range from 8.4 to 300 reinforcements per hour. The rate of responding also increased as time passed within the individual intervals of a given schedule. In Exp. 2 and 3, several variable-interval schedules made up of different sequences of intervals were examined. In each schedule, the rate of responding at a particular time within an interval was shown to depend at least in part on the local rate of reinforcement at that time, derived from a measure of the probability of reinforcement at that time and the proximity of potential reinforcements at other times. The functional relationship between rate of responding and rate of reinforcement at different times within the intervals of a single schedule was similar to that obtained across different schedules in Exp. 1. Experiments 4, 5, and 6 examined fixed-interval and two-valued (mixed fixed-interval fixed-interval) schedules, and demonstrated that reinforcement at one time in an interval had substantial effects on responding maintained at other times. It was concluded that the rate of responding maintained by a given interval schedule depends not on the overall rate of reinforcement provided but rather on the summation of different local effects of reinforcement at different times within intervals.     

A comparison of ratio and interval reinforcement schedules with comparable interreinforcement times

Pigeons were trained to peck keys on fixed-ratio and fixed-interval schedules of food reinforcement. Both schedules produced a pattern of behavior characterized as pause and run, but the relation of pausing to time between reinforcers differed for the two schedules even when mean time between reinforcers was the same. Pausing in the fixed ratio occupied less of the time between reinforcers for shorter interreinforcer times. For two of three birds, the relation was reversed at longer interreinforcer times. As an interreinforcer time elapsed, there was an increasing tendency to return to responding for the fixed interval, but a roughly constant tendency to return to responding for the fixed-ratio schedule. In Experiment 1 these observations were made for both single-reinforcement schedules and multiple schedules of fixed-ratio and fixed-interval reinforcement. In Experiment 2 the observations were extended to a comparison of fixed-ratio versus variable-interval reinforcement schedules, where the distribution of interreinforcement times in the variable interval approximated that for the fixed ratio.     

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.     

A comparison of two models for performance under fixed interval schedules of reinforcement

Two models are proposed for responding under fixed-interval schedules of reinforcement. The first model is a Poisson model and seems suitable for situations in which responding produces a classical “FI scallop”. A second model is then developed to describe “break and run” performance, which is also known to occur under some Fixed Interval schedules. The models do not however give any indication of the circumstances under which a particular mode of responding should arise. A comparison of the models to a small set of data collected from rats performing under an FI 60 sec schedule indicates that for the data considered, the second model (a State model) produced by far the best fit.     

Sequence schedules of reinforcement

The performance of pigeons was studied under a second-order schedule composed of fixed-interval components, each of which was associated with a different discriminative stimulus, the stimuli occurring in a fixed order. In one condition, food presentation followed the completion of the fourth component. This was designated a fixed-ratio sequence schedule. In another condition, responses in the first component completed after a fixed time were reinforced. This was designated a fixed-interval sequence schedule. Although the stimulus order and maximum reinforcement frequency were identical under the two schedules, considerably more responding occurred under the fixed-interval sequence schedule in all components. Relatively few food presentations occurred after responding during any but the terminal components of the fixed-interval sequence schedule, a feature independent of the parameter values investigated. In addition, while a pattern of increased responding between food presentations prevailed under both schedules, under the fixed-interval sequence schedule the rate in the terminal component was frequently less than in the penultimate component. The fixed-interval sequence schedule appeared to have several properties of simple fixed-interval schedules.     

Interlocking schedules of reinforcement

Four male pigmented rats were exposed to a procedure designed to investigate the relation between several performance measures and a schedule continuum ranging from FR 36 to FI 2 through four intermediate interlocking schedules. On all schedules, each subject developed a stable performance that was generally break-and-run. Analysis of the cumulative records, post-S^R breaks, and running rates showed a continuum of performance related to the schedule continuum.     

Resistance to extinction in the goldfish following schedules of continuous and variable interval reinforcement

Four goldfish (Carassius auratus, comet) were reinforced with food when they intercepted a beam of light. Each fish performed on both CRF and VI 50-sec schedules. In subsequent extinctions, the CRF schedule produced more responses on the first day than did VI, but after the first day the post-CRF rate dropped much more rapidly. These results agree with those previously obtained in birds and mammals.     

Relative and absolute reinforcement frequency as determinants of choice in concurrent variable interval schedules

Rats were trained under concurrent schedules consisting of two equal variable interval component shedules providing sucrose solutions of different concentrations (0.6 M, 0.2 M; 50 μl in each case) as the reinforcers. The mean interreinforcement interval specified by the schedules was varied from 10 to 640 sec. Absolute response rate in each component was an increasing hyperbolic function of reinforcement frequency. Relative response rate and relative time allocation revealed a consistent preference for the more concentrated solution; neither measure of preference was systematically related to reinforcement frequency. The results are consistent with Baum and Rachlin's (1969) extension of the matching law, and with a derivation of the matching law from the hyperbolic relation between absolute response rate and reinforcement frequency in variable interval schedules (Herrnstein, 1970).     

Preference for simple interval schedules of reinforcement in concurrent chains: Effects of segmentation ratio

A concurrent-chains procedure was used to examine pigeons' preferences between segmented and unsegmented terminal-link schedules of reinforcement. During the initial link, a pair of independent, concurrent variable-interval 60-s schedules was in effect. In the terminal link, reinforcement was provided by a chain fixed-interval fixed-interval schedule on one key and by a simple fixed-interval schedule with an equal interreinforcement interval in the other. The relative duration between the first and second components (segmentation ratio) in the terminal-link chained schedule was systematically varied while the terminal-link duration was kept constant at either 15 s or 30 s in two sets of conditions. With few exceptions, the simple schedule was preferred to the chained schedule. Furthermore, this preference was inversely related to the size of the segmentation ratio in the segmented schedule. When the segmentation ratio was smaller than 1:1, preference was more extreme for a 30-s condition than for a 15-s condition. However, preference decreased more rapidly in conditions with the longer terminal-link duration when the ratio increased. Taken together, these results were consistent with previous findings concerning the effect of the terminal-link duration on choice between segmented and unsegmented schedules. In addition, the data suggested that segmentation ratio in a segmented schedule constitutes another potent factor influencing preference for the unsegmented schedule.     

Effects of variations in local reinforcement rate on local response rate in variable interval schedules

Rats trained to lever press for sucrose were exposed to variable-interval schedules in which (i) the probability of reinforcement in each unit of time was a constant, (ii) the probability was high in the first ten seconds after reinforcement and low thereafter, (iii) the probability was low for ten seconds and high thereafter, (iv) the probability increased with time since reinforcement, or (v) the probability was initially zero and then increased with time since reinforcement. All schedules generated similar overall reinforcement rates. A peak in local response rate occurred several seconds after reinforcement under those schedules where reinforcement rate at this time was moderate or high ([i], [ii], and [iv]). Later in the inter-reinforcement interval, local response rate was roughly constant under those schedules with a constant local reinforcement rate ([i], [ii], and [iii]), but increased steadily when local reinforcement rate increased with time since reinforcement ([iv] and [v]). Postreinforcement pauses occurred on all schedules, but were much longer when local reinforcement rate was very low in the ten seconds after reinforcement ([iii]). The interresponse time distribution was highly correlated with the distribution of reinforced interresponse times, and the distribution of postreinforcement pauses was highly correlated with the distribution of reinforced postreinforcement pauses on some schedules. However, there was no direct evidence that these correlations resulted from selective reinforcement of classes of interresponse times and pauses.     

Synthetic variable-interval schedules of reinforcement

Three pigeons pecked for food on a synthetic variable-interval schedule of reinforcement that had two independent parts: a variable-interval schedule that arranged a distribution of interreinforcement intervals, and a device that randomly assigned each reinforcement to one of 10 classes of interresponse times. The frequencies of reinforcement for the 10 classes of interresponse times were systematically varied, while the overall frequency of reinforcement was held within a comparatively narrow range. The 10 classes extended either from 0.1 to 0.6 sec in 0.05-sec intervals, or from 1.0 to 6.0 sec in 0.5-sec intervals. In the former case, some control by reinforcement was obtained, but it was weak and no simple relationships were discernible. In the latter case, the relative frequency of an interresponse time was a generally increasing function of its relative frequency of reinforcement, and two simple controlling relationships were found. First, the function relating interresponse times per opportunity to reinforcements per opportunity was, over a restricted range, approximately linear with a slope of unity. Second, when all 10 classes of interresponse times were reinforced equally often, the relative frequency of an interresponse time approximately equalled the relative reciprocal of its length.     

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.